m^- 


THE  LIBRARY 

OF 

THE  UNIVERSITY 

OF  CALIFORNIA 


GIFT  OF 


(MrJ 

Emmet   P.  X.   Sheehan 


■^ "^ 


IVV/l  V*-*.  1  ^  V.I 


SYSTEM  OF  LOGIC, 


RATIOGIIATIVE  AND  INDUCTIVE; 


:1NG     A     CONNECTED     VIEW     OF 


THE    PRINCIPLES    OF    EVIDENCE   AND    THE    METHODS 
OF    SCIENTIFIC    INVESTIGATION. 


BY   JOHN    STUART   MILL 


NEW-YORK: 

HARPER  &  BROTHERS,   PUBLISHERS, 
82    CLIFF    STREET. 

18  4  6. 


ig^i; 


PREFACE. 


This  book  makes  no  pretence  of  giving  to  the  world  a  new 
theory  of  our  intellectual  operations.  Its  claim  to  attention,  if  it 
possess  any,  is  grounded  on  the  fact  that  it  is  an  attempt  not  to 
supersede,  but  to  embody  and  systematize,  the  best  ideas  which 
have  been  either  promulgated  on  its  subject  by  speculative  writers, 
or  conformed  to  by  accurate  thinkers  in  their  scientific  inquiries. 

To  cement  together  the  detached  fragments  of  a  subject,  never 
yet  treated  as  a  whole  ;  to  harmonize  the  true  portions  of  discordant 
theories,  by  supplying  the  links  of  thought  necessary  to  connect 
them,  and  by  disentangling  them  from  the  errors  with  which  they 
are  always  more  or  less  interwoven  ;  must  necessarily  require  a 
considerable  amount  of  original  speculation.  To  other  originality 
than  this,  the  present  work  lays  no  claim.  In  the  existing  state  of 
the  cultivation  of  the  sciences,  there  would  be  a  very  strong  pre- 
sumption against  any  one  who  should  imagine  that  he  had  effected 
a  revolution  in  the  theory  of  the  investigation  of  truth,  or  added 
any  fundamentally  new  process  to  the  practice  of  it.  The  im- 
provement which  remains  to  be  effected  in  methods  of  philoso- 
phizing (and  the  author  believes  that  they  have  much  need  of 
improvement)  can  only  consist  in  performing,  more  systematically 
and  accurately,  operations  with  which,  at  least  in  their  elementary 
form,  the  human  intellect  in  some  one  or  other  of  its  employments 
is  already  familiar. 

In  the  portion  of  the  work  which  treats  of  Ratiocination,  the 
author  has  not  deemed  it  necessary  to  enter  into  technical  details 
which  may  be  obtained  in  so  perfect  a  shape  from  the  existing 
treatises  on  what  is  termed  the  Logic  of  the  Schools.  In  the  con- 
tempt entertained  by  many  modern  philosophers  for  the  syllogistic 
art,  it  will  be  seen  that  he  by  no  means  participates ;  although  the 
scientific  theory  on  which  its  defence  is  usually  rested  appears  to 
him  eri'oneous  :  and  the  view  which  he  has  suggested  of  the  nature 
and  functions  of  the  Syllogism  may,  perhaps,  afford  the  means  of 


IV  PREFACE. 

conciliating  the  principles  of  the  Art  with  as  much  as  is  well- 
grounded  in  the  doctrines  and  objections  of  its  assailants. 

The  same  abstinence  from  details  could  not  be  observed  in  the 
First  Book,  on  Names  and  Propositions  ;  because  many  useful 
principles  and  distinctions  which  were  contained  in  the  old  Logic, 
have  been  gradually  omitted  from  the  writings  of  its  later  teachers  ; 
and  it  appeared  desirable  both  to  revive  these,  and  to  reform  and 
rationalize  the  philosophical  foundation  on  which  they  stood.  The 
earlier  chapters  of  this  preliminary  Book  will  consequently  appear, 
to  some  readers,  needlessly  elementary  and  scholastic.  But  those 
who  know  in  what  darkness  the  nature  of  our  knowledge,  and  of 
the  processes  by  which  it  is  obtained,  is  often  involved  by  a  con- 
fused appz'ehension  of  the  import  of  the  different  classes  of  Words 
and  Assertions,  will  not  regai'd  these  discussions  as  either  frivolous, 
or  irrelevant  to  the  topics  considered  in  the  later  Books. 

On  the  subject  of  Induction,  the  task  to  be  performed  was  that 
of  generalizing  the  modes  of  investigating  truth  and  estimating 
evidence,  by  which  so  many  important  and  recondite  laws  of 
nature  have,  in  the  various  sciences,  been  aggregated  to  the  stock 
of  human  knowledge.  That  this  is  not  a  task  free  from  difficulty 
may  be  presumed  from  the  fact,  that  even  at  a  very  recent  period, 
eminent  writers  (among  whom  it  is  sufficient  to  name  Archbishop 
Whately,  and  the  author  of  a  celebrated  article  on  Bacon  in  the 
Edinburgh  Review),  have  not  scrupled  to  pronounce  it  impossible. 
The  author  has  endeavored  to  combat  their  theory  in  the  manner 
in  which  Diogenes  confuted  the  skeptical  reasonings  against  the 
possibility  of  motion  ;  remembering  that  Diogenes'  argument  would 
have  been  equally  conclusive,  although  his  individual  perambula- 
tions might  not  have  extended  beyond  the  circuit  of  his  own  tub. 

Whatever  may  be  the  value  of  what  the  author  has  succeeded 
in  effecting  on  this  branch  of  his  subject,  it  is  a  duty  to  acknowledge 
that  for  much  of  it  he  has  been  indebted  to  several  important  trea- 
tises, partly  historical  and  partly  philosophical,  on  the  generalities 
and  processes  of  physical  science,  which  have  been  published  within 
the  last  few  years.  To  these  treatises,  and  to  their  authors,  he  has 
endeavored  to  do  full  justice  in  the  body  of  the  work.  But  as  with 
one  of  these  writers,  Mr.  Whewell,  he  has  occasion  frequently  to 
express  differences  of  opinion,  it  is  more  particularly  incumbent  on 
him  in  this  place  to  declare,  that  without  the  aid  derived  from  the 
facts  and  ideas  contained  in  that  gentleman's  History  of  the  Induc- 
tive Sciences,  the  corresponding  portion  of  this  work  would  probably 
not  have  been  written. 


PREFACE.  V 

The  concluding  Book  is  an  attempt  to  contribute  towards  the 
solution  of  a  question,  which  the  decay  of  old  opinions,  and  the 
agitation  that  disturbs  European  society  to  its  inmost  depths,  render 
as  important  in  the  present  day  to  the  practical  interests  of  human 
life,  as  it  must  at  all  times  be  to  the  completeness  of  our  speculative 
knowledge :  viz..  Whether  moral  and  social  phenomena  are  really 
exceptions  to  the  general  certainty  and  uniformity  of  the  course  of 
nature ;  and  how  far  the  methods,  by  which  so  many  of  the  laws 
of  the  physical  world  have  been  numbered  among  truths  irrevo- 
cably acquired  and  universally  assented  to,  can  be  made  instru- 
mental to  the  gradual  formation  of  a  similar  body  of  received 
doctrine  in  moral  and  political  science. 

While  the  views  promulgated  in  these  volumes  still  await  the 
verdict  of  competent  judges,  it  would  have  been  useless  to  attempt 
to  make  the  exposition  of  them  so  elementary,  as  to  be  suited  to 
readers  wholly  unacquainted  with  the  subject.  It  can  scarcely  be 
hoped  that  the  Second  Book  will  be  throughout  intelligible  to  any 
one  who  has  not  gone  carefully  through  some  one  of  the  common 
treatises  on  Logic ;  among  which  that  of  Archbishop  Whately  is, 
on  every  account,  to  be  preferred.  And  the  Third  Book  presup- 
poses some  degree  of  acquaintance  with  the  most  general  truths 
of  mathematics,  as  well  as  of  the  principal  branches  of  physical 
science,  and  with  the  evidence  on  which  those  doctrines  rest. 
Among  books  professedly  treating  of  the  mental  phenomena,  a 
previous  familiarity  with  the  earlier  portion  of  Dr.  Brown's  Lec- 
tures, or  with  his  treatise  on  Cause  and  Effect,  would,  though  not 
indispensable,  be  advantageous ;  that  philosopher  having,  in  the 
author's  judgment,  taken  a  more  correct  view  than  any  other 
English  writer  on  the  subject  of  the  ultimate  intellectual  laws  of 
scientific  inquiry;  while  his  unusual  powers  of  popularly  stating  ond 
felicitously  illustrating  whatever  he  understood,  render  his  works 
the  best  preparation  which  can  be  suggested,  for  speculations  sim- 
ilar to  those  contained  in  this  Treatise. 


CONTENTS. 


INTRODUCTION.  ''"s« 

^  1 .  A  definition  at  the  commencement 

of  a  subject  must  be  provisional    .       1 

2.  Is  logic  the  art  and  science  of  rea- 

soning ?  2 

3.  Or  the  art  and  science  of  the  pursuit 

of  truth? ib. 

4.  Logic  is  concerned  with  inferences, 

not  with  intuitive  truths        .        .      3 

5.  Relation  of  logic  to  the  other  sci- 

ences       5 

6.  Its  utility,  how  shown      ...      6 

7.  Definition  of  logic  stated  and  illus- 

trated      ~ 

BOOK  I. 

OF   NAMES   AND   PROPOSITIONS. 

CHAPTER  I. 

Of  the  necessity  of  commencing  with  an  Anaylsis 

of  Language.  j 

^  1.  Theory  of  names,  why  a  necessary 

part  of  logic 11 

2.  First  step  in  the  analysis  of  Propo- 

sitions     12 

3.  Names    must    be    studied    before 

Things 13 

CHAPTER  II. 

Of  Names, 
(f  1.  Names  are  names  of  things,  not  of 

our  ideas 15 

2.  Words  which  are  not  names,  but 

parts  of  names 

3.  General  and  Singular  names  . 

4.  Concrete  and  Abstract     . 

5.  Connotative  and  Non-connotative 

6.  Positive  and  Negative      . 

7.  Relative  and  Absolute      . 

8.  Univocal  and  ^Equivocal 

CHAPTER  III. 
Of  the  Things  denoted  by  Names, 
i)  1.  Necessity    of   an    enumeration    of 
Namable  Things.    The  Categories 
of  Aristotle 

2.  Ambiguity    of    the    most    general 

names 

3.  Feelings,  or  states  of  consciousness 

4.  Feelings    must    be    distinguished 

from  their  physical  antecedents. 
Perceptions,  what 

5.  "Volitions,  and  Actions,  what  . 

6.  Substance  and  Attribute 


Pago 
^  7.  Body 38 

8.  Mind 41 

9.  Qualities 42 

10.  Relations 44 

11.  Resemblance 46 

12.  Quantity 43 

13.  All  attributes  of  bodies  are  grounded 

upon  states  of  consciousness         .    49 

14.  So  also  all  attributes  of  mind  .    50 

15.  Recapitulation  .        .        .        .51 

CHAPTER  IV. 

Of  Propositions. 
()  1.  Nature  and  office  of  the  copula       .    52 

2.  Affirmative  and  Negative  proposi- 

tions        54 

3.  Simple  and  Complex        .        ,        .55 

4.  Universal,  Particular,  and  Singular    57 

CHAPTER  V. 

Of  the  Import  of  Propositions. 
§  1.  Doctrine  that  a  proposition  is  the 
expression  of  a  relation  between 
two  ideas 59 

2.  Doctrine  that  it  is  the  expression  of 

a  relation  between  the  meanings 

of  two  names  .         .         .         .01 

3.  Doctrine  that  it  consists  in  referring 

something  to,  or  excluding  some- 
thing from,  a  class         .        .        .63 

4.  What  it  really  is       .        .        .        .66 

5.  It  asserts  (or  denies)  a  sequence,  a 

coexistence,  a  simple  existence,  a 
causation 67 

6.  — or  a  resemblance  .        .        .        .69 

7.  Propositions  of  which  the  terms  are 

abstract 71 

CHAPTER  VI. 

Of  Propositions  merely  Verbal. 
(J  1.  Essential   and  Accidental   proposi- 
tions        73 

2.  All  essential  propositions  are  identi- 

cal propositions      .        .        .        .74 

3.  Individuals  have  no  essences  .        .    77 

4.  Real  propositions,  how  distinguished 

from  verbal T8 

5.  Two  modes  of  representing  the  im- 

port of  a  Real  proposition      .        .    79 

CHAPTER  VII. 

Of  the  Nature  of  Classification,  and  the  Five 

Predicables. 
ij  1.  Classification,  how  connected  with 

Naming 80 


CONTENTS. 


Vll 


Page 

§  2.  The  Predicables,  what     ...  81 

3.  Genus  and  Species  ....  ib. 

4.  Kinds  have  a  real  existence  in  nature  83 

5.  Differentia 8C 

G.  Differentiae  for  general  purposes,  acd 

differentise  for  special  or  technical 

purposes 88 

7.  Proprium 89 

8.  Accidens 90 

CHAPTER  VIII. 

Of  Definition. 
•^  1.  Definition,  why  treated  of  in  this 

place 91 

2.  A  definition,  what    .        .        .        .     (6. 

3.  Every  name  can  be  defined,  whose 

meaning  is  susceptible  of  analysis    92 

4.  Complete,  how  distinguished  from 

incomplete  definitions    .        .        .94 

5.  — and  from  descriptions  .        .        .95 
G.  What  are  called  definitions  of  Things 

are  definitions  of  Names  with  an 
imphed  assumption  of  the  e.xistence 
of  Things  corresponding  to  them  .    98 

7.  — even  when  such  things  do  not  in 

reality  exist 101 

8.  Definitions,  though  of  tiames  only, 

must  be  grounded  on  knowledge 
of  the  corresponding  Things  .  103 

BOOK  II. 

OF  REASONING. 
CHAPTER  J. 

Of  Inference,  or  Reasoning,  in  general. 
^  1.  Retrospect  of  the  preceding  Book    .  107 

2.  Inferences  improperly  so  called       .  108 

3.  Inferences  proper,  distinguished  into 

inductions  and  ratiocinations         .111 

CHAPTER  II. 

Of  Ratiocination,  or  Syllogism. 
§  1.  Analysis  of  the  Syllogism        .        .112 

2.  The  dictum  de  omui  not  the  founda- 

tion of  reasoning,  but  a  mere  iden- 
tical proposition     .        .        .        .  IIG 

3.  What  is  the  really  fundamental  ax- 

iom of  Ratiocmation      .        .        .  119 

4.  The  other  form  of  the  axiom    .        .  120 

CHAPTER  HI. 

Of  the  Functions,   and  Logical   Value,  of  the 

Syllogism. 
§   1.  ]s  \.\ie  SyWogism  a  petitio  priricipii  ?  .   122 

2.  Insufficiency  of  the  common  theory    ih. 

3.  All  inference  is  from  particulars  to 

particulars 124 

4.  General  propositions  are  a  record  of 

such  inferences,  and  the  rules  of 
the  syllogism  are  rules  for  the  in- 
terpretation of  the  record       .        .  129 

5.  The  syllogism  not  the  type  of  rea- 

soning, but  a  test  of  it    .        .        .  131 

6.  The  true  type,  what         .        .        .134 

7.  Relation  between  Induction  and  De- 

duction   136 

CHAPTER  IV. 
Of  Trains  of  Reasoning,  and  Deductive  Sciences. 
§  1.  For  what  purpose  trains  of  reasoning 

exist 137 


Pago 

'J  2.  A  tram  of  reasoning  is  a  series  of 

inductive  inferences       .  .  138 

3.  — from    particulars    to    particulars 

through  marks  of  marks        .        .  139 

4.  Why  there  are  deductive  sciences  .  141 

5.  — and  why  other  sciences  still  re- 

mam  experimental         .        .        .  144 
G.  Experimental  sciences  may  become 
deductive  by  the  progress  of  experi- 
ment        145 

7.  In  what  manner  this  usually  takes 
place 14G 

CHAPTER  V. 

Of  Demonstration,  and  Necessary  Truths. 
^  1.  The  theorems  of  geometry  arc  only 
necessary  truths  in  the  sense  of 
necessarily  following  from  hypoth- 
eses         148 

2.  Those  hypotheses  are  real  facts  with 

some  of  their  circumstances  omit- 
ted  150 

3.  Some  of  the  first  principles  of  geom- 

etry are  axioms,  and  these  are  not 
hypothetical 151 

4.  — but  are  experimental  truths  .        .  152 

5.  An  objection  answered     .        .        .  154 

6.  Mr.  Vvhewell's  opinions  on  axioms 

examined 155 

CHAPTER  VI. 

The  same  Subject  continued. 
^  1.  All  deductive  sciences  are  inductive  162 

2.  The  propositions  of  the  science  of 

number  are  not  verbal,  but  gener- 
alizations from  experience     ,        .  164 

3.  In  what  sense  hypothetical      .        .  168 

4.  The  characteristic  property  of  dem- 

onstrative science  is  to  be  hypo- 
thetical   169 

5.  Definition  of  demonstrative  evidence 

and  of  logical  necessity .        .        .170 

BOOK  III. 

OF  INDUCTION. 

CHAPTER  I. 

Preliminary  Observations  on  Induction  in  general, 
§  1.  Importance  of  an  Inductive  Logic    .  171 
2.  The  logic  of  science  is  also  that  of 
business  and  life    ....  172 

CHAPTER  II. 

Of  Inductions  improperly  so  called. 
§  1.  Inductions  distinguished  from  verbal 

transformations     ....  174 

2.  — from  inductions,  falsely  so  called, 

in  mathematics       ....  175 

3.  —and  from  descriptions    .         .         .  177 

4.  Examination  of  I\lr.  Whewell's  the- 

ory of  induction      ....  178 

CHAPTER  III. 
On  the  Ground  of  Induction. 
5  1.  Axiomofthe  uniformity  of  the  course 

of  nature 183 

2.  Not  true  in  every  sense.     Induction 

per  enumerationem  simplicem     .         .180 

3.  Tne   question   of  Inductive  Logic 

stated 187 


VUl 


CHAPTER  IV. 
Of  Laws  of  Nature. 
(l  1.  The  general  regularity  in  nature  is 
a  tissue  of  partial  regularities,  call- 
ed laws 189 

2.  Scientific  induction  must  be  ground- 

ed upon  previous  spontaneous  in- 
ductions   191 

3.  Are  there  any  inductions  fitted  to  be 

a  test  of  all  others  ?        .        .        .192 

CHAPTER  V. 
Of  the  Law  of  Universal  Caxisation. 

^  1.  Theuniversallawof  successive  phe- 
nomena is  the  Law  of  Causation  .  194 

2.  — i.  e.  the  law  that  every  consequent 

has  an  invariable  antecedent  .  196 

3.  The  cause  of  a  phenomenon  is  the 

assemblage  of  its  conditions  .        .  197 

4.  The  distinction  of  agent  and  patient 

illusory 201 

5.  The  cause  is  not  the  invariable  ante- 

cedent, Ijut  the  unconditional  invari- 
able antecedent      ....  202 

6.  Can  a  cause  be  simultaneous  with 

its  effect  ? 204 

7.  Idea  of  a  Permanent  Cause,  or  ori- 

ginal natural  agent         .        .        .  206 

8.  Uniformities  of  coexistence  between 

effects     of    different     permanent 
causes,  are  not  laws       .        .        .  208 

9.  M.  Comte's  objections  to  the  word 

cause 209 

CHAPTER  VI. 

Of  ihe  Compositimi  of  Causes. 

ij  1.  Two  modes  of  the  conjunct  action 
of  causes,  the  arechanical  and  the 
chemical 210 

2.  The  composition  of  causes  the  gen- 

eral rule ;   the  other  case  excep- 
tional       212 

3.  Are    effects    proportional    to   their 

causes? 214 

CHAPTER  Vn. 

Of  Observation  and  Experiment. 

^  1.  The  first  step  of  inductive  inquiry  is 
a  mental  analysis  of  complex  phe- 
nomena into  their  elements  .        .  216 

2.  The  next  is  an  actual  separation  of 

those  elements       ....  217 

3.  Advantages  of  experiment  over  ob- 

servation          218 

4.  Advantages  of  observation  over  ex- 

periment          220 

CHAPTER  VIII. 

Of  the  Four  Methods  of  Experimental  Inqxary. 

(j  1.  Method  of  Agreement      .        .        .  222 

2.  Method  of  Difference        .         .         .224 

3.  Mutual  relation  of  these  two  meth- 

ods  225 

4.  Joint  Method  of  Agreement  and  Dif- 

ference   227 

5.  Method  of  Residues  .        .        .229 

6.  Method  of  Concomitant  Variations .  230 

7.  Limitations  of  this  last  method        .  234 


Page 

CHAPTER  IX. 

Miscellaneous  Examples  of  the  Fowr  Methods. 
(}  1.  Liebig's  theory  of  metallic  poisons  .  237 

2.  — how  far  a  perfect  example    .         .  239 

3.  Theory  of  induced  electricity  .        .  240 

4.  Dr.  Wells'  theory  of  dew  .         .         .242 

5.  Examples  ofthe  Method  of  Residues  247 

CHAPTER  X. 
Of  Plurality  of  Causes ;  and  of  the  Intermixture 

of  Effects. 
()  1.  One  effect  may  have  several  causes  250 

2.  —  which  is  the  source  of  a  character- 

istic imperfection  of  the  Method  of 
Agreement 251 

3.  Plurahty  of  Causes,  how  ascertained  253 

4.  Concurrence  of  causes  which  do  not 

compound  their  effects  .        .        .  254 

5.  Difiiculties    of    the    investigation, 

when  causes  compound  their  ef- 
fects         256 

0.  Three  modes   of  investigating  the 
laws  of  complex  effects  .        .  259 

7.  The  method  of  simple  observation 

inapplicable 260 

8.  The  purely  experimental  method  in- 

applicable        261 

CHAPTER  XL 
Of  the  Deductive  Method. 
^  1.  First  stage  ;    ascertainment  of  ttie 
laws  of  the  separate  causes  by  di- 
rect induction        ....  264 

2.  Second   stage ;    ratiocination   from 

the  simple  laws  to  the  complex 
cases 267 

3.  Third  stage  ;  verification  by  specific 

experience      .        .        .        .        .  268 

CHAPTER  XII. 

Of  the  Explanation  of  Laws  of  Nature. 

9  1.  Explanation  defined         .        .        .  271 

2.  First  mode  of  explanation,  by  resolv- 

ing the  law  of  a  complex  effect  into 
the  laws  of  the  concurrent  causes 
and  the  fact  of  their  coexistence  .    ib. 

3.  Second  mode;  by  the  detection  of  an 

intermediate  link  in  the  sequence  .  272 

4.  Laws  are  always  resolved  into  laws 

more  general  than  themselves       .    ib. 

5.  Third  mode ;   the   subsumption   of 

less  general  laws  under  a  more 
general  one    .        .  .        .  274 

6.  What  the  explanation  of  a  law  of 

nature  amounts  to .        .        .        .  276 

CHAPTER  Xni. 
Miscellaneous  Examples  of  the  Explanation  of 

Laws  of  Nature, 
(j  1.  Liebig's  theory'  of  the  contagious- 
ness of  chemical  action  .        .277 

2.  His  theory  of  respiration  .        .        .  280 

3.  Other  speculations  of  Liebig    .        •  282 

4.  Examples   of  following  newly-dis- 

covered laws  into  their  complex 
manifestations        ....  283 

5.  Examples  of  empirical  generaliza- 

tions, afterwards  confirmed  and 
explained  deductively    .        .        .  284 

6.  Example  from  mental  science  .        .  285 


CONTENTS. 


^  7.  The  dctluctive  method  henceforth 
the  main  instrument  of  scientilic 
iniiuir>' 286 

CHAPTER  XIV. 
Of  the  Limits   to  the  Explanation   of  Laws  of 

Aature  ;  and  of  Hypotheses. 
^  1.  Can  all  the  sequences  in  nature  be 
resolvable  into  one  law  ? 

2.  Ultimate  laws  cannot  be  less  numer 

ous  than  the  distinguishable  feel 
ings  of  our  nature  ....  287 

3.  Ill  what  sense  ultimate  facts  can  be 

explained 289 

•1.  The  proper  use  of  scientific  liypoth 

eses 290 

5.  Their  indispensableness  .        .        .  294 
ti.  Legitimate,  how  distinguished  from 

illegitimate  hypotheses 
7.  Some  inquuies  apparently  hypothet 

ical  are  really  ijiductive 

CHAPTER  XV. 

Of  Progressive  Effects ;   and  of  the  Continued 
Action  of  Causes. 

<;>  1.  How  a  progressive  effect  results 
from  the  simple  continuance  of 
the  cause 300 

2.  — and  from  the  progressiveness  of 

the  cause 302 

3.  Derivative  laws  generated  from  a 

single  ultimate  law        .        .        .  301 

CHAPTER  XVI. 

Of  Empirical  Laws. 
§  1.  Definition  of  an  empirical  law  .  305 

2.  Derivative  laws  commonly  depend 

upon  collocations  ....  306 

3.  The  collocations  of  the  permanent 

causes  are  not  reducible  to  any  law  307 

■i  And  hence  empirical  laws  cannot  be 
relied  upon  beyond  the  limits  of 
actual  experience  ....    ib. 

5.  Generalizations  which  rest  only  on 
the  Method  of  Agreement  can  only 
be  received  as  empirical  laws        .  308 

C.  Signs  from  which  an  observed  uni- 
formity of  sequence  may  be  pre- 
sumed to  be  resolvable  .         .         .  309 

7.  Most,  if  not  all,  cases  of  sequence 
from  very  complex  antecedents, 
are  resolvable  .         .         .         .311 

3.  Two  kinds  of  empirical  laws   .        .  312 

CHAPTER  XVII. 

Of  Chance,  and  its  Elimination. 
%  1.  The  proof  of  empirical  laws  depends 

on  the  theon,' of  chance         .        .  312 

2.  Chance  defined  and  characterized   .313 

3.  The  elimination  of  chance       .        .  316 

4.  Discovery  of  a  residual  phenomena 

by  eliminating  chance    .        .        .317 

5.  The  doctrine  of  chances  .        .        .  318 

CHAPTER  XVJII. 
Of  the  Calculation  of  Chances. 
<i  1.  The  foundation  of  the  doctrine  of 
chances,  as  taught  by  Laplace,  de- 
fective      319 

2.  The  real  foundation,  what       .        .  320 


Pago 

§  3.  Theorem  of  the  doctrine  of  chances, 
which  relates  to  the  cause  of  a 
given  event 322 

4.  In  what  cases  the  doctrine  is  practi- 

cally applicable      ....  320 

5.  How  applicable  to  the  elimination 

oi  chance ib. 

CHAPTER  XIX. 

Of  the  Extension  of  Derivative  Laws  to  adjacent 
Cases. 

^  1.  Derivative  laws,  when  not  causal, 
are  almost  always  contingent  upon 
collocations 327 

2.  On  what  grounds  they  can  be  ex- 

tended to  cases  beyond  the  bounds 
of  actual  experience       .        .        .  328 

3.  Those  cases  must  be  adjacent  cases  329 

CHAPTER  XX. 

Of  Analogy. 
^  1.  Various  senses  of  the  word  analogy  332 

2.  Nature  of  analogical  evidence         .    ib. 

3.  On  what   circumstances  its  value 

depends 335 

CHAPTER  XXI. 

Of  the  Evidence  of  the  Law  of  Universal 
Causation. 
^  1.  The  law  of  causality  rests  upon  an 

induction  by  simple  enumeration  .  337 

2.  In   what  cases   such    induction  is 

allowable 339 

3.  The  universal  prevalence  of  the  law 

of  causality  may  once  have  been 
doubtful. 340 

4.  Ground  of  its  present  certainty        .  341 

5.  Limits  of  the  reliance  due  to  it        .  342 

CHAPTER  XXU. 

Of  Uniformities  of  Coexistence  7wt  dependent 
upon  Causation. 
^  1.  The    uniformities    of    coexistence 
which    result   from  laws    of   se- 
quence     343 

2.  The  properties  of  Kinds  are  unifor- 

mities of  coexistence     .        .        .  344 

3.  Some  are  derivative,  others  ultimate  345 

4.  No  universal  axiom  of  coexistence  .  346 

5.  The  evidence  of  uniformities  of  co- 

existence, how  measured       .        .  347 
0.  When  derivative,  their  evidence  is 
that  of  empirical  laws    .        .        .  348 

7.  So  also  when  ultmiaie     .        .        .349 

8.  The  evidence  stronger  in  proportion 

as  the  law  is  more  general    .        .     ib. 

9.  Every  distinct   Kind  must   be  ex- 

amined    350 

CHAPTER  XXIIL 
Of  Approximate  Generalizations,  and  Probable 

Evidence. 
%  1.  The  inferences  called  probable,  rest 

upon  approximate  generalizations  351 

2.  Approximate    generalizations    less 

useful  in  science  than  in  life         .  352 

3.  In  what  cases   they   must  bo  re- 

sorted to 353 

4.  In  what  manner  proved   .        .        .  354 

5.  With  what  precautions  employed  .  356 


CONTENTS. 


The  two  modes  of  combining  proba- 
bilities     356 

How  approximate  generalizations 
may  be  converted  into  accurate 
generalizations  equivalent  to  them  358 


CHAPTER  XXIV. 

Of  the  Remaining  Laws  of  Nature. 
Propositions  which  assert  mere  ex- 

sub- 


360 


istence    .... 

Resemblance,  considered  as 
ject  of  science        ....  361 

The  axioms  and  theorems  of  mathe- 
matics comprise  the  principal  laws 
of  resemblance       ....  363 

—  and  those  of  order  in  place,  and 
rest  upon  induction  by  simple 
enumeration 364 

The  propositions  of  arithmetic  affirm 
the  modes  of  formation  of  some 
given  number         .        .        .        .    ib. 

Those  of  algebra  affirm  the  equiva- 
lence of  different  modes  of  forma- 
tion of  numbers  generally      .        .  367 

The  propositions  of  geometry  are 
laws  of  outward  nature  .        .369 

Why  geometry  is  almost  entirely 
deductive 371 

Function  of  mathematical  truths  in 
the  other  sciences,  and  limits  of 
that  function 372 

CHAPTER  XXV. 

Of  the  Grounds  of  Disbelief . 

Improbability  and  impossibility        .  374 

Examination  of  Hume's  doctrine  of 
miracles ib. 

The  degrees  of  improbability  cor- 
respond to  differences  in  the  na- 
ture of  the  generalization  with 
which  an  assertion  contlicts  .        .  377 

A  fact  is  not  incredible  because  the 
chances  are  against  it    .        .        .  379 

An  opinion  of  Laplace  examined     .  380 

BOOK  IV. 


CHAPTER  I. 

Of  Observation  and  Description. 
^  1.  Observation,  how  far  a  subject  of 

logic .383 

2.  A  great  part  of  what  seems  observa- 

tion is  really  inference  .        .        .  384 

3.  The  description  of  an  observation 

affirms  more  than  is  contained  in 
the  observation      .        .        .        .386 

4.  —  natnely,an  agreement  among  phe- 

nomena ;  and  the  comparison  of 
phenomena  to  ascertain  such 
agreements  is  a  preliminary  to  in- 
duction   387 

CHAPTER  n. 

Of  Abstraction,  or  the  Formation  of  Conceptions. 

(j  1.  The    comparison  which  is  a   pre- 
liminary   to     induction     implies 
general  conceptions        .         .         .  389 
2.  — but  these  need  not  be  preexistent   390 


Page 

§  3  A  general  conception.  Originally  the 
result  of  a  comparison,  becomes 
itself  the  type  of  comparison         .  392 

4.  What  is  meant  by  appropriate  con- 

ceptions   394 

5.  —  and  by  clear  conceptions     .         .  395 

6.  Cases  in  which  the  conception  must 

preexist 396 

CHAPTER  III. 

Of  Naming,  as  subsidiary  to  Induction. 

^  1.  The  fundamental  property  of  names 

as  an  instrument  of  thought  .        .  397 

2.  Names  are  not  indispensable  to  in- 

duction    398 

3.  In  what  manner  subservient  to  it    .  399 

4.  General  names  not  a  mere  contriv- 

ance to  economize  the  use  of  lan- 
guage      400 

CHAPTER  IV. 

Of  the  Requisites  of  a  Philosophical  Language  ; 
and  the  Principles  of  Definition. 

^  1.  First  requisite  of  philosophical  lan- 
guage, a  steady  and  determinate 
meaning  for  every  general  name  .  400 

2.  Names  in  common  use  have  often  a 

loose  connotation  ....  401 

3.  — which  the  logician  should  fix,  with 

as  little  alteration  as  possible         .  402 

4.  Why  definition  is  often  a  question 

not  of  words  but  of  things     .        .  404 

5.  How  the  logician  should  deal  with 

the  transitive  applications  of  words  406 
0.  Evil  consequences  of  casting  off  any 
portion  of  the  customary  connota- 
tion of  words 409 


CHAPTER  V. 

Of  the  Natural  History  of  the  Variations  in  the 
Meaning  of  Terms. 

()  1.  How  circumstances  originally  acci- 
dental become  incorporated  into 
the  meaning  of  words    .        .        .  414 

2.  —  and  sometimes  become  the  whole 

meaning 415 

3.  Tendency  of  words  to  become  gen- 

eralized   410 

4.  —  and  to  become  specialized  .        .  418 

CHAPTER  VI. 

The   Principles   of  a   Philosophical   Language 
further  considered. 

ij  1.  Second  requisite  of  philosophical 
language,  a  name  for  every  im- 
portant meaning    ....  421 

2.  —  viz.,  first,  an  accurate  descriptive 

terminology ib. 

3.  —  secondly,  a  name  for  each  of  the 

more  important  results  of  scientific 
abstraction 424 

4.  —  thirdly,  a  nomenclature,  or  system 

of  the  names  of  kinds    .        .        .  426 

5.  Peculiar  nature  of  the  connotation 

of  names  which  belong  to  a  no- 
menclature      427 

6.  In  what  cases  language  may,  and 

may  not,  be  used  mechanically     .  423 


CONTENTS. 


CHAPTER  VII. 
Of  Classification,  as  subsidiary  to  Induction. 

()  1.  Classification,  as  here  treated  of, 
wherein  diflerent  from  the  classi- 
fication implied  in  naming     .        .  432 

2.  Theory  of  natural  groups         .        .  433 

3.  Are  natural  groups  given  by  type,  or 

by  definition  ?         .        .        .        .  436 

4.  Kinds  are  natural  groups         .        .  438 

5.  How  the  names  of  Kinds  should  be 

constructed 441 

CHAPTER  VIII. 
Of  Classification  by  Series. 

i)  1.  Natural  groups  should  be  arranged 

in  a  natural  series  ....  443 

2.  The  arrangement  should  follow  the 

degrees  of  the  main  phenomenon  .  4-14 

3.  —  which  implies  the  assumption  of 

a  type-species         ....  445 

4.  How  the  divisions    of   the    series 

should  be  determined    .        .        .  446 

5.  Zoology  aflfords  the  completest  type 

of  scientific  classification    .        .    447 

BOOK  V. 

ON    FALLACIES. 

CHAPTER  I. 
Of  Fallacies  in  general. 

()  1.  Theory  of  fallacies  a  necessary  part 

of  logic 448 

2.  Casual  mistakes  are  not  fallacies    .  449 

3.  The  moral    sources    of   erroneous 

opinion,  how  related  to  the  intel- 
lectual     450 

CHAPTER  II. 

Classification  of  Fallacies. 

i)  1.  On  what  criteria  a  classification  of 

fallacies  should  be  grounded         .  451 

2.  The  five  classes  of  fallacies     .        .  452 

3.  The  reference  of  a  fallacy  to  one  or 

other  class  is  sometimes  arbitrary  451 

CHAPTER  III. 

Fallacies  of  Simple  Inspection,  or  a  priori 

Fallacies. 

§  1.  Character  of  this  class  of  fallacies  .  456 

2.  Natural  prejudice  of  mistaking  sub- 

jective laws  for  objective,  exempli- 
fied in  popular  superstitioi^s  .        .  457 

3.  Natural     prejudices,    that     things 

which  we  thmk  of  together  must 
exist  together,  and  that  what  is 
inconceivable  must  be  false  .        .  459 

4.  Natural  prejudice  of  ascribing  ob- 

jective existence  to  abstractions   .  463 

5.  Fallacy  of  the  Sufficient  Reason     .  464 

6.  Natural  prejudice,  that  the  differ- 

ences in  nature  correspond  to  the 
distinctions  iii  language         .        .  466 

7.  Prejudice,  that  a  phenomenon  can- 

not have  more  than  one  cause       .  468 

8.  Prejudice,  that  the  conditions  of  a 

phenomenon  must  resemble  the 
phenomenon 470 


CHAPTER  IV.  ^'^'' 

Fallacies  of  Observation. 
^  I.  Non-observation,  and  Mal-observa- 

tion 475 

2.  Non-observation  of  instances,  and 

non-observation  of  circumstances,    ib 

3.  Examples  of  the  former   .        .        .  476 

4.  —  and  of  the  latter  .        .        .        .479 

5.  Mal-observation  characterized  and 

exemplified 482 

CHAPTER  V. 

Fallacies  of  Generalization. 
ij  1.  Character  of  the  class      .        .        .485 

2.  Certain  kinds  of  generalization  must 

always  be  groundless     .        .        .    ib. 

3.  Attempts  to  resolve  radically  differ- 

ent phenomena  into  the  same        .  486 

4.  Fallacy  of  mistaking  empirical  for 

causal  laws 497 

5.  Post  hoc,  ergo  propter  hoc  ;  and  the 

deductive    fallacy    corresponding 
to  it 490 

6.  Fallacy  of  False  Analogies       .        .  491 

7.  Function  of  metaphors  in  reasoning  495 

8.  How  fallacies  of  generalization  grow 

out  of  bad  classification         .        .  497 

CHAPTER  VI. 

Fallacies  of  Ratiocination. 
^  1.  Introductory  remarks       .        .        .498 

2.  Fallacies  in  the  conversion  and  aequi- 

pollency  of  propositions         .        .    ib. 

3.  Fallacies  in  the  syllogistic  process  .  499 

4.  Fallacy  of  changing  the  premisses  .    ib. 


CHAPTER  VII. 

Fallacies  of  Confusion. 
^  1.  Fallacy  of  Ambiguous  Terms  .        .  502 

2.  Fallacy  of  Petitio  Principii      .        .  510 

3.  Fallacy  of  Ignoratio  Elenchi    .        .515 

BOOK  VI. 

ON  THE  LOGIC  OF  THE  MORAL  SCIENCES. 

CHAPTER  I. 

Introductory  Remarks. 
%  1.  The  backward  state  of  the  Moral 
Sciences  can  only  be  remedied  by 
applying  to  them  the  methods  of 
Physical  Science,  duly  extended 
and  generalized  ....  519 
2.  How  far  this  cati  be  attempted  in 
the  present  work    .        •        .        .520 

CHAPTER  U. 

Of  Liberty  and  Necessity. 
^  1.  Are  human  actions  subject  to  the 

law  of  causality  ?   .         .         .         .  521 

2.  The  doctrine  commonly  called  Phil- 

osophical Necessity,  in  what  sense 
true 522 

3.  Inappropriatcness    and    pernicious 

effect  of  the  term  Necessity  .        .  523 

4.  A  motive  not  always  the  anticipa- 

tion of  a  pleasure  or  a  pain    .        .  526 


CONTENTS. 


CHAPTER  III. 

That  there  is,  or  may  be,  a  Science  of  Human 
Nature. 
§  1.  There  may  be  sciences  which  are 

not  exact  sciences  .        .        .  527 

2.  To  what  scientific  type  the  Science 
of  Human  Nature  corresponds      .  528 

CHAPTER  IV. 

Of  the  Laws  of  Mind 
^  1.  What  is  meant  by  Laws  of  Mind?  .  530 

2.  Is  there  a  science  of  Psychology  ?   .     ib. 

3.  The  nrincipal  investigations  of  Psy- 

chology characterized    .        .        .  532 

4.  Relation  of  mental  facts  to  physical 

conditions 534 

CHAPTER  V. 

Of  Ethology,  or  the  Science  of  the  Formation  of 
Character. 

^  1.  The   Empirical    Laws    of    Human 

Nature 537 

2.  —  are  merely  approximate  generali- 

zations. The  universal  laws  are 
those  of  the  formation  of  char- 
acter        538 

3.  The  laws  of  the  formation  of  char- 

acter cannot  be  ascertamed  by 
observation  and  experiment  .        .  540 

4.  —  but    must    be    studied    deduc- 

tively       542 

5.  The    Principles    of    Ethology  are 

the  axiomata  media  of  mental 
science 544 

6.  Ethology  characterized    .        .        .545 

CHAPTER  VL 

General  considerations  on  the  Social  Science. 

^  1.  Are  Social  Phenomena  a  subject  of 

Science '! 547 

2.  Of  what  nature  the  Social  Science 
must  be 548 

CHAPTER  VJ 

Of  the  Chemical,  or  Experimental  Method  m 
the  Social  Science. 
^  \.  Characters  of  the  mode  of  thinking 
which  deduces  political  doctrines 
from  specific  experience        .        .  550 

2.  In  the  Social  Science  experiments 

are  impossible        ....  551 

3.  —  the  Method  of  Diflference  inap- 

plicable   552 

4.  —  and  the  Methods  of  Agreement, 

and  of  Concomitant  Variations, 
inconclusive 553 

5.  The  Method   of  Residues  presup- 

poses Deduction    .        .        .        .554 


CHAPTER  Vm. 

Of  the  Geometrical,  or  Abstract  Method. 
^  1 .  Characters  of  this  mode  of  thinking  555 

2.  Examples      of     the     Geometrical 

Method 557 

3.  The  interest-philosophy  of  the  Ben- 

tham  School 16. 

CHAPTER  IX. 

Of  the  Physical,  or  Concrete  Deductive  Method. 
^  1.  The  Direct  and  Inverse  Deductive 

Methods 561 

2.  Difficulties  of  the  Direct  Deductive 

Method  in  the  Social  Science       .  563 

3.  To    what     extent     the     diflerent 

branches  of  sociological  specula- 
tion can  be  studied  apart.  Po- 
litical Economy  characterized       .  565 

4.  Political  Ethology,  or  the  science 

of  national  character      .        .        .  569 

5.  The  Empirical  Laws  of  the  Social 

Science 570 

6.  The    Verification    of    the    Social 

Science 572 

CHAPTER  X. 

Of  the  Inverse  Deductive,  or  Historical  Method. 

I)  1.  Distinction  between  the  general 
Science  of  Society,  and  special 
sociological  inquiries     .        .        .  574 

2.  What  is  meant  by  a  State  of  Society    ib. 

3.  The  Progressiveness  of  Man   and 

Society 575 

4.  The  laws  of  the  succession  of  states 

of  society  can  only  be  ascertained 
by  the  Inverse  Deductive  Method  577 

5.  Social  Statics,  or  the  science  of  the 

Coexistences     of     Social     Phe- 
nomena .        .        .        .        .        .  578 

0.  Social  Dynamics,  or  the  science  of 
the  Successions  of  Social  Phe- 
nomena   583 

7.  Outlines  of  the  Historical  Metlwd  .  584 

8.  Future  prospects    of    Sociological 

inquiry 686 

CHAPTER  XL 

Of  the  Logic  of  Practice,  or  Art ;  including 
Morality  and  Policy, 
{)  1.  Morality  not  a  Science,  but  an  Art .  588 

2.  Relation  between  rules  of  art  and 

the  theorems  of  the  corresponding 
science ib. 

3.  What  is  the  proper  function  of  rules 

of  art? 589 

4.  Art  cannot  be  Deductive  .        .        .  590 

5.  Art  consists  of  the  truths  of  Science, 

arranged  in  the  order  suitable  for 
practical  use 591 

6.  Application  of  the  preceding  princi- 

ples to  Morality     .        .        .        .592 

7.  Conclusion 593 


A  SYSTEM   OF   LOGIC, 


INTRODUCTION. 

§  1.  There  is  as  great  diversity  among  authors  in  tlie  modes  which 
they  have  adopted  of  defining  logic,  as  in  their  treatment  of  the  details 
of  it.  This  is  what  might  naturally  be  expected  on  any  subject  on 
which  -writers  have  availed  themselves  of  the  same  language,  as  a  means 
of  delivering  different  ideas.  Ethics  and  jurisprudence  are  liable  to 
the  remark  in  common  with  logic.  Almost  every  philosopher  having 
taken  a  different  view  of  some  of  the  particulars  which  these  branches 
of  knowledge  are  usually  understood  to  include ;  each  has  so  framed 
his  definition  as  to  indicate  beforehand  his  owii  peculiar  tenets,  and 
Bometimes  to  beg  the  question  in  their  favor. 

This  diversity  is  not  so  much  an  evil  to  be  complained  of,  as  an  in- 
evitable and  in  some  degree  a  proper  result  of  the  imperfect  state  of 
those  sciences.  There  cannot  be  agreement  about  the  definition  of  a 
thing,  until  there  is  agreement  about  the  thing  itself  To  define  a 
thing,  is  to  select  from  among  the  whole  of  its  properties  those  which 
shall  be  understood  to  be  designated  and  declared  by  its  name ;  and 
the  properties  must  be  very  well  known  to  us  before  we  can  be  com- 
petent to  determine  which  of  them  are  fittest  to  be  chosen  for  this  pur- 
pose. Accordingly,  in  the  case  of  so  complex  an  aggregation  of  par- 
ticulars as  are  comprehended  in  anything  which  can  be  called  a  science, 
the  definition  we  set  out  with  is  seldom  that  which  a  more  extensive 
knowledge  of  the  subject  shows  to  be  the  most  appropriate.  Until 
we  know  the  particulars  themselves,  we  cannot  fix  upon  the  most  correct 
and  compact  mode  of  circumscribing  them  by  a  general  description. 
It  was  not  till  after  an  extensive  and  accurate  acquaintance  with  the 
details  of  chemical  phenomena,  that  it  was  found  possible  to  frame  a 
rational  definition  of  chemistry ;  and  the  definition  of  the  science  of  life 
and  organization  is  still  a  matter  of  dispute.  So  long  as  the  sciences 
are  imperfect,  the  definitions  must  partake  of  their  imperfections;  and 
if  the  former  are  progi-essive,  the  latter  ought  to  be  ^o  too.  As  much, 
therefore,  as  is  to  be  expected  from  a  definition  placed  at  the  com- 
mencement of  a  subject,  is  that  it  should  define  the  scope  of  our  in- 
quiries :  and  the  definition  which  I  am  about  to  offer  of  the  science  of 
logic,  pretends  to  nothing  more,  than  to  be  a  statement  of  the  question 
which  I  have  put  to  myself,  and  which  this  book  is  an  attemjit  to  re- 
solve. The  reader  is  at  hberty  to  object  to  it  as  a  definition  of  logic; 
but  it  is  at  all  events  a  correct  definition  of  the  subject  of  this 
volume. 

A 


2  INTRODUCTION'. 

§  2.  Lo,gic  has  often  been  called  the  Art  of  Reasoning.  A  writer* 
who  has  done  more  than  any  other  living  person  to  restore  this  study 
to  the  rank  from  which  it  had  fallen  in  the  estimation  of  the  cultivated 
classes  in  our  o\vn  country,  has  adopted  the  above  definition  wth  an 
amendment;  he  has  defined  logic  to  be  the  Science,  as  well  as  the  Art, 
of  reasoning ;  meaning,  by  the  fonner  term,  the  analysis  of  the  mental 
process  which  takes  place  whenever  we  reason,  and  by  the  latter,  the 
rules,  grounded  upon  that  analysis,  for  conducting  the  process  correctly. 
There  can  be  no  doubt  as  to  the  propriety  of  the  emendation.  A  right 
understanding  of  the  mental  process  itself,  of  the  conditions  it  depends 
upon,  and  the  steps  of  which  it  consists,  is  the  only  basis  on  which  a 
system  of  rules,  fitted  for  the  direction  of  the  process,  can  possibly  be 
founded.  Art  necessarily  presupposes  knowledge ;  art,  in  any  but  its 
infant. state,  presupposes  scientific  knowledge;  and  if  every  art  does 
not  bear  the  name  of  the  science  upon  which  it  rests,  it  is  only  because 
several  sciences  are  often  necessary  to  form  the  groundwork  of  a  single 
art.  Such  is  the  complication  of  human  affairs,  that  to  enable  one  thing 
to  be  done,  it  is  often  requisite  to  hioio  the  nature  and  properties  of 
many  things. 

Logic,  then,  comprises  the  science  of  reasoning,  as  well  as  an  art, 
founded  on  that  science.  But  the  word  Reasoning,  again,  like  most 
other  scientific  terms  in  popular  use,  abounds  in  ambiguities.  In  one 
of  its  acceptations,  it  means  syllogizing;  or  the  mode  of  inference 
which  may  be  called  (vnth.  sufficient  accuracy  for  the  present  pui-pose) 
concluding  fi'om  generals  to  particulars.  In  another  of  its  senses,  to 
reason,  is  simply  to  infer  any  assertion,  from  assertions  already  admitted : 
and  in  this  sense,  induction  is  as  much  entitled  to  be  called  reasoning 
as  the  demonstrations  of  geometry. 

Writers  on  logic  have  generally  preferred  the  former  acceptation  of 
the  teiTn ;  the  latter,  and  more  extensive  signification,  is  that  in  which 
I  mean  to  use  it.  I  do  this  by  ^Hrtue  of  the  right  I  claim  for  eveiy 
author,  to  give  \vhatever  prorisional  definition  he  pleases  of  his  ovra 
subject.  But  sufficient  reasons  will,  I  believe,  uiifold  themselves  as 
we  advance,  why  this  should  be  not  only  the  prorisional  but  the  final 
definition.  It  involves,  at  all  events,  no  arbitrary  change  in  the  mean- 
ing of  the  word;  for,  with  the  general  usage  of  the  English  language, 
the  wider  signification,  I  believe,  accords  better  than  the  more  re- 
stricted one. 

§  3.  But  reasoning,  even  in  the  widest  sense  of  which  the  word  is 
susceptible,  does  not  seem  to  include  all  that  is  included,  either  in  the 
best,. or  even  in  the  most  cuiTent,  conception  of  the  scope  and  province 
of  our  science.  The  employment  of  the  word  Logic  to  denote  the 
theory  of  ai-gumentaiion,  is  derived  from  the  Aristotelion,  or,  as  they 
are  commonly  termed,  the  scholastic  logicians.  Yet  even  with  them, 
in  their  systerpatic  treatises,  argumentation  was  the  subject  only  of  the 
third  part :  the  two  former  treated  of  terms,  and  of  propositions ;  under 
one  or  other  of  which  heads  were,  moreover,  included,  Definition  and 
Division.  Professedly,  indeed,  these  prerious  topics  were  introduced 
only  on  account  of  their  connexion  with  reasoning,  and  as  a  prepara- 
tion for  the  doctrine  and  rules  of  syllogism.  Yet  they  were  treated 
with  greater  mnuteness,  and  dwelt  upon  at  greater  length,  than  was 

*  Archbishop  Whately. 


DEFINITION    AND    PROVINCE    OF    LOGIC.  3 

requii'ed  for  that  pui-pose  alone.  INIorc  recent  Avi-iters  on  logic  have 
genei-ally  understood  the  term  as  it  was  employed  by  the  able  authors 
of  the  Port  Royal  Logic ;  viz.,  as  equivalent  to  the  Art  of  Thinking. 
Nor  is  this  acceptation  confined  to  philosophers,  and  works  of  science. 
Even  in  conversation,  the  ideas  usually  connected  with  the  word  Logic, 
include  at  least  precision  of  language,  and  accuracy  of  classification : 
and  we  perhaps  oftener  hear  pei'sons  speak  of  a  logical  arrangement, 
or  expressions  logically  defined,  than  of  conclusions  logically  deduced 
from  premisses.  Moreover,  a  man  is  often  called  a  gi'cat  logician,  or  a 
man  of  powerful  logic,  not  for  the  accuracy  of  his  deductions,  but  for 
the  extent  of  his  command  over  premisses ;  because  the  general  propo- 
sitions required  for  explaining  a  difficulty  or  refuting  a  sophism,  copi- 
ously and  promptly  occur  to  him ;  as  in  the  case  of  Chillingworth,  or 
Samuel  Johnson.  Wliether,  therefore,  we  conform  to  the  jiractice  of 
those  who  have  made  the  subject  their  particular  study,  or  to  that  of 
popular  wi'iters  and  common  discourse,  the  province  of  logic  will 
include  several  operations  of  the  intellect  not  usually  considei'ed  to  fall 
within  the  meaning  of  the  terms  Reasoning  and  Argumentation. 

These  various  operations  might  be  brought  within  the  compass  of  the 
science,  and  the  additional  advantage  be  obtained  of  a  very  simple 
definition,  if,  by  an  extension  of  the  term,  sanctioned  by  high  authori- 
ties, we  were  to  define  logic  as  the  science  which  treats  of  the  opera- 
tions of  the  human  understanding  in  the  pursuit  of  truth.  For  to  this 
ultimate  end,  naming,  classification,  definition,  and  all  the  other  opera- 
tions over  which  logic  has  ever  claimed  jurisdiction,  are  essentially 
subsidiary.  They  may  all  be  regarded  as  contrivances  for  enabling  a 
person  to  know  the  truths  which  are  needful  to  him,  and  to  know 
them  at  the  precise  moment  at  which  they  are  needful.  Other  pur- 
poses, indeed,  are  also  served  by  these  operations ;  for  instance,  that 
of  imparting  our  knowledge  to  others.  But,  viewed  with  regard  to 
this  purpose,  they  have  never  been  considered  as  within  the  province 
of  the  logician.  The  sole  object  of  Logic  is  the  guidance  of  one's 
own  thoughts;  the  communication  of  those  thouglits  to  others  falls 
under  the  consideration  of  Rhetoric,  in  the  large  sense  in  whicll  that 
art  was  conceived  by  the  ancients ;  or  of  the  still  more  extensive  art 
of  Education.  Logic  takes  cognizance  of  all  intellectual  operations, 
only  as  they  conduce  to  our  own  knowledge,  and  to  our  command 
(jver  that  knowledge  for  our  own  uses.  If  there  ■u^ere  but  one  rational 
being  in  the  universe,  that  being  might  be  -a  perfect  logician  ;  and  the 
science  and  art  of  logic  would  be  the  same  for  that  one  person,  as  for 
the  whole  human  race* 

§  4.  But,  if  the  definition  which  we  formerly  examined  included  too 
little,  that  wliich  is  now  suggested  has  the  opposite  fault  of  including 
too  much. 

Truths  are  known  to  us  in  two  ways :  Some  are  knOwn  directly, 
and  of  themselves ;  some  through  the  medium  of  other  truths.  The 
former  are  the  subject  of  Intuition,  or  Consciousness ;  the  latter,  of 
Inference.  The  truths  known  by  intuition  are  the  original  premisses 
from  which  all  others  are  inferred.  Our  assent  ta  the  cpnclusion 
being  grounded  upon  the  truth  of  the  premisses,  we  never  could  amve 
at  any  knowledge  by  reasoning,  unless  something  could  be  known 
antecedently  to  all  reasoning. 


INTRODUCTION. 


Examples  of  truths  known  to  us  by  immediate  consciousness,  are 
our  own  bodily  sensations  and  mental  feelings.  I  know  directly,  and 
of  my  own  knowledge,  that  I  was  vexed  yesterday,  or  that  I  am  hun- 
gry to-day.  Examples  of  truths  which  we  know  only  by  way  of 
inference,  are  occun-ences  which  took  place  while  we  were  absent,  the 
events  recorded  in  history,  or  the  theorems  of  mathematics.  The  two 
fonner  we  infer  from  the  testimony  adduced,  or  from  the  traces  of 
those  past  occuiTences  which  still  exist ;  the  latter,  from  the  premisses 
laid  down  in  books  of  geometry,  under  the  title  of  definitions  and  ax- 
ioms. Whatever  we  are  capable  of  knowing  must  belong  to  the  one 
class  or  to  the  other ;  must  be  in  the  number  of  the  primitive  data,  or 
of  the  conclusions  which  can  be  drawn  therefrom. 

With  the  original  data,  or  ultimate  premisses  of  our  knowledge ; 
with  their  number  or  nature,  the  mode  in  which  they  are  obtained,  or 
the  tests  by  which  they  may  be  distinguished;  logic,  in  a  direct  way 
at  least,  has,  in  the  sense  in  which  I  coticeive  the  science,  nothing  to 
do.  These  questions  are  partly  not  a  subject  of  science  at  all,  partly 
that  of  a  veiy  different  science. 

'  Whatever  is  known  to  us  by  consciousness,  is  known  beyond  possi- 
bility of  question.  What  one  sees,  or  feels,  whether  bodily  or  men- 
tally, one  cannot  but  be  sure  that  one  sees  or  feels.  No  science  is 
required  for  the  purpose  of  establishing  such  ti-uths ;  no  rules  of  art 
can  render  our  knowledge  of  them  more  certain  than  it  is  in  itself. 
There  is  no  logic  for  this  portion  of  our  knowledge. 

But  we  may  fancy  that  we  see  or  feel  what  we  in  reality  infer. 
Newton  saw  the  truth  of  many  propositions  of  geometry  without  read- 
ing the  demonstrations,  but  not,  we  may  be  sure,  without  their  flashing 
through  his  mind.  A  truth,  or  supposed  truth,  which  is  really  the  re- 
sult of  a  very  rapid  inference,  may  seem  to  be  apprehended  intuitively. 
It  has  long  been  agreed  by  philosophers  of  the  most  opposite  schools, 
that  this  mistake  is  actually  made  in  so  familiar  an  instance  as  that  of 
the  eyesight.  There  is  nothing  which  we  appear  to  ourselves  more 
directly  conscious  of,  than  the  distance  of  an  object  from  us.  Yet  it 
has  long  been  ascertained,  that  what  is  perceived  by  the  eye,  is  at  most 
nothing  more  than  a  variously  colored  surface ;  that  when  we  fancy 
we  see  distance,  all  we  really  see  is  certain  variations  of  apparent 
size,  and  more  or  less  faintness  of  color ;  and  that  our  estimate  of  the 
object's  distance  fi'om  us  is  the  result  of  a  comparison  (made  with  so 
much  rapidity  tliat  we  are  unconscious  of  making  it)  between  the  size 
and  color  of  the  object  as  they  appear  at  the  time,  and  the  size  and 
color  of  the  same  or  of  similar  objects  as  they  appeared  when  close  at 
hand,  or  when  their  degree  of  remoteness  was  known  by  other  evi- 
dence. The  perception  of  distance  by  the  eye,  which  seems  so  like 
intuition,  is  thus,  in  reality,  an  inference  grounded  on  experience ; 
an  inference,  too,  which  we  learn  to  make  ;  and  which  we  make  with 
more  and  more  correctness  as  our  experience  increases;  though  in 
familiar  cases  it  takes  place  so  rapidly  as  to  appear  exactly  on  a  par 
with  those  perceptions  of  sight  which  are  really  intuitive,  our  percep- 
tions of  color.* 

*  This  celebrated  theorj-  has  recently  been  called  in  question  by  a  writer  of  deserved 
reputation,  Mr.  Samuel  BaUey  ;  but  I  do  not  conceive  that  the  grounds  on  which  it  has 
been  received  by  philosophers  for  a  century  past,  have  been  at  all  shaken  by  that  gentle- 
man's objections.  I  have  elsewhere  said  what  appeared  to  me  necessary  in  reply  to  his 
arguments. — Westminster  Review,  for  October,  1842. 


DEFINITION    AND    PROVINCE    OF    LOGIC.  5 

Of  the  science,  therefore,  which  exjjounds  the  operations  of  the  hu- 
man understanding  in  the  pursuit  of  truth,  one  essential  part  is  the 
inquiry  ;•  What  are  the  truths  which  arc  the  objects  of  intuition  or 
consciousness,  and  what  arc  those  which  we  merely  infer  I  lint  this 
inquiry  has  never  been  considered  a  portion  of  logic.  Its  place  is  in 
another  and  a  perfectly  distinct  department  of  science,  which  may  be 
called  the  higher  or  transcendental  metaphysics.  For  such  is  the  title 
which  has  been  given  to  that  portion  of  mental  philosophy  which 
attempts  to  determine  what  part  of  the  furniture  of  the  mind  belongs 
to  it  orighially,  and  what  part  is  constructed  by  itself  out  of  materials 
furnished  from  without.  To  this  science  appertain  the  great  and 
much  debated  questions  of  the  existence  of  matter ;  of  the  existence 
of  spirit,  and  the  distinction  between  it  and  matter;  of  the  reality  of 
time  and  space,  as  things  without  the  mind,  and  distinguishable  from 
the  objects  which  are  said  to  exist  i/i  them.  For,  in  the  present  state 
of  the  discussion  on  these  topics,  it  is  universally  allowed  that  the 
existence  of  matter  or  of  spirit,  of  space  or  of  time,  is,  in  its  nature, 
unsusceptible  of  being  proved  ;  and  that  whatever  is  known  of  them, 
is  known  by  immediate  intuition.  To  the  same  science  belong  the 
inquiries  into  the  nature  of  Conception,  Perception,  Memory,  and 
Belief;  all  of  which  are  operations  of  the  understanding  in  the  pursuit 
of  truth ;  but  with  which,  as  phenomena  of  the  mind,  or  with  the  pos- 
sibility which  may  or  may  not  exist  of  analyzing  any  of  them  into 
simpler  phenomena,  the  logician  as  such  has  no  concern.  To  this 
science  must  also  be  refeiTed  the  following,  and  all  analogous  ques- 
tions :  To  what  extent  our  intellectual  faculties  and  our  emotions  are 
innate — to  what  extent  the  result  of  association.  "Wliether  God,  and 
duty,  are  realities,  the  existence  of  which  is  manifest  to  us  a  2>riori  by 
the  constitution  of  our  rational  faculty ;  or  whether  our  ideas  of  them 
are  acquired  notions,  the  origin  of  which  we  are  able  to  trace  and 
explain ;  and  the  reality  of  the  objects  themselves  a  question  not  of 
consciousness  or  intuition,  but  of  evidence  and  reasoning. 

The  province  of  logic  must  be  restricted  to  that  portion  of  our  knowl- 
edge which  consists  of  inferences  from  truths  previously  known; 
whether  those  antecedent  data  be  general  propositions,  or  particular 
observations  and  perceptions.  Logic  is  not  the  science  of  Belief,  but 
the  science  of  Proof,  or  Evidence.  So  far  forth  as  belief  professes  to 
be  founded  upon  proof,  the  office  of  logic  is  to  supply  a  test  for  ascer- 
taining whether  or  not  the  bfilief  is  well  grounded.  With  the  claims 
which  any  proposition  has  to  belief  on  its  own  intrinsic  evidence, 
that  is,  without  evidence  in  the  proper  sense  of  the  word,  logic  has 
nothing  to  do, 

§  5.  As  the  far  greatest  portion  of  our  knowledge,  whether  of  gen- 
eral truths  or  of  particular  facts,  is  avowedly  matter  of  inference, 
nearly  the  whole,  not  only  of  science,  but  of  human  conduct,  is  amen- 
able to  the  authority  of  logic.  To  draw  inferences  has  been  said  to  be 
the  great  business  of  life.  Every  one  has  daily,  hourly,  and  moment- 
ary need  of  ascertaining  facts  which  he  has  not  directly  observed  ;  not 
from  any  general  pur|iose  of  adding  to  his  stock  of  knowledge,  but 
because  the  facts  themselves  are  of  importance  to  his  interests  or  to  his 
occupations.  The  business  of  the  magistrate,  of  the  military  com- 
mander, of  the  navigator,  of  the  physician,  of  the  agriculturist,  is  merely 


6  INTRODUCTION. 

to  judge  of  evidence,  and  to  act  accordingly.  They  all  have  to  ascer- 
tain certain  facts,  in  order  that  they  may  afterwards  apply  certain  rules, 
either  devised  by  themselves,  or  prescribed  for  their  gmdance  by 
others ;  and  as  they  do  this  well  or  ill,  so  they  discharge  well  or  ill  the 
duties  of  their  several  callings.  It  is  the  only  occupation  in  which  the 
mind  never  ceases  to  be  engaged;  and  is  the  subject,  not  of  logic,  but 
of  knowledge  in  general.  Our  definition  of  logic,  therefore,  will  be  in 
danger  of  including  the  whole  field  of  knowledge,  unless  we  qualify  it 
by  some  further  limitation,  showing  distinctly  where  the  domain  of  the 
other  arts  and  sciences,  and  of  common  prudence  ends,  and  that  of 
logic  begins. 

The  distinction  is,  that  the  science  or  knowledge  of  the  particular 
subject-matter  fmiiishes  the  evidence,  while  logic  furnishes  the  prin- 
cij)les  and  rules  of  the  estimation  of  evidence.  Logic  does  not  pre- 
tend to  teach  the  surgeon  what  are  the  symptoms  which  indicate  a 
violent  death.  This  he  must  learn  fi-om  his  own  experience  and  obser- 
vation, or  from  that  of  others,  his  predecessors  in  his  peculiar  science. 
But  logic  sits  in  judgment  on  the  sufficiency  of  that  observation  and 
experience  to  justify  his  rules,  and  on  the  sufficiency  of  his  rules  to 
justify  his  conduct.  It  does  not  give  him  proofs,  but  teaches  him  what 
makes  them  proofs,  and  how  he  is  to  judge  of  them.  Logic  alone  can 
never  show  that  the  fact  A  proves  the  fact  B ;  but  it  can  point  out  to 
what  conditions  all  facts  must  conform,  in  order  that  they  may  prove 
other  facts.  To  decide  whether  any  given  fact  fulfils  these  conditions, 
or  whether  facts  can  be  found  which  fulfil  them  in  any  given  case, 
belongs,  exclusively,  to  the  particular  art  or  science,  or  to  ovir  knowl- 
edge of  the  particular  subject. 

It  is  in  this  sense  that  logic  is,  what  Bacon  so  expressively  calls  it, 
ars  artmm  ;  the  science  of  science  itself.  All  science  consists  of  data 
and  conclusions  from  those  data — of  proofs,  and  what  they  prove  :  now, 
logic  points  out  what  relations  must  subsist  between  data  and  what- 
ever can  be  concluded  from  them — between  proof  and  everything 
which  it  can  prove.  If  there  be  any  such  indispensable  relations,  and 
if  these  can  be  precisely  determined,  every  particular  branch  of  science, 
as  well  as  every  individual  in  the  guidance  of  his  conduct,  is  bound  to 
conform  to  those  relations,  under  the  penalty  of  making  false  infer- 
ences, of  drawing  conclusions  which  are  not  gi'ounded  in  the  realities 
of  things.  Wliatever  has  at  any  time  been  concluded  justly,  whatever 
knowledge  has  been  acquired  otherwise  than  by  immediate  intuition, 
depended  upon  the  observance  of  the  laws  which  it  is  the  province  of 
logic  to  investigate.  If  the  conclusions  are  just,  and  the  knowledge 
sound,  those  laws  have  actually  been  observed. 

§  6.  "We  need  not,  therefore,  seek  any  further  for  a  solution  of  the 
question,  so  often  agitated,  respecting  the  utility  of  logic.  If  a  science 
of  logic  exists,  or  is  capable  of  existing,  it  must  be  useful.  If  there  be 
rules  to  which  every  mind  conforms  in  every  instance  in  which  it 
judges  rightly,  there  seems  little  necessity  for  discussing  whether  a 
person  is  more  likely  to  observe  those  rules,  when  he  knows  the  rules, 
than  when  he  is  unacquainted  with  them. 

A  science  may  imdoubtedly  be  brought  to  a  certain,  not  inconsider- 
able, stage  of  advancement,  without  the  application  of  any  other  logic 
to  it  than  what  all  persons,  who  are  said  to  have  a  sound  understand- 


DEFINITION    AND    PUOVINCE    OF    LOGIC.  7 

ing,  acquire  empirically  in  the  course  of  their  studies.  Men  judged  of 
evidence,  and  often  very  coiTectly,  before  logic  was  a  science,  or  they 
nevei'  could  have  made  it  one.  And  they  executed  great  mechanical 
works  before  they  understood  the  laws  of  mechanics.  But  there  are 
limits  both  to  what  mechanicians  can  do  without  principles  of  mechan- 
ics, and  to  what  thinlcers  can  do  without  principles  of  logic.  And  the 
limits,  in  the  two  cases,  are  of  the  same  kind.  The  extent  of  what 
man  can  do  without  understanding  the  theoiy  of  what  he  is  doing,  is 
in  all  cases  much  the  same :  he  can  do  whatever  is  very  easy;  what 
requires  only  time,  and  patient  industry.  But  in  the  progress  of 
science  fi-om  its  easiest  to  its  more  difficult  problems,  every  gi-eat  step 
in  advance  has  had  either  as  its  precursor  or  as  its  accompaniment  and 
necessary  condition,  a  coiTosponding  improvement  in  the  notions  and 
principles  of  logic  received  among  the  most  advanced  thinkers.  And 
if  several  of  the  more  difficult  sciences  are  still  in  so  defective  a  state  ; 
if  not  only  so  little  is  proved,  but  disputation  has  not  terminated  even 
about  the  little  which  seemed  to  be  so ;  the  reason,  perhaps,  is,  that 
men's  logical  notions  have  not  yet  acquired  the  degree  of  extension, 
or  of  accuracy,  requisite  for  the  estimation  of  the  evidence  proper  to 
those  particular  departments  of  knowledge. 

§  7.  Logic,  then,  is  the  science  of  the  operations  of  the  understand- 
ing which  are  subservient  to  the  estimation  of  evidence :  both  the 
process  itself  of  proceeding  from  known  truths  to  unknown,  and  all 
intellectual  operations  auxiliary  to  this.  It  includes,  therefore,  the 
operation  of  Naming ;  for  language  is  an  instrument  of  thought,  as 
well  as  a  means  of  communicating  our  thoughts.  It  includes,  also, 
Definition,  and  Classification.  For,  the  use  of  these  operations  (putting 
all  other  minds  than  one's  own  out  of  consideration)  is  to  serve  not 
only  for  keeping  our  evidences  and  the  conclusions  fi'om  them  perma- 
nent and  readily  accessible  in  the  memory,  but  for  so  marshaling  the 
facts  which  we  may  at  any  time  be  engaged  in  investigating,  as  to 
enable  us  to  perceive  more  clearly  what  evidence  there  is,  and  to  judge 
with  fewer  chances  of  eiTor  whether  it  be  sufficient.  The  analysis  of 
the  instruments  we  employ  in  the  investigation  of  truth,  is  part  of  the 
analysis  of  the  investigation  itself;  since  no  art  is  complete,  unless 
another  art,  that  of  constructing  the  tools  and  fitting  them  for  the 
purposes  of  the  art,  is  embodied  in  it. 

Our  object,  therefore,  will  be  to  attempt  a  correct  analysis  of  the 
intellectual  process  called  Reasoning  or  Inference,  and  of  such  other 
mental  operations  as  are  intended  to  facilitate  this :  as  well  as,  on  the 
foundation  of  this  analysis,  and  pari  passu  with  it,  to  bring  together  or 
frame  a  set  of  rules  or  canons  for  testing  the  sufficiency  of  any  given 
evidence  to  prove  any  given  proposition. 

With  respect  to  the  first  part  of  this  undertaking,  I  do  not  attempt 
to  decompose  the  mental  operation^  in  qne-stion  into  their  ultimate 
elements.  It  is  enough  if  the  analysis  as  far  as  it  goes  is  coiTect,  and 
if  it  goes  far  enough  for  the  practical  purposes-  of  logic  considered  as 
an  art.  The  separation  of  a  complicated  phenomenon  into  its  compo- 
nent parts,  is  not  like  a  connected  and  interdependent  chain  of  proof. 
If  one  link  of  an  argument  breaks,  the  whole  drops  to  the  ground  ;  but 
one  step  towards  an  analysis  holds  good,  and  has  an  independent  value, 
though  we  should  never  be  able  to  make  a  second.     The  results  of 


8  INTRODUCTION. 

analytical  cliemlsti-y  are  not  the  less  valuable,  though  it  should  be  dis- 
covered that  all  which  we  novs^  call  simple  substances  are  really  com- 
pounds. All  other  things  are  at  any  rate  compounded  of  those 
elements  :  whether  the  elements  themselves  admit  of  decomposition, 
is  an  important  inquiry,  but  does  not  affect  the  certainty  of  the  science 
up  to  that  point. 

I  shall,  accordingly,  attempt  to  analyze  the  process  of  inference, 
and  the  processes  subordinate  to  inference,  so  far  only  as  may  be 
requisite  for  ascertaining  the  difference  between  a  correct  and  an 
incorrect  perfonnance  of  those  processes.  The  reason  for  thus  hmit- 
ing  our  design,  is  evident.  It  has  been  said  by  objectors  to  logic,  that 
we  do  not  learn  to  use  our  muscles  by  studying  their  anatomy.  The 
fact  is  not  quite  fairly  stated ;  for  if  the  action  of  any  of  om*  muscles 
were  vitiated  by  local  weakness,  or  other  physical  defect,  a  knowledge 
of  their  anatomy  might  be  very  necessaiy  for  effecting  a  cvire.  But 
we  should  be  justly  liable  to-  the  criticism  involved  in  this  objection, 
were  we,  in  a  treatise  on  Logic,  to  carry  the  analysis  of  the  reasoning 
process  beyond  the  point  at  which  any  inaccuracy  which  may  have 
crept  into  it  must  become  visible.  In  learning  bodily  exercises  (to 
carry  on  the  same  illustration)  we  do,  and  must  analyze  the  bodily 
motions,  so  far  as  is  necessary  for  distinguishing  those  which  ought  to 
be  performed  fi-om  those  which  ought  not.  To  a  similar  extent,  and 
no  further,  it  is  necessaiy  that  the  logician  should  analyze  the  mental 
processes  with  which  Logic  is  concerned.  Any  ulterior  and  minuter 
analysis  must  be  left  to  transcendental  metaphysics ;  which  in  this,  as 
in  other  parts  of  our  mental  nature,  decides  what  are  ultimate  facts, 
and  what  are  resolvable  into  other  facts.  And  I  believe  it  will  be 
found  that  the  conclusions  arrived  at  in  this  work  have  no  necessary 
connexion  with  any  particular  views  respecting  the  ulterior  analysis. 
Logic  is  common  gi'ound  on  which  the  partisans  of  Hartley  and  of 
Reid,  of  Locke  and  of  Kant,  may  meet  and  join  hands.  Particular 
and  detached  opinions  of  all  these  philosophers  will  no  doubt  occasion- 
ally be  controverted,  since  all  of  them  were  logicians  as  well  as  meta- 
physicians ;  but  the  field  on  which  their  great  battles  have  been  fought, 
lies  beyond  the  boundaries  of  our  science ;  and  the  views  which  will 
be  here  promulgated,  may,  I  believe,  be  held  in  conjunction  with  the 
principal  conclusions  of  any  one  of  their  systems  of  philosophy. 

It  cannot,  indeed,  be  pretended  that  logical  principles  can  be  alto- 
gether iiTelevant  to  those  more  abstruse  discussions ;  nor  is  it  possible 
but  that  the  view  we  are  led  to  take  of  the  problem  which  logic  pro- 
poses, must  have  a  tendency  favorable  to  the  adoption  of  some  one 
opinion  on  these  controverted  subjects  rather  than  another.  Logic, 
although  differing  from  the  higher  metaphysics  like  the  other  half  of  a 
great  whole  (the  one  being  the  science  of  the  appreciation  of  evidence, 
the  other  having  for  its  main  object  to  determine  what  are  the  propo- 
sitions for  the  establishment  of  which  evidence  is  not  required),  yet 
when  viewed  under  another  of  its  aspects,  stands  in  the  same  relation 
to  this,  its  sister  science,  as  it  does  to  all  the  other  sciences.  For 
metaphysics,  in  endeavoring  to  solve  its  own  peculiar  problem,  must 
employ  means,  the  validity  ofwhich  falls  under  the  cognizance  of  logic. 
It  proceeds,  no  doubt,  as  far  as  possible,  merely  by  a  closer  and  more 
attentive  interrogation  of  our  consciousness,  or,  more  properly  speak- 
ing, of  our  memory ;  and  so  far  is  not  amenable  to  logic.     But  where- 


DEFINITION    AND    PROVINCE    OF    LOGIC.  [f 

ever  this  method  is  insufRcient  to  attain  the  end  of  its  inquiries,  it  must 
proceed,  like  other  sciences,  by  means  of  evidence.  Now,  the  moment 
this  science  begins  to  draw  inferences  from  evidence,  logic  becomes 
the  sovereign  judge  whether  its  inferences  are  well-gi'ounded,  or  what 
other  inferences  would  be  so. 

This  influence,  however,  of  logic  over  the  questions  which  have 
divided  philosophers  in  the  higher  regions  of  metaphysics,  is  indirect 
and  remote  ;  and  I  can  conscientiously  affirm,  that  no  one  proposition 
laid  do-\vn  in  this  work  has  been  adopted  for  the  sake  of  establishing, 
or  with  any  reference  to  its  fitness  for  being  employed  in  establishing, 
preconceived  opinions  in  any  department  of  knowledge  or  of  inquiry 
on  which  the  speculative  world  is  still  undecided. 
B 


BOOK  I. 

OF  NAMES  AND  PROPOSITIONS. 


"  La  scolastique,  qui  produisit  dans  la  logique,  comme  dans  la  morale,  et  dans  une  partie 
de  la  mctaphysique,  une  subtilitc,  une  precision  d'idees,  dont  I'habitude  inconnue  aux  an- 
ciens,  a  contribue  plus  qu'on  nacroit  au  progrtis  de  la  bonne  philosoplrie."— Condorcet, 
Vie  de  Turcot. 


CHAPTER  I. 

OF  THE  NECESSITY  OF  COMMENCING  WITH  AN  ANALYSIS  OF  LANGUAGE. 

§  1.  It  is  SO  much  the  estabhshed  practice  of  wi-iters  on  logic  to 
commence  their  treatises  by  a  few  general  observations  (in  most  cases, 
it  is  true,  rather  meagre)  on  Terms  and  their  varieties,  that  it  will,  per- 
haps, scarcely  be  required  from  me,  in  merely  following  the  common 
usage,  to  be  as  particular  in  assigning  my  reasons,  as  it  is  usually  ex- 
pected that  those  should  be  who  deviate  from  it. 

The  practice,  indeed,  is  recommended  by  considerations  far  too  ob- 
vious to  require  a  formal  justification.  Logic  is  a  portion  of  the  Art 
of  Thinking :  Language  is  evidently,  and  by  the  admission  of  all  phi- 
losophers, one  of  the  principal  instruments  or  helps  of  thought ;  and 
any  imperfection  in  the  instrument,  or  in  the  mode  of  employino-  it,  is 
confessedly  liable,  still  more  than  in  almost  any  other  art,  to  confuse 
and  impede  the  process,  and  desti'oy  all  gi-ound  of  confidence  in  the 
result.  For  a  mind  not  previously  versed  in  the  meaning  and  right  use 
of  the  various  kinds  of  words,  to  attempt  the  study  of  methods  of  phi- 
losophizing, would  be  as  if  some  one  should  attempt  to  make  himself 
an  astronomical  observer,  having  never  learned  to  adjust  the  focal  dis- 
tance of  his  optical  instruments  so  as  to  see  distinctly. 

Since  Reasoning,  or  Inference,  the  principal  subject  of  logic,  is  an 
operation  which  usually  takes  place  by  means  of  words,  and  in  all 
complicated  cases  can  take  place  in  no  other  way,  those  who  have  not 
a  thorough  insight  into  the  signification  and  purposes  of  words,  will  be 
imder  almost  a  necessity  of  reasoning  or  infen-ing  incon-ectly.  And 
logicians  have  generally  felt  that  unless,  in  the  very  first  stage,  they 
removed  this  fertile  source  of  error;  unless  they  taught  their  pupil  to 
put  away  the  glasses  which  distort  the  object,  and  to  use  those  which 
are  adapted  to  his  purpose  in  such  a  manner  as  to  assist,  not  perplex, 
his  vision ;  he  would  not  be  in  a  condition  to  practise  the  remaining 
part  of  their  discipline  with  any  prospect  of  advantage.  Therefore  it 
is  that  an  inquiry  into  language,  so  far  as  is  needful  to  guard  against 
the  errors  to  which  it  gives  rise,  has  at  all  times  been  deemed  a  neces- 
sary preliminary  to  the  science  of  logic. 

But  there  is  another  reason,  of  a  still  more  fundamental  nature,  why 


12  NAMES    AND    PROPOSITIONS. 

the  import  of  words  should  be  the  earliest  subject  of  the  logician's  con- 
sideration :  because  without  it  he  cannot  examine  into  the  import  of 
Propositions.  Now  this  is  a  subject  which  stands  on  the  very  thresh- 
hold  of  the  science  of  logic. 

The  object  of  logic,  as  defined  in  the  Introductory  Chapter,  is  to 
ascertain  how  we  come  by  that  portion  of  our  knowledge  (much  the 
greatest  portion)  which  is  not  intuitive  ;  and  by  what  criterion  we  can, 
in  matters  not  self-evident,  distinguish  between  things  proved  and  things 
not  proved,  between  what  is  worthy  and  what  is  unworthy  of  belief. 
Of  the  various  questions  which  the  universe  presents  to  our  inquiring 
faculties,  some  are  soluble  by  direct  consciousness,  others  only  by 
means  of  evidence.  Logic  is  concerned  with  these  last.  The  solution, 
by  means  of  evidence,  of  questions  respecting  the  universe  and  the 
things  contained  in  it,  is  the  pm'pose  of  logic.  But  before  inquiring 
into  the  mode  of  resolving  questions,  it  is  necessary  to  inquire,  what 
are  the  questions  which  present  themselves  1  what  questions  are  con- 
ceivable I  what  inquiries  are  there,  to  which  men  have  either  obtained, 
or  been  able  to  imagine  it  possible  that  they  should  obtain,  an  answer  ? 
This  point  is  best  ascertained  by  a  survey  and  analysis  of  Propositions. 

§  2.  The  answer  to  every  question  wnich  it  is  possible  to  frame,  is 
contained  in  a  Proposition,  or  Assertion.  Whatever  can  be  an  object 
of  belief,  or  even  of  disbelief,  must,  when  put  into  words,  assume  the 
form  of  a  proposition.  All  truth  and  all  eiTor  lie  in  propositions. 
What,  by  a  convenient  misapplication  of  an  abstract  term,  we  call  a 
Truth,  is  simply  a  True  Proposition  ;  and  eiTors  are  false  propositions. 
To  know  the  import  of  all  possible  propositions,  would  be  to  know  all 
questions  which  can  be  raised,  all  matters  which  are  susceptible  of'be- 
ing  either  believed  or  disbelieved.  How  many  kinds  of  inquiries  can 
be  propounded;  how  many  kinds  of  judgments  can  be  made;  and 
how  many  kinds  of  propositions  it  is  possible  to  frame  with  a  meaning, 
are  but  different  forms  of  one  and  the  same  question.  Since,  then,  the 
objects  of  all  Belief  and  of  all  Inquiry  express  themselves  in  propo- 
sitions ;  a  sufficient  scrutiny  of  Propositions  and  of  their  varieties  will 
apprise  us  what  questions  mankind  have  actually  asked  themselves, 
and  what,  in  the  nature  of  answers  to  those  cjuestions,  they  have  actu- 
ally thought  they  had  gi'ounds  to  believe. 

Now  the  first  glance  at  a  proposition  shows  that  it  is  fomied  by  put- 
ting together  two  names.  A  proposition,  according  to  the  common 
simple  definition,  which  is  sufficient  for  our  purpose,  is,  discourse,  in 
which  something  is  affirmed  or  denied  of  something.  Thus,  in  the  prop- 
osition, Gold  is  yellow,  the  quality  yellow  is  affirmed  of  the  substance 
gold.  In  the  proposition,  Franklin  was  not  bom  in  England,  the 
fact  expressed  by  the  words  born  in  England  is  denied  of  the  man 
Franklin. 

Every  p'roposition  consists  of  three  parts:  the  Subject,  the  Predi- 
cate, and  the  Copula.  The  predicate  is  the  name  denoting  that  which 
is  affirmed  or  denied.  The  subject  is  the  name  denoting  the  person 
or  thing  which  something  is  affirmed  or  denied  of  The  copula  is  the 
sign  denoting  that  there  is  an  affirmation  or  denial ;  and  thereby  ena- 
bling the  hearer  or  reader  to  distinguish  a  proposition  from  any  other 
kind  of  discourse.  Thus,  in  the  proposition,  The  earth  is  round,  the 
Predicate  is  the  word  round,  which  denotes  the  quality  affirmed,  or 


NECESSITY    OF    AN    ANALYSIS    OP    NAMES.  13 

(as  the  phrase  is)  predicated :  the  eartJi,  words  denoting  the  object 
which  that  quaUty  is  affirmed  of,  compose  the  Subject;  the  word  is, 
which  serves  as  the  connecting  mark  between  the  subject  and  predi- 
cate, to  show  that  one  of  them  is  affirmed  of  the  other,  is  called  the 
Copula. 

Dismissing,  for  the  present,  the  copula,  of  which  more  will  be  said 
hereafter,  every  proposition,  then,  consists  of  at  least  two  names ; 
brings  together  two  names,  in  a  particular  manner.  This  is  already  a 
first  step  towards  what  we  are  in  quest  of.  It  appears  from  this,  that 
for  an  act  of  belief,  one  object  is  not  sufficient;  the  simplest  act  of  be- 
lief supposes,  and  has  something  to  do  with,  two  objects  :  two  names, 
to  say  the  least ;  and  (since  the  names  must  be  names  of  something) 
two  namcable  things.  A  large  class  of  thinkers  would  cut  the  matter 
short  by  saying,  two  ideas.  They  would  say,  that  the  subject  and 
predicate  are  both  of  them  names  of  ideas ;  the  idea  of  gold,  for  in- 
stance, and  the  idea  of  yellow ;  and  that  what  takes  place  (or  a  part 
of  what  takes  place)  in  the  act  of  belief,  consists  in  bringing  (as  it  is 
often  expressed)  one  of  these  ideas  under  the  other.  But  this  we  are 
not  yet  in  a  condition  to  say :  whether  such  be  the  coiTect  mode  of 
describing  the  phenomenon,  is  an  after  consideration.  The  result 
with  which  for  the  present  we  must  be  contented,  is,  that  in  every  act 
of  belief  two  objects  are  in  some  manner  taken  cognizance  of;  that 
there  can  be  no  belief  claimed,  or  question  propounded,  which  does 
not  embrace  two  distinct  (either  material  or  intellectual)  subjects  of 
thought :  each  of  them  capable  or  not  of  being  conceived  by  itseH",  but 
incapable  of  being  believed  by  itself. 

I  may  say,  for  instance,  "  the  sun."  The  word  has  a  meaning,  and 
suggests  that  meaning  to  the  mind  of  any  one  who  is  listening  to  me. 
But  suppose  I  ask  him,  Whether  it  is  true :  whether  he  believes  it  ? 
He  can  give  no  answer.  There  is  as  yet  nothing  to  believe,  or  to  dis- 
believe. Now,  however,  let  me  make,  of  all  possible  assertions  respect- 
ing the  sun,  the  one  which  involves  the  least  of  reference  to  any  object 
besides  itself;  let  me  say,  "  the  sun  exists."  Here,  at  once,  is  some- 
thing which  a  person  can  say  he  believes.  But  here,  instead  of  only 
one,  we  find  two  distinct  objects  of  conception  :  the  sun,  is  one  object; 
existence,  is  another.  Let  it  not  be  said,  that  this  second  conception, 
existence,  is  involved  in  the  first ;  for  the  sun  may  be  conceived  as  no 
longer  existing,  "  The  sun"  does  not  convey  all  the  meaning  that  is 
conveyed  by  "the  sun  exists:"  "my  father"  does  not  include  all  the 
meaning  of  "  my  father  exists,"  for  he  may  be  dead  ;  "  a  round  square" 
does  not  include  the  meaning  of  "  a  round  square  exists,"  for  it  does 
not,  and  cannot  exist.  When  I  say,  "the  sun,"  "my  father,"  or  a 
"  round  square,"  I  call  upon  the  hearer  for  no  belief  or  disbelief,  nor 
can  either  the  one  or  the  other  be  affiarded  me  ;  but  if  I  say,  "  the  sun 
exists,"  "  my  father  exists,"  or  "  a  rovmd  square  exists,"  I  call  for  be- 
lief; and  should,  in  the  first  of  the  three  instances  i^ect  with  it ;  hi  the 
second,  with  belief  or  disbelief,  as  the  case  might  be ;  in  the  third, 
with  disbelief. 

§  3.  This  first  step  in  the  analysis  of  the  object  of  belief,  which, 
though  so  obvious,  will  be  found  to  be  not  unimportant,  is  the  only  one 
which  we  shall  find  it  practicable  to  make  without  a  preliminary  sur- 
vey of  language.     If  we  attempt  to  proceed  further  in  the  same  path. 


14  NAMES    AND    PROPOSITIONS, 

that  is,  to  analyze  any  further  the  import  of  Propositions ;  we  find 
forced  upon  us,  as  a  subject  of  previous  consideration,  the  import  of 
Names.  For  every  proposition  consists  of  two  names ;  and  every 
proposition  afiiiTQS  or  denies  one  of  these  names,  of  the  other.  Now 
what  we  do,  what  passes  in  our  mind,  when  we  affirm  or  deny  two 
names  of  one  another,  must  depend  upon  what  they  are  names  of; 
since  it  is  with  refer-ence  to  that,  and  not  to  the  mere  names  them- 
selveSj  that  we  make  the  affinnation  or  denial.  Here,  therefore,  we 
find  a  new  reason  why  the  signification  of  names,  and  the  relation, 
generally,  between  names  and  the  things  signified  by  them,  must  oc- 
cupy the  preHminary  stage  of  the  inquiry  we  are  engaged  in. 

It  may  be  objected,  that  the  meaning  of  names  can  guide  us  at  most 
only  to  the  opinions,  possibly  the  foolish  and  gi'oundless  opinions, 
which  mankind  have  formed  concerning  things,  and  that  as  the  object 
of' philosophy  is  truth,  not  opinion,  the  philosopher  should  dismiss 
words  and  look  into  things  themselves,  to  ascertain  what  questions  can 
be  asked  and  answered  in  regard  to  them.  This  advice  (which  fortu- 
nately no  one  has  it  in  his  power  to  follow)  is  in  reality  an  exhortation 
to  discard  the  whole  fi-uits  of  the  labors  of  his  predecessors,  and  de- 
mean himself  as  if  he  were  the  first  person  who  had  ever  turned  an 
inquiring  eye  upon  nature.  What  does  any  one's  personal  knowledge 
of  Things  amount  to,  aft:er  subtracting  all  which  he  has  acquired  by- 
means  of  the  w^ords  of  other  people  ]  Even  after  he  has  leanit  as 
much  as  men  usually  do  learn  from  others,  mil  the  notions  of  things 
contained  in  his  indi\"idual  mind  afford  as  sufficient  a  basis  for  a  cata- 
logue raisonnee  as  the  notions  wliich  are  in  the  minds  of  all  man- 
kind? 

In  any  enumeration  and  classification  of  Things,  which  does  not  set 
out  from  their  names,  no  varieties  of  things  will  of  course  be  compre- 
hended but  those  recognized  by  the  particular  inquirer ;  and  it  "will 
still  remain  for  him  to  establish,  by  a  subsequent  examination  of  names, 
that  his  enumeration  has  omitted  nothing  which  ought  to  have  been 
included.  But  if  we  begin  with  names,  and  use  them  as  our  clue  to 
the  things,  we  bring  at  once  before  us  all  the  distinctions  which  have 
been  recognized,  not  by  a  single  inquirer  of  perhaps  hmited  views,  but 
by  the  collective  intelligence  of  mankind.  It  doubtless  may,  and  I 
believe  it  will,  be  found,  that  mankind  have  multiplied  the  varieties 
unnecessarily,  and  have  imagined  distinctions  among  things  where 
there  were  only  distinctions  in  the  manner  of  naming  them.  But  we 
are  not  entitled  to  assume  this  in  the  commencement.  We  must  begin 
by  recognizing  the  distinctions  made  by  ordinaiy  language.  If  some 
of  these  appear,  on  a  close  examination,  not  to  be  fundamental,  our 
enumeration  of  the  different  kinds  of  realities  may  be  abridged  accord- 
ingly. But  to  impose  upon  the  facts  in  the  first  instance  the  yoke  of 
a  theory,  while  the  grounds  of  the  theory  are  resei"A-ed  for  discussion  in 
a  subsequent  stage,js  evidently  not  a  course  which  a  logician  can  rea- 
sonably adopt. 


CHAPTER  11. 

OF  NAMES. 

§  1.  "A  NAME,  says  Hobbes,*  "  is  a  word  taken  at  pleasure  to  serve 
for  a  mark,  wliicli  may  raise  in  our  mind  a  thought  Uke  to  some  thought 
we  had  before,  and  which  being  pronounced  to  others,  may  be  to  them 
a  sign  of  what  thought  the  speaker  hadf  before  iji  his  mind."  This 
simple  definition  of  a  name,  as  a  word  (or  set  of  words)  serving  the 
double  pui-pose,  of  a  mark  to  recall  to  ourselves  the  likeness  of  a 
foiTQer  thought,  and  a  sign  to  make  it  known  to  others,  appears  unex- 
ceptionable. Names,  indeed,  do  much  more  than  this ;  but  whatever 
else  they  do,  grows  out  of,  and  is  the  result  of  this :  as  will  appear  in 
its  proper  place. 

Are  names  more  properly  said  to  be  the  names  of  things,  or  of  our 
ideas  of  things  ?  The  first  is  the  expression  in  common  use  ;  the  last  is 
that  of  some  philosophers,  who  conceived  that  in  adopting  it  they  were 
introducing  a  highly  important  distinction.  The  eminent  thinker  just 
quoted  seems  to  countenance  the  latter  opinion.  "  But  seeing,"  he 
continues,  "  names  ordered  in  speech  (as  is  defined)  are  signs  of  our 
conceptions,  it  is  manifest  they  are  not  signs  of  the  things  them- 
selves ;  for  that  the  sound  of  this  word  stone  should  be  the  sign  of  a 
stone,  cannot  be  understood  in  any  sense  but  this,  that  he  that  hears  it 
collects  that  he  that  pronounces  it  thinks  of  a  stone." 

If  it  be  merely  meant  that  the  conception  alone,  and  not  the  thing 
itself,  is  recalled  by  the  name,  or  imparted  to  the  hearer,  this  of  course 
cannot  be  denied.  Nevertheless,  there  seems  good  reason  for  adher- 
ing to  the  common  usage,  and  calling  the  word  sun  the  name  of  the 
sun,  and  not  the  name  of  our  idea  of  the  sun.  For  names  are  not 
intended  only  to  make  the  hearer  conceive  what  we  conceive,  but  also 
to  inform  him  what  we  believe.  Now,  when  I  use  a  name  for  the 
purpose  of  expressing  a  belief,  it  is  a  belief  concerning  the  thing  itself, 
not  concerning  my  idea  of  it.  When  I  say,  "  the  sun  is  the  cause  of 
day,"  I  do  not  mean  that  my  idea  of  the  sun  causes  or  excites  in  me 
the  idea  of  day ;  but  that  the  physical  object,  the  sun  itself,  is  the 
cause  fi'om  which  the  outward  phenomenon,  day,  follows  as  an  effect. 
It  seems  proper  to  consider  a  word  as  the  name  of  that  which  we 
intend  to  be  understood  by  it  when  we  use  it ;  of  that  which  any  fact 
that  we  assert  of  it  is  to  be  understood  of;  that,  in  short,  concerning 
which,  when  we  employ  the  word,  we  intend  to  give  infonnation. 
Names,  therefore,  shall  always  be  spoken  of  in  this  work  as  the  names 
of  things  themselves,  and  not  merely  of  our  ideas  of  things. 

But  the  question  now  arises,  of  what  things  ]  and  to  answer  this  it 
is  necessary  to  take  into  consideration  the  different  kinds  of  names. 

§  2.  It  is  usual,  before  examining  the  various  classes  into  which 
names  are  commonly  divided,  to  begin  by  distinguishing  from  names 
of  every  description,  those  words  which  are  not  names,  but  only  parts 

*  Compulation  or  Losic,  chap.  ii. 

+  In  the  original,  "  had,  or  had  not."  These  last  words,  as  involving  a  subtlety  foreign  to 
our  present  purpose,  I  have  forborne  to  quote. 


16  NAMES    AND    PROPOSITIONS. 

of  names.  Among  such  are  reckoned  particles,  as  of,  to,  truly ^  often  ; 
the  inflected  cases  of  nouns  substantive,  as  77ie,  Mm,  John's  ;*  and  even 
adjectives,  as  large,  heavy.  These  words  do  not  express  things  oi 
which  anything  can  be  affirmed  or  denied.  We  cannot  say.  Heavy 
fell,  or  A  heavy  fell ;  Truly,  or  A  truly,  was  asserted  ;  Of,  or  An  of, 
was  in  the  room.  Unless,  indeed,  we  are  speaking  of  the  mere  words 
themselves,  as  when  we  say,  Truly  is  an  English  word,  or.  Heavy  is 
an  adjective.  In  that  case  they  are  complete  names,  viz.  names  of 
those  particular  sounds,  or  of  those  particular  collections  of  wi-itten 
characters.  This  employment  of  a  word  to  denote  the  mere  letters 
and  syllables  of  which  it  is  composed,  was  tenned  by  the  schoolmen 
the  suppositio  materialis  of  the  word.  In  any  other  sense,  we  cannot 
introduce  one  of  these  words  into  the  subject  of  a  proposition,  unless 
in  combination  with  other  words ;  as,  A  heavy  hody  fell,  A  tiaily  impor- 
tant fact  was  asserted,  A  memher  o^ parliament  was  in  the  room. 

An  adjective,  however,  is  capable  of  standing  by  itself  as  the  predi- 
cate of  a  proposition  ;  as  when  we  say.  Snow  is  white  ;  and  occasion- 
ally even  as  the  subject,  for  we  may  say,  "White  is  an  agreeable  color. 
The  adjective  is  often  said  to  be  so  used  by  a  gi'ammatical  ellipsis : 
Snow  is  white,  instead  of.  Snow  is  a  white  object ;  White  is  an  agree- 
able color,  instead  of,  A  w^hite  color,  or.  The  color  of  white,  is  agi-eeable. 
The  Greeks  and  Romans  were  permitted,  by  the  rules  of  their  lan- 
guage, to  employ  this  ellipsis  universally  in  the  subject  as  well  as  in 
the  predicate  of  a  proposition.  In  English,  this  cannot,  generally 
speaking,  be  done.  We  may  say.  The  earth  is  round  ;  but  we  cannot 
say.  Round  is  easily  moved ;  we  must  say,  A  round  object.  This  dis- 
tinction, however,  is  rather  grammatical  than  logical.  Since  there  is 
no  difference  of  meaning  between  round  and  a  round  ohject,  it  is  only 
custom  which  prescribes  that  on  any  given  occasion  one  shall  be  used, 
and  not  the  other.  We  shall  therefore,  without  scruple,  speak  of 
adjectives  as  names,  whether  in  their  own  right,  or  as  representative 
of  the  more  circuitous  forms  of  expression  above  exemplified.  The 
other  classes  of  subsidiary  words  have  no  title  whatever  to  be  con- 
sidered as  names.  An  adverb,  or  an  accusative  case,  cannot  under  any 
circumstances  (except  when  their  mere  letters  and  syllables  are  spoken 
of)  figure  as  one  of  the  terms  of  a  proposition. 

Words  which  are  not  capable  of  being  used  as  names,  but  only  as 
parts  of  names,  were  called  by  some  of  the  schoolmen  SjTicategore- 
matic  terms:  from  ovv,  with,  and  Karrf/opEO),  to  predicate,  because  it 
was  only  with  some  other  word  that  they  could  be  predicated.  A 
word  which  could  be  used  either  as  the  subject  or  pi-edicate  of  a  pro- 
position, without  being  accompanied  by  any  other  word,  was  termed 
by  the  same  authorities  a  Categorematic  tenn.  A  combination  of  one 
or  more  Categorematic,  and  one  or  more  Syncategorematic  words,  as, 
A  heavy  body,  or  A  court  of  justice,  they  sometimes  called  a  mixed 
term  ;  but  this  seems  a  needless  multiplication  of  technical  expressions. 
A  mixed  term  is,  in  the  only  useful  sense  of  the  word,  Categore- 
matic. '  It  belongs  to  the  class  of  what  have  been  called  many-worded 
names. 

*  It  would,  perhaps,  be  more  correct  to  say  that  inflected  cases  are  names  and  something 
more  ;  and  that  this  addition  prevents  th.em  from  being  used  as  the  subjects  of  propositions. 
But  the  purposes  of  our  inquiry  do  not  demand  that  we  should  enter  with  scrupulous  accu- 
racy into  similar  minutiK. 


NAMES.  "  17 

For,  as  one  word  is  frequently  not  a  name,  but  only  part  of  a  name, 
so  a  number  of  wortls  often  compose  one  single  name,  and  no  more. 
Thus,  in  the  opening  of  the  Faradi/ic  Lost,  these  lines — 

the  fruit 

Of  that  forbidckMi  tree,  whose  mortal  taste 
Brought  death  iiito  ihe  vvorki,  and  all  our  woe, 
With  loss  of  Eden,  til^  one  greater  Mail 
Restore  us,  and  regain  the  bhssful  seat, — 

form  in  tlie  estimation  of  the  logician  only  one  name  j-one  C.ategOre- 
matic  term.  A  mode  of  determining  whether  any  set  of  Words  makes 
only  one  name,  or  more  than  one,  is  by  predicating  something  of  it,  apd' 
obsei'ving  whether,  by  this  predication,  we  make  only  one  assertion"  or 
several.  Thus,  when  we  say,  John  Nokes,  who  was  the  mayor  of  the  , 
town,  died  yesterday, — by  this  predication  we  make  but  one  assertion ; 
whence  it  appears  that  "  John  Nokes,  who  was  the  mayor  of  the  town," 
is  no  more  than  one  name.  It  is  true  diat  in  this  proposition,  besides 
the  assertion  that  John  Nokes  died  yesterday,  there  is  included  another 
assertion,  namely,  that  John  Nokes  was  mayor  of  the  town.  But  this 
last  assertion  was  already  made :  we  did  not  make  it  by  adding  the 
predicate,  "  died  yestei'day."  Suppose,  however,  that  the  words  had 
been,  John  Nakes,  aiicl  the  mayor  of  the  town,  they  would  have  formed 
two  names  instead  of  one.  For  when  we  say,  John  Nokes  and  the 
mayor  of  the  town  died  yesterday,  we  mg-ke  two  assertions  ;  one,  that 
John  Nokes  died  yesterday ;  the  other,  that  the  mayor  of  the  tovra 
died  yesterday. 

It  being  needless  to  illusti-ate,  at  any  greater  length,  the  subject  of 
many-worded  names,  we  proceed  to  the  distinctions  which  have  been 
established  among  names,  not  according  to  the  words  they  are  com- 
posed of,  but  according  to  theii-  signification. 

§  3.  All  names  are  names  of  something,  real  or  imaginary ;  but  all 
things  have  not  names  appropriated  to  them  individually.  For  some 
individual  objects  we  require,  and  consequently  have,  separate  distin- 
guishing names ;  there  is  a  name  for  every  person,  and  for  every  re- 
markable place.  Other  object36,  of  which  we  haA^e  not  occasion  to 
speak  so  frequently,  we  <3o  not  designate  by  a  naine  of  their  own ;  but 
when  the  necessity  arises  for  naming  them,  we  do  so  by  putting  to- 
gether several  words,  each  of  which,  by  itself,  miglit  be  and  is  used  for 
an  indefinite  number  of  other  objects  ;  as  when  I  say,  this  stone:  "this" 
and  "  stene"  being,  each  of  them,  names  that  may  be  used  of  many 
other  objects  besides  the  particular  one  meant,  although  the  only  ob- 
ject of  which  they  can  both  be  used  at  the  given  moment,  consistently 
with  their  signification,  may  be  the  one  of  which  I  wish  to  speak. 

Were  this  the  sole  purpose  for  which  names  that  are  common  to 
more  things  than  one,  could  be  employed ;  if  they  oidy  served,  by 
mutually  limiting  each  other,  to  aiibrd  a  designation  for  such  individual 
objects  as  have  no  names  of  their  own ;  they  could  only  be  ranked  among 
contrivances  for  economizing  the  tise  of  language.  But  it  is  evident 
that  this  is  not  their  solo  function.  It  is  by  their  means  that  we  are 
enabled  to  assert  general  propositions ;  to  affinn  or  deny  any  predicate 
of  an  indefinite  number  of  things  at  once.  The  disthiction,  therefore, 
between  general  names,  and  individiuil  or  singular  names,  is  funda- 
mental ;  and  may  be  considered  as  the  first  gi'and  division  of  names. 
C 


18  NAMES    AND    PROPOSITIONS. 

A  genei'al  name  is  familiarly  defined,  a  name  which  is  capable  of 
being  truly  affirmed,  in  the  same  sensfe,  of  each  of  an  indefinite  number 
of  things.  An  individual  or  singular  naine  is  a  name  which  is  only  ca- 
pable of  being  truly  affinned,  in  the  same  sense,  of  one  thing. 

Thus,  man  is  capable  of  being  truly  affirmed  of  John,  Peter,  George, 
and  other  persons  without  assignable  limits  :  and  it  is  affirmed  of  all  of 
them  in  the  same  sense ;  for  the  word  man  expresses  certain  qualities, 
and  when  we  predicate  it  of  those  persons,  we  assert  that  they  all 
possess  those  cj^ualities.  But  Jo7m. is  only  capable  of  being  truly  af- 
,  firmed  of  one  single  persen,  at  least  in  the  same  sense.  For  although 
there  are  many  persons  who  bear  that  name,  it  is  not  confeiTed  ujjon 
them  to  indicate  any  qualities,  or  anything  which  belongs  to  them  in 
common ;  and  cannot  be  said  to  be  affinned  of  them  in  any  sense  at  all, 
consequently  not  in  the  same  sense.  ",The  present  king  of  England" 
is  also  an  individual  name.  For,  that  there  never  can  he  more  than 
one  person  at  a  time  of  whom  it  can  be  truly  affirmed,  is  implied  in 
the  meaning  of  the  words. 

It  is  not  unusual,  by  way  of  explaining  what  is  meant  by  a  general 
name,  to  say  that  it  is  the  name  of  a  class.  But  this,  though  a  conve- 
nieilt  mode  of  expression  for  some  purposes,  is  objectionable  as  a  defi- 
nition, since  it  explains  tlifi  clearer  of  two  things  by  the  more  obscure. 
It  would  be  more  logical  to  reverse  the  proposition,  and  turn  it  into  a 
definition  of  the  word  class:  "A  class  is  the  indefinite  multitude  of  in- 
dividuals denoted  by  a  general  name." 

It  is  necessary  to  distinguish  general  from  collective  names.  A  gen- 
eral name  is  one  which  can  be  predicated  of  cacli  individual  of  a  mul- 
titude ;  .  a  collective  name  cannot  be  predicated  of  each  separately,  but 
only  of  all  taken  together.  "  The  76th  regiment  of  foot,"  winch  is  a 
collective  name,  is  not  a  general  bvit  an  individual  name ;  for  although 
it  can  be  predicated  of  a  multitude  of  individual  soldiers  taken  jointly, 
it  cannot  be  predicated  of  them  severally.  We  may  say,  Jones  is  a 
soldier,  and  Thompson  is  a  soldier,  and  Smith  is  a  soldier,  but  we  can- 
not say,  Jones  is  the  76th  regiment,  and  Thompson  is  the  76th  regi- 
ment, aixl  Sn;iith  is  the  76th  regiment.  We  can  only  say,  Jones, 
and  Thompson,^  and  Staith,  and  Brown,  and  so  forth,  (enumerating  all 
the  sol^liers,)  Hre  the  76th  regiment. 

*'  The  76th  regiment"  is  a  collective  name,  but  not  a  general  one  : 
"a  regimen,t"  is  both  a  collective  and  a  general  name.  General  with 
respect  to  all  individual  regiments,  of  each  of  which  separately  it  can 
oe  affirmed  \  collective  with  respect  to  the  individual  soldiers, -of  whom 
any  regiment  is  composed. .         '  '  .  > 

§  4.  The  second  general  division  of  names  is  into  concrete  and  ah- 
stract.  A  concrete  name  is  a  name  which  stands  for  a  thing ;  an  ab- 
stract name  is  a  name  which  stands  for  an  attribute  of  a  thing.  Thus, 
Jolm,  the  sea;  this  table,  are  ijames  of  things.  White,  also,  is  a  name 
of  a  thing,  or  rather  of  things.  AVliiteness,  agdn,  is  the  name  of  a 
quality  or  atti'ibute  of  those  things.  Man  is  a  name  of  many  things  ; 
humanity  is  a  name  of  an  attribute  of  those  things.  Old  is  a  name  of 
things ;   old  age  is  a  name  of  otie  of  their  attributes. 

I  have  used  the  words  concrete  and  abstract  in  the  sense  annexed  to 
them  by  the  schoolmen,  who,  notwiths=tanding  the  impci-fections  of  their 
philosophy,  were  unrivalled  in  the  construction  of  technical  language. 


NAMES.  19 

and  wHose  clofinitions/  in  logic  at  least,  thongli  tlioy  never  went  more 
than  a  little  way  into  the  subject,  have  seldom,  I  think,  been  altered 
but  to  be  spoiled.  A  practice,  however,  lias  gi'own  up  in  more  mod- 
em times,  which,  if  not  introduced  by  Locke,  has  gained  cun-ency 
chiefly  from  his  example,  of  applying  the  expression  "  abstract  name" 
to  all  names  which  are  the  result  of  abstraction  or  generalization,  and 
consequently  to  all  general  names,  instead  of  contining  it  to  the  names 
of  atti'ibutes.  The  metaphysicians  of  the  Condillac  school — Whose  ad- 
miration of  Locke,  passing  over  the  profoundest  speculations  of  that 
ti'uly  original  genius,  usually  fastens  with  peculiar  eagerness  upon  his 
weakest  points — ^liave  gone  on  imitating  him  in  this  abuse  oflanguage, 
until  there  is  now  some  difficulty  in  restoring  the  word  to  its  original 
signification.  A  more  wanton  alteration  in  the  meaning  of  a  word  is 
rarely  to  be  met  with ;  for  the  exprcssioir  general  nanie,  the  exact 
equivalent  of  which  exists  in  all  languages  I  am  acquainted  with,  was 
already  available  for  the  purpose  to  which  abstract  has  .ibeen  misap- 
propriated, while  the  misappropriation  leaves  that  important  class  of 
words,  the  names  of  attributes,  without  any  compact  distinctive  appel- 
lation. The  old  acceptation,  however,  has  nt3t  gone  so  completely  out 
of  use,  as  to  deprive  those  who  still  adhere  to  it  of  all  chance  of  being 
miderstood.  By  abstract,  then,  I  shall  always  mean  the  opposite  of 
concrete :  by  an  abstract  name,  the  name  of  an  attribute ;  by  a  con- 
crete name,  the  name  of  an  object. 

Do  abstract  names  belong  to  the  class  of  general,  or  to  that  of  sin- 
gular names  ?  Some  of  them  are  certainly  general.  I  mean  those 
which  are  names  not  of  one  single  and  definite  attribute,  but  of  ^  class 
of  attributes.  Such  is  the  word  color,  which  is  a  name  common  to 
whiteness,  redness,  &c.  Such  is  even  the  word  whiteness,  in  respect 
of  the  different  shades  of  whiteness  to  which  it  is  applied  in  common ; 
the  word  magnitude,  in  respect  of  the  various  degrees  of  magnitude 
and  the  various  dimensions  of  space ;  the  word  weight,  in  xespect  of 
the  various  degrees  of  weight.  Such  also  is  the  word  attribute  itself, 
the  common  name  of  all  particular  attributes.  But  when  only  one  at- 
tribute, neither  variable  in  degree  nor  in  kind,  is  designated  b.Y  the 
name;  as.  visibleness ;  tangibleness  ;  equality;  squareness;  milkwhite- 
ness ;  then  the  name  can  hardly  be  considered  general ;  for  though  it 
denotes  an  attribute  of  many  different  objects,  the  attribute  itself  is  al- 
ways conceived  as  one,  not  many.  The  question  is,  however,  of  no 
moment,  and  perhaps  the  best  way  of  deciding  it  would  be  to  consider 
these  names  as  neither  general  nor  individual,  but  to  place  them  in  a 
class  ajrart. 

It  may  be  objected  to  our  definition  of  an  abstract  name^  that  not 
only  the  names  which  we  have  called  abstract,  biit  adjectives,  which 
We  have  placed  in  the  concrete  class,  are  names  of  attribut<!s ;  that 
white,  for  example,  is  as, much  the  name  of  the  color,  as  whiteness  is. 
But  (as  before  remarked)  a  word  ought  to  bo  considered  as  the  name 
of  that  which  we  intend  to  be  understood  by  it  when  we  put  it  to  its 
principal  use,  that  is,  when  we  employ  it  in  predication.  Wlien  we 
say,  snow  is  white,  milk  is  white,  linen  is  white,  v^e  do  not  mean  it  to 
be  understood  that  snow,  or  linen,  or  milk,  is  a  color.  We  mean  that 
they  are  things  having  the  color.  The  reverse  is  the  '<:ase  with  the 
word  whiteness ;  what  wo  affirra  to  be  wliiteness  is  not  snow  but  the 
color  of  snow.     Whiteness,  therefore,  is  the  name  of  the  color  exclu- 


20  NAME3    AND    PROPOSITIONS. 

sively  :  white  is  a  name  of  all  things,  whatever  having  the  color ;  a  name 
not  of  the  quality  whiteness,  but  of, every  white  object.  It  is  true,  this 
name  w^as  given  to  all  those  various  objects  on  account  of  the  quality ;  and 
we  may  therefore  say,  without  impropriety,  that  the  quality  forms  part 
of  its  signification ;  but  a  name  can  only  be  said  to  stand  for,  or  to  be  a 
name  of,  the  things  of  which  it  can  be  predicated.  We  shall  presently 
see  that  all  names  which  can  be  said  to  have  any  signification,  all 
names  by  applying  which  to  an  individual  we  give  any  information 
respecting  that  individual,  may  be  said  to  imply  an  attribute  of  some 
sort ;  but  they  are  not  names  of  the  attribute ;  it  has  its  own  proper 
abstract  name. 

§  5.  This  leads  us  to  the  consideration  of  the  third  great  division 
of  names,  into  connotative  and  ?ion.-connotativc,  the  latter  sometimes, 
but  improperly,  called  absolute.  This  is  one  of  the  most  important 
distinctions  which  we  shall  have  occasion  to  point  out,  and  one  of 
those  which  go  deepest  into  the  nature  of  language, 

A  non-connotative  term  is  one  which  signifies  a  subject  only,  or  an 
attribute  only,  A  connotative  tei-m  is  one  which  denotes  a  subject 
and  implies  an  atti-ibute.  By  a  subject  is  liere  meant  anything  which 
possesses  attributes.  Thus  John,  or  London,  or  England,  are  names 
which  signify  a  subject  only.  Whiteness,  length,  virtue,  signify  an 
attribute  only.  None  of  these  names,  therefore,  are  connotative.  But 
white,  long,  virtuous,  are  connotative.  The  word  white,  denotes  all 
Avhite  things,  as  snow,  paper,  the  foam  of  the  sea,  &c.,  and  implies,  or 
as  it  was  termed  by  the  schoolmen,  connotes*  the  attribute  whiteness. 
The  w^ord  white  is  not  predicated  of  the  attribute,  but  of  the  subjects, 
snow,  &:c. ;  but  when  we  predicate  it  of  them  we  imply,  or  connote, 
that  the  attribute  whiteness  belongs  to  them.  The  same  may  be  said 
of  the  other  words  above  cited.  Virtuous,  for  example,  is  the  name 
of  a  class,  which  includes  Socrates,  Howard,  the  man  of  Ross,  and  an 
undefined  number  of  other  individuals,  past,  present,  and  to  come. 
These  individuals,  collectively  and  severally,  can  alone  be  said,  with 
propriety  to  be  denoted  by  the  word  :  of  them  alone  can  it  properly 
be  said  to  be  a  name.  But  it  is  a  name  applied  to  all  of  them  in  con- 
sequence of  an  attribute  which  they  possess  in  common,  the  attribute 
which  men  have  agreed  to  call  virtue.  It  is  applied  to  all  beings  that 
are  considered  to  possess  this  attribute;  and, to  none  whicli  are  not  so 
considered. 

All  concrete  general  names  are  connotative.  The  word  man,  for 
example,  denotes  Peter,  Paul,  John,  and  an  indefinite  number  of  other 
individuals,  of  whom,  taken  as  a  class,  it  is  the  name.  But  it  is 
applied  to  them,  because  they  possess,  and  to  signify  that  they  possess, 
certain  attributes.  These  seem  to  be,  coi-poreity,  animal  life,  ration- 
ality, and  a  certain  external  fonn,  which  for  distinction  we  call  the 
human.  Every  existing  thing,  which  possessed  all  these  attiibutes, 
would  be  called  a  rnan ;  and  anything  which  possessed  none  of  them, 
or  only  one,  or  two,  or  even  three  of  them  without  the  fourth,  would 
not  be  so  called..  Eor  example,  if  in  the  interior  of  Africa  there  were 
to  be  discovered  a  race  of  animals  possessing  reason  equal  to  that  of  hu- 
man beings,  but  with  the  form  of  an  elephant,  they  would  not  be  called 

*  Notare,  to  mark ;  co7motare,  to  mark  along  with :  to  mark  one  thing  uith  or  m  addition 
to  another. 


NAMES.  21 

men.  Swift's  HouyhnhjTis  were  not  so  called.  Or  if  such  newly- 
discovered  beings  possessed  the  form  of  man  without  any  vestige  of 
reason,  it  i«  probable  that  some  other  name  than  that  of  man  would  bo 
found  for  them.  How  it  happens  that  there  can  be  any  doubt  about 
the  matter,  will  appear  hereafter.  The  word  man,  therefore,  signifies 
all  these  attributes,  and  all  subjects  which  possess  these  atti'ibutes. 
But  it  can  be  predicated  only  of  the  subjects.  What  we  call  men,  are 
the  subjects,  the  individual  Stiles  and  Nokes ;  not  the  qualities  by 
which  their  humanity  is  constituted.  The  name,  therefore,  is  said  to 
signify  the  subjects  directly,  the  attributes  indirectly ;  it  denotes  the 
subjects,  and  implies,  or  involves,  or  indicates,  or  as  we  sh^ir  say 
henceforth,  connotes,  the  attributes.     It  is  a  connotative  name. 

Connotative  names  have  hence  been  also  called  denominative, 
because  the  subject  which  they  denote  is  denominated  by,  or  receives 
a  name  from,  the  attiibute  which  they  connote.  Snow,  and  other 
objects,  receive  the  name  white,  because  they  possess  the  attribute 
which  is  called  whiteness ;  James  and  Robert  receive  the  name  man, 
because  they  possess  the  attributes  which  are  considered  to  constitute 
humanity.  The  attribute,  or  attributes,  may  therefore  be  said  to 
denominate  those  objects,  or  to  give  them  a  common  name. 

It  has  been  seen  that  all  concrete  general  names  are  connotative. 
Even  abstract  names,  though  the  names  only  of  attributes,  may  in 
some  instances  be  justly  considered  as  connotative;  for  attributes 
themselves  may  have  attributes  ascribed  to  them  ;  and  a  word  which 
denotes  attributes  may  connote  an  attribute  of  those  attributes.  It  is 
thus,  for  exainple,  with  such  a  word  as  fault;  equivalent  to  had  or 
hurtful  quality.  This  word  is  a  name  common  to  many  attributes, 
and  connotes  hurtfulness,  an  attribute  of  those  various  attributes. 
When,  for  example,  we  say  that  slowness,  in  a  horse,  is  a  fault,  we  do 
not  mean  that  the  slow  m.ovement,  the  actual  change  of  place  of  the 
slow  horse,  has  any  mischievous  effects,  but  that  the  property  or 
peculiarity  of  the  horse,  from  which  it  derives  that  name,  the  quality 
of  being  a  slow  mover,  is  an  undesirable  peculiarity. 

In  regard  to  those  concrete^  names  which  are  not  general  btit 
individual,  a.  distinction  must  be  made. 

Proper  names. are  not  connotative  ;  they  denote  the  individuals  who 
are  called  by  them ;  but  they  do  not  indicate  or  imply  any  attributes 
as  belonging  to  those  individuals.  When  we  name  a  child  by  the 
name  Mary,  or  a  dog  by  the  name  Cassar,  these  names  are  simply 
marks  used  to  enable  those  individuals  to  be  made  subjects  of  discourse. 
It  may  be  said,  indeed,  that  we  must Jiave  had  some  reason  forgiving 
them  those  names  rather  than  any  others :  and  this  is  true ;  but  the 
name,  once  given,  becomes  independent  of  the  reason.  A  man  may 
have  been  named  John  because  that  was  the  name  of  his  father ;  a 
town  may  have  been  named  Dartmouth,  because  it  is  situated  at  the 
mouth  of  the  Dart.  But  it  is  no  part  of  the  signification  of  the  word 
John,  that  the  father  of  the  person  so  called  bore  the  same  name ;  nor 
even  of  the  v/ord  Dartmouth,  to  be  situated  at  the  moUth  of  the  Dart, 
If  sand  should  choke  up  the  mouth  of  the  river,  or  an  earthcpiake 
change  its  course,  and  remove  it  to  a  distance  from  the  town,  there  is 
no  reason  to  think  that  the  name  of  the  town  would  be  changed.  That 
fact,  therefore,  can  form  no  part  of  the  signification  of  the  word ;  for 
Otherwise,  when  the  fact  ceased  to  be  trae,  the  name  would  cease  to 


22  NAMES   AND   PROPOSITIONS. 

be  applied.  Proper  names  are  attached  to  the  objects  themselves,  and 
are  not  dependent  upon  the  continuance  of  any  attiibute  of  the  object. 
But  there  is  another  kind  of  names,  which,  although  they  are 
individual  names,  that  is,  predicable  only  of  one  object,  are  really 
connotative.  For,  although  we  may  give  to  an  individual  a  name 
utterly  .unmeaning,  which  we  call  a  proper  name, — a  word  which 
answers  the  purpose  of  showing  what  thing  it  is  we  are  talking  about, 
but  not  of  telling  anything  about  it ;  yet  a  name  peculiar  to  an 
individual  is  not  necessarily  of  this  description.  It  may  be  significant 
of  some  attribute,  or  some  union  of  attributes,  which  being  possessed  by 
no  object  but  one,  deteiTnines  the  name  exclusively  to  that  individual. 
"  The  sun  "  is  a  name  of  this  desci'iption ;  "  God,"  when  used  by  -a 
Christian,  is  another.  These,  however,  are  scarcely  examples  of  what 
we  are  now  attempting  to  illustrate,  being,  in  strictness,  of  language, 
general,  and  not  individual  names  :  for,  however  they  may  be  in  fact 
predicable  only  of  one  object,  there  is  nothing  in  the  meaning  of  the 
words  themselves  which  implies  this  :  and,  accordingly,  when  we  ai'e 
imagining  and  .not  affirming,  we  may  speak  of  many  suns  j  and  the 
majority  of  mankind  have  believed,  and  still  believe,  that  there  are 
many  gods.  But  it  is  easy  to  produce  words  which  are  real  instances 
of  connotative  individual  names.  It  may  be  part  of  the  meaning  of 
the  connotative  name  itself,  that  there  exists  but  one  individual  possess- 
ing the  attribute  which  it  connotes;  as,  for  instance,  "the  onlij  son  of 
John  Stiles;"  "  the  Jirst  emperor  of  Rome."  Or  the  attribute  con- 
noted may  be  a  connexion  with  some  determinate  event,  and  the 
connexion  may  be  of  such  a  kind  as  only  one  individual  could  have ; 
or  may  at  least  be  such  as  only  one  individual  actually  had ;  and  this 
may  be  implied  in  the  form  of  (the  expression.  "The  father  of 
Socrates,"  is  an  example  of  the  one  kind  (since  Socrates  could  not 
have  had  two  fathers);  "the  author  of  the  Iliad,"  "the  murderer  of 
Henri  Quatre,"  of  the  second.  For,  although  it  is  conceivable  that 
more  persons  than  one  might  have  participated  in  the  authorship  of  the 
Iliad,  or  in  the  murder  of  Henri  Quatre,  the  employment  of  the  article 
t7(,e  implies  that,  in  fact,  this  was  not  the  case.  What  is  here  done  by 
the  vvord  the,  is  done  in  other  cases  by  the  context :  thus,  "  Caesar's 
army  "  is  an  individual  name,  if  it  appears  from  the  context,  that  the 
army  meant  is  that  which  Caesar  commanded  in  a  particular  battle. 
The  still  more  general  expressions,  "  the  Roman  anny,"  or  "the 
Christian  army,"  may  be  individualized  in  a  similar  manner.  Another 
case  of  frequent  occurrence  has  alrfeady  been  noticed ;  it  is  the  follow- 
ing. The  name,  being  a  many-worded  one,  may  consist,  in  the  first 
place,  of  a  general  name,  capable  therefore  in  itself  of  being  affirmed 
of  more  things  than  one,  but  which  is,  in  the  second  j^jlace,  so  limited 
by  other  words  joined  with  it,  that  the  entire  expression  can  only  be 
predicated  of  one  object,  consistently  with  the  meaning  of  the  general 
term.  This  is  exemplified  in  such  an  instance  as  the  following :  *'  the 
present  prime  minister  of  England."  Prime  Minister  of  England  is  a 
general  name ;  the  attributes  which  it  connotes  may  be  possessed  by 
an  indefinite  number  of  persons :  in  succession  however,  not  simulta- 
neously;  since  the  meaning  of  the  word  itself  imports  (among  other 
things)  that  there  can  be  only  one  such  person  at  a  time.  This  being 
the  case,  and  the  application  of  the  name  being  afterwards  limited  by 
the  word  present,  to  such  individuals  as  possess  the  attributes  at  one 


NAMES.  23 

indivisible  point  of  time,  it  becomes  applicable  only  to  one  individual. 
And  as  this  appears  from  the  moaning  of  the  name,  witliout  any 
extrinsic  proof,  it  is  strictly  an  individual  name. 

From  the  preceding  observations  it  will  easily  be  collected,  that 
whenever  the  names  given  to  objects  convey  any  information,  that  is, 
whenever  they  have  properly  Jiny  meaning,  the  meaning  resides  not 
in  \vhat  they  denote,  but  in  what  they  connote.  The  only  names  of 
objects  which  connote  nothing  are  fro])er  names ;  and  these  have, 
strictly  speaking,  nO  signification. 

If,  like  the  robber  in  the  Arabian  Nights,  we  make  a  mark  with 
chalk  upon  a  house  to  enable  us  to  know  it  again,  the  mark  has  a 
purpose,  but  it  has  not  pix)perly  any  meaning.  The  chalk  does  not 
declare  anything  about  the  house ;  it  does  not  mean,  This  is  such  a 
person's  house,  or  This  is  a  house  which  contains  booty.  The  object 
of  making  the  mark  is  merely  distinction.  I  say  to  myself.  All  these 
houses  are  so  nearly  alike,  that  if  I  lose  sight  of  them  I  shall  not  again 
be  able  to  distinguish  that  which  I  am  now  looking  at  from  any  of 
the  others ;  I  must  therefore  contrive  to  make  the  appearance  of  this 
one  house  unlike  that  of  the  others,  that  I  may  hereafter  know,  when 
I  see  the  mark — not  indeed  any  attribute  of  the  house — but  simply 
that  it  is  the  same  house  which  I  am  now  looking  at.  Morgiana 
chalked  all  the  other  houses  in  a  similar  manner,  and  defeated  the 
scheme :  how  ]  simply  by  obliterating  the  difference  of  appearance 
between  that  house  and  the  others.  The  chalk  was  still  there,  but  it 
no  longer  served  the  purpose  of  a  distinctive  mark. 

'When  we  impose  a  proper  name,  we  perform  an  operation  in  some 
degree  analogous  to  what  the  robber  intended  in  chalking  the  house. 
We  put  a  mark,  not  indeed  upon  the  object  itself,  but,  if  I  may  so 
speak,  upon  the  idea  of  the  object.  A  proper  name  is  but  an  unmean- 
ing mark  which  we  connect  in  our  minds  with  the  idea  of  the  object, 
in  order  that  whenever  the  mark  meets  our  eyes  or  occurs  to  our 
thoughts,  we  may  think  of  that  individual  object.  Not  being  attached 
to  the  thing  itself,  it  does  not  enable  us,  as  the  chalk  did,  to  distin- 
guish the  object  when  we  see  it;  but  it  enables  us  to  distinguish  it 
when  it  is  spoken  of,  either  in  the  records  of  our  own  experience,  or 
in  the  discourse  of  others ;  to  know  that  what  we  find  asserted  in  any 
proposition  of  which  it  is  the  subject,  is  asserted  of  the  individual  thing 
with  which  we  were  previously  acquainted. 

When  we  predicate  of  anything  its  proper  name ;  when  we  gay, 
pointing  to  a  man,  this  is  Brown  or  Smith,  or  pointing  to  a  city,  that 
it  is  York,  we  do  not,  merely  by  so  doing,  convey  to  the  hearer  any 
information  about  tliem,  except  that  those  are  their  names.  By 
enabling  him  to  identify  the  individuals,  we  may  connect  them  with 
information  previously  possessed  by  him ;  by  saying,  This  is  York, 
we  may  tell  him  that  it  contains  the  Minster.  But  this  is  in  virtue  of 
what  he  has  previously  heard  concerning  York ;  not  by  anything 
implied  in  the  name.  It  is  otherwise  when  objects  are  spoken  of  by 
connotative  names.  When  we  say.  The  town  is  built  of  marble,  we 
give  the  hearer  what  may  be  entirely  new  information,  and  this  merely 
by  the  signification  of  the  many-worded  connotative  name,  "  built  of 
marble."  Such  names  are  not  signs  of  the  mere  objects,  invented 
because  we  have  occasion  to  think  and  speak  of  those  objects  individ- 
ually ;  but  signs  which  accorajiany  an  attribute  :  a  kind  of  livery  in 


?4  N-AMES    AND    PROPOSITIONS. 

which  the  attribute  clothes  all  objects  which  are  recognized  as  possess- 
ing it.  They  ai-e  not  mere  marks,  but  more,  that  is  to  say,  significant 
marks ;  and  the  connotation  is  what  constitutes  their  significance. 

As  a  proper  name  is  said  to  be  the  name  of  the  one  individual 
which  it  is  predicated  of,  so  (as  well  fi'om  the  importance  of  adhering 
to  analogy,  as  for  the  other  reasons  fonnerly  assigned)  a  connotative 
name  ought  to  be  considered  a  name  of  all  the  various  individuals 
which  it  is  predicable  of,  or  in  other  words  denotes,  and  not^of  what  it 
connotes.  But  by  learning  what  things  it  is  a  na,me  of,  we  do  not 
learn  the  meaning  of  the  najne  :  for  to  the  sande  thing  we  may,  wth 
equal  propriety,  apply  many  names,  not  equivalent  in  meaning.  Thus, 
I  call  a  certain  man  by  the  name  Sophtoniscus :  I  call  him  by  another 
name.  The  father  of  Socrates.  Both  these  are  names  of  the  same 
individual,  but  their  meaning  is  altogether  different ;  they  are  applied 
to  that  individual  for  two  different  purposes ;  the  one,  merely  to 
distinguish  him  from  other  persons  who  are  spoken  of;  the  other,  to 
indicate  a  fact  relating  to  him,  the  fact  that  Socrates  was  his  son.  I 
frirther  apply  to  him  these  other  expressions :  a  man,  a  Greek,  an 
Athenian,  a  sculptor,  an  old  man,  an  honest  man,  a  brave  man.  All 
these  are  names  of  Sophi-oniscus,  not  indeed  of  him  alone,  but  of  him 
and  each  of  an  indefinite  number  of  other  human  beings.  Each  of 
these  names  is  applied  to  Sophroniscus  for  a  different  reason,  and  by 
each  whoever  understands  its  meaning  is  apprised  of  a  distinct  fact  or 
number  of  facts  concerning  him  ;  but  those  who  knew  nothing  about 
the  names  except  that  they  were  applicable  to  Sophroniscus,  would 
be  altogether  igiiorant  of  their  meaning.  It  is  even  conceivable  that 
I  might  know  every  single  individual  of  whom  a  given  name  could  be 
Avith  truth  affirmed,  and  yet  could  not  be  said  to  know  the  meaning  of 
the  name.  A  child  knows  who  are  its  brothers  and  sisters,  long  before 
it  has  any  definite  conception  of  the  nature  of  the  facts  which  are 
involved  in  the  signification  of  those  words. 

In  some  cases  it  is  not  easy  to  decide  precisely  how  much  a  particular 
word  does  or  does  not  connote ;  that  is,  we  do  not  exactly  know  (the 
case  not  having  arisen)  what  degree  of  difference  in  the  object  would 
occasion  a  difference  in  the  name.  Thus,  it  is  clear  that  the  word 
Tnan,  besides  animal  life  and  rationality,  connotes  also  a  certain  ex- 
ternal form ;  but  it  would  be  impossible  to  say  precisely  what  form  ; 
that  is,  to  decide  how  gi-eat  a  deviation  from  the  form  ordinarily  found 
in  the  beings  whom  we  are  accustomed  to  call  men,  would  suffice  in  a 
newly-discovered  race  to  make  us  refuse  them  the  name  of  man. 
Rationality,  also,  being  a  quality  which  admits  of  degrees,  it  has  never 
been  settled  what  is  the  loAvest  degree  of  that  quality  which  would 
entitle  any  creature  to  be  considered  a  human  being.  In  all  such 
cases,  the  meaning  of  the  general  name  is  so  far  unsettled,  and  vague  ; 
mankind  have  not  come  to  any  positive  agi'eement  about  the  Tnatter. 
^\^len  we  come  to  ti-eat  of  classification,  we  shall  have  occasion  to 
show  under  what  conditions  this  vagueness  may  exist  Avithout  practical 
inconvenience  ;  and  cases  will  appear,  in  •which  the  ends  of  language 
are  better  promoted  by  it  than  by  complete  precision ;  in  order  that, 
in  natural  history,  for  instance,  individuals  or  species  of  no  very 
marked  character  may  be  ranged  ^rith  those  more  strongly  character- 
ized individuals  or  species  to  whicli,  in.  all  their  properties  taken 
together,  they  bear  the  nearest  resemblance. 


NAMES.  25 

But  this  partial  uncertainty  in  the  connotation  of  names  can  only  bo 
free  from  mischief  when  guarded  by  strict  precaution*.  One  of  the 
chief  sources,  indeed,  of  lax  habits  of  thouglit,  is  the  ctistom  of  using 
connotative  terms  without  a  distinctly  ascertained  connotation,  and  with 
no  more  precise  notion  of  their  meaning  than  can  be  loosely  collected 
fi-om  observing  what  objects  they  arc  used  to  denote.  It  is  m  this 
manner  that  we  all  acquire,  and  inevitably  so,  our  first  knowledge  of 
our  vernacular  language.  A  child  learns  the  meaning  of  the  words 
man,  or  ic/iitc,  by  hearing  them  applied  to  a  variety  of  individual  objects, 
and  finding  out,  by  a  process  of  generalization  and  analysis  of  which 
he  is  but  imperfectly  conscious,  what  those  ditTcrent  objects  have  in 
common-  In  the  case  of  these  two. words  the  process  is  so  easy  as' to 
retjuirc  no  assistance  fi'om  culture;  the  objects  called  human  beings, 
and  the  oljjects  called  white,  differing  from  all  others  by  qualities  of 
a  peculiarly  definite  and  obvious  character.  But  in  many  other  cases, 
objects  bear  a  general  resemblance  to  one  another,  which  leads  to  their 
being  familiarly  classed  together  under  a  common  name,  while,  without 
more  analytic  habits  than  the  generality  of  mankind  possess,  it  is  not 
immediately  apparent  what  are  the  particular  attributes,  upon  the  pos- 
session of  which  in  common  by  them  all,  their  general  resemblance 
depends.  When  this  is  the  case,  men  use  the  name  wdthout  any  re- 
cognized connotation,  that  is,  without  any  precise  meaning;  they  talk, 
aiid  consequently  think,  vaguely,  and  remain  contented  to  attach  only 
the  same  degi'ee  of  significance  to  their  own  words,  which  a  child  three 
years  old  attaches  to  the  words  brother  and  sister.  The  child  at  least 
is  seldom  puzzled  by  the  starting  up  of  new  indixaduals,  on  whom  ho 
is  ignorant  whether  or  not  to  confer  the  title ;  because  there  is  usually 
an  authority  close  at  hand  competent  to  solve  all  doubts.  But  a  similar 
resource  does  not  exist  in  the  generality  of  cases;  and  new  objects  are 
continually  presenting  themselves  to  men,  women,  and  children,  which 
they  are  called  upon  to  class  proprio  motu.  They,  accordingly,  do 
this  on  no  other  princij)lo  than  that  of  superficial  similarity,  giving  to 
each  new  object  the  name  of  that  familiar  object,  the  idea  of  wltich  it 
most  readily  recalls;  or  which,  on  a  cursory  inspection,  it  seem*  to 
them  most  to  resemble :  as  an  Unknown  substance  found  in  the  ground 
will  be  called,  according  to  its  texture,  earth,  sand,  or  a  stone.  In  this 
manner,  names  creep  on  fi'om  subject  to  subject,  until  all  traces  of  a 
common  meaning  sometimes  disappear,  and  the  word  cofnes  to  denote 
a  number  of  things  not  only  independently  of  any  common  attribute, 
but  which  have  actually  no  attribute  in  common;  or  none  but  what  is 
shared  by  other  things  to  which  the  name  is  capriciously  refused.* 
Even  philosophers  have  aided  in  this  perversion  of  general  language 
fi-om  its  purpose ;  sometimes  because,  like  the  vulgar,  they  knew  no 
better;  and  sometimes  in  deference  to  that  avei'sion  to.  admit  new 

*  It  would  be  well  if  this  natural  degeneracy  of  language  took  place  only  in  the  hands  of 
the  ignorant  vulgar ;  but  some  of  the  most  remarkable  instances  are  to  be  found  in  terms 
of  art,  and  among  technically  educated  persons,  such  as  English  lawyers.  Felony,  for  ex- 
ample, is  a  law  term,  with  the  sound  of  which  all  ears  are  familiar ;  but  there  is  no  lawyer 
who  would  undertake  to  tell  what  a  fdlony  is,  otherwise  than  by  enumerating  the  various 
kinds  of  offences  which  arc  so  called.  Originally  the  word  felony  had  a  meaning  ;  it  deno- 
ted all  offences,  the  penalty  of  which  included  forfeiture  of  goods ;  but  subsequent  acts  of 
Parliament  have  declared  various  offences  to  be  felonies  without  enjoining  that  penalty, 
and  have  taken  away  the  penalty  from  others  which  continue  nevertheless  to  be  called  falo. 
nies,  insomuch  that  the  acts  so  called  have  now  no  property  whatever  in  common,  savo  that 
of  being  unlawful  and  punishable. 
D 


26  NAMES    AND    PROPOSITIONS. 

words,  which  induces  mankind,  on  all  subjects  not  considered  technical, 
to  attempt  to  make  the  original  small  stock  of  names  serv'e  with  but 
little  augmentation  to  express  a  constantly  increasing  number  of  objeCt!§ 
and  distinctions,  and,  consequently,  ,to,  express  them  in  a  manner  pro- 
gressively more  and  more  imperfect. 

To  what  degree  this  loose  mode  of  classing  and  denominating  objects 
has  rendered  the  vocabulary  of  mental  and  moi-al  philosophy  unfit  for 
the  piu'poses  of  accurate  thinking,  is  best  known  to  whoever  has  most 
reflected  on  the  present  condition  of  those  branches  of  knowledge. 
Since,  however,  the  introduction  of  a  new  technical  language  as  the- 
vehicle  of  speculations  on  hioral  subjects,  would  not,  in  this  country  at 
least,  be  tolerated,  and  if  tolerated,  would  deprive  those  subjects  of 
the  benefit  of  the  habitual  feelings,  which  have  gi-own  round  the- estab- 
lished phrases  and  the  recognized  groups,  and  which  would  not  for  a 
long  time  take  an  equally  strong  hold  of  new  ones ;  the  problem  for 
the  philosopher,  and  one  of  the  most  difficult  which  he  has  to  resolve, 
is,  in  retaining  the  existing  phraseology,  how  best  to  alleviate  its  im- 
perfections. This  can  only  be  accomplished  by  giving  to  every  general 
concrete  name  which  he  has  fi'equent  occasion  to  predicate,  a  definite 
and  fixed  connotation  ;  in  or-der  that  it  may  be  known  what  attributes, 
when  we  call  an  object  by  that  name,  we  really  moan  to  predicate  of 
the  object.  And  the  question  of  most  nicety  is,  how  to  give  this  fixed 
connotation  to  a  name,  with  the  least  possible  change  in  the  objects 
which  the  name  is  habitually  employed  to  denote ;  with  the  least  pos- 
sible disarrangement,  either  by  adding  or  subtraction,  of  the  gi'oup  of 
objects  which  it  serves,  in  however  imperfect  a  manner,  to  circumscribe 
and  hold  together ;  and  with  the  least  vitiation  of  the  truth  of  any 
propositions  which  are  commonly  received  as  true. 

This  desirable  pui-pose,  of  giving  a  fixed  connotation  where  it  is 
wanting,  is  the  encl  aimed  at  whenever  any  one  attempts  to  give  a  defi- 
nition of  a  general  name  already  in  use ;  every  definition  of  a  conno- 
"  tative  name  being  an  attempt  either  merely  to  declare,  or  to  declare 
and  analyze,  the  connotation  of  the  name.  And  the  fact,  that  no  ques- 
tions which  have  arisen  in  the  moral  sciences  have  been  subjects  of 
keener  controversy  than  the  definitions  of  almost  all  the  leading  expres- 
sions, is  a  proof  how  gi'eat  an  extent  the  evil  to  which  we  have 
9,dverted  has  attained. 

Names  with  indeterminate  connotation  are  not  to  be  confounded 
with  names  which  have  more  than  one  connotation,  that  is  to  say,  wdth 
ambiguous  words.  A  word  may  have  several  meanings,  but  all  of 
them  fixed  and  recognized  ones  ;  as  the  word  post,  for  example,  or  the 
work  hox,,  the  various  senses  of  which  it  would  be  endless  to  enumer- 
ate. And  the  paucity  of  existing  names,  in  comparison  with  the 
demand  for  them,  may  often  render  it  advisable  and  even  necessary  to 
retain  a  name  in  this  multiplicity  of  acceptations,  distinguishing  these 
BO  clearly  as  to  prevent  their  being  confounded  with  one  another. 
Such  a  word  may  be  considered  as  two  or  more  names,  accidentally 
^vritten  and  spoken  alike.* 

*  Before  quitting  the  subject  of  connotative  names,  it  is  proper  to  observe,  that  the  only 
recent  writer  who,  to  my  knowledge,  has  adopted  from  the  schoolmen  the  word  to  connote, 
Mr.  Mill,  in  his  Analysig  of  the  Phenomena  of  the  Human  Mind,  employs  it  in  a  signification 
different  from  that  in  which  it  is  here  used.  He  uses  the  word  in  a  sense  coextensive  with 
its  etymology,  applying  it  to  every  case  in  which  a  name,  while  pointing  directly  to  one 
thing,  (which  is,  consequently,  termed  its  signification),  jncludes.also  a  tacit  reference  to 


NAMES.  27 

§6.  The  fourth  principal  dinsion  of  names,  is  mtoj^os/tire  and«ey«//re. 
Positive,  as  man,  tree,  good ;  negative,  as  not-^7nan,  not-free^  not-good. 
To  every  positive  concrete  name,  a  corresponding  negative  ohe  might 
be  framed.  After,  giving  a  name  to  any  one  thing,  or  to  any  plurality 
of  things,  we  ifnight  create  a  second  name  which  should  be  a  name  of 
all  things  whatever  except  tliat  particular  thing  or  things.  These  neg- 
ative names  are  employed  whenever  wo  have  occasion  to  speali  collec- 
tively of  all  things  other  than  some  thing  or  class  of  -things.  When 
the  positive  name  is  connotative,  the  coiTcsponding  negative  name  is 
connotative  likewise ;  but  in  a  peculiar-  way,  connoting  not  the  pres- 
ence but  the  absence  of  an  attribute.  Thus,  not-ioMte  denotes  all 
things  whatever  except  white  tilings  ;  and  connotes  t^  attinbutc  of  not 
possessing  whiteness.  For  the  non-possession  of  any  given  attribute 
is  also  an  attribute,  and  may  receive  a  name  as  such ;  and  thus  nega- 
tive concrete  names  may  obtain  negative  abstract  names  to  correspond 
to  them. 

Names  which  are  positive  in  form  are  often  negative  in  reality,  and 
others  are  really  positive  though  their  form  is  negative.  The  word 
inconvenient,  for  example,  does  not  express  the  mere  absence  of  con- 
venience ;  it  expresses  a  positive  attribute,  that  of  being  the  cause  ,of 
discomfort  or  annoyance.  So  the  word  unpleasant,  notwithstanding  its 
negative  form,  does  not  connote  the  mere  absence  of  pleasantness,  but 
a  less  degree  of  what  is  signified  by  the  word  painful,  which,  it  is 
hardly  necessary  to  say,  is  positive.  Idle,  on  the  other  hand,  is  a  word 
which,  though  positive  in  form,  expresses  nothing  but  what  would  be 
signified  either  by  the  phrase  not  working,  or  by  the  phrase  not  dis- 
posed to  work  ;    and  sober,  either  by  not  drunk  or  by  not  drimkcn. 

There  is  a  class  of  names  called  privative.     A  privative  name  is 

some  other  thin^.  In  the  case  considered  in  the  text,  that  of  concrete  general  names',  his 
language  and  mine  are  the  converse  of  one  another.  Considering  (very  justly)  the  signifi- 
cation of  the  name  to  lie  in  the  attribute,  he  speaks  of  the  word  as  notitig  the  attribute-,  and 
connoting  the  things  possessing  the  attribute.  And  he  describes  abstract  names  as  being 
properly  concrete  names  with  their  connotation  dropped :  whereas,  in  my  view,  it  is  the 
denotation  which  would  be  said  to  be  dropped,  what  was  previously  connoted  becoming  the 
whole  signification. 

In  adopting  a  phraseology  at  variance  with  that  which  so  high  an  authority,  and  one 
which  1  am  less  likely  than  any  other  person  to  undervalue,  has  deliberately  sanctioned,  I 
have  been  influenced  by  the  urgent  necessity  for  a  term  exclusively  appropriated  to  express 
the  manner  in  which  a  concrete  general  name  serves  to  mark  the  attributes  which  are  in- 
volved in  its  signification.  This  necessity  cpn  scarcely  be  felt  in  its  full  force  by  any  odq 
who  has  not  found  by  experience,  how  vain  is  the  attempt  to  communicate  clear  ideas  on 
the  philosophy  of  language  without  such  a  word.  It  is  hardly  an  exaggeration  to  say,  that 
some  of  the  most  prevalent  of  the  errors  with  which  logic  has  been  infected,  and  a  large 
part  of  the  cloudiness  and  confusion  of  ideas  which  have  enveloped  it,  would,  in  all  proba- 
bility, have  been  avoided,  if  a  term  had  been  in  common  use  to  express  exactly  what  I  have 
signified  by  the  term  to  connote.  And  the  schoolmen,  to  whom  we  are  indebted  for  the 
greater  part  of  our  logical  language,  gave  us  this  also,  and  in  this  very  sense.  For,  although 
some  of  their  general  expressions  countenance  the  use  of  the  word  in  the  more  extensive 
and  vague  acceptation  in  which  it  is  taken  by  Mr.  Mill,  yet  when  they  had  to  define  it  spe- 
cifically as  a  technical  term,  and  to  fix  its  meaning  as  such,  with  that  admirable  precision 
which  always  characterized  their  definitions,  they  clearly  explaineti  that  nothing  was  said 
to  be  connoted  except /orms,  which  word  may  generally,  in  their  writings,  be  understood  as 
synonymous  with  attributes. 

Now,  if  the  word  to  connote,  so  well  suited  to  the  purpose  to  which  they  applial  it,  be  di. 
verte<l  from  that  purpose  by  being  taken  to  fulfil  another,  for  which  it  does  not  seem  to  me  ta 
be  at  all  required  ;  I  am  unable  to  find  any  expression  to  replace  it,  but  suc-h  as  are  commonly 
employed  in  a  sense  so  much  more  general,  that  it  would  be  uselessattempting  to  associato 
them  peculiarly  with  this  precise  idea.  Such  are  the  words,  to  involve,  to  imply,  &c.  By 
employing  these,  I  should  fail  of  attaining  the  object  for  which  alone  the  name  is  needed, 
namely,  to  distinguish  this  particulat  kind  of  involving:  and  implying  from  all  other  kiods, 
and  to  assure  to  it  the  degree  of  habitual  attention  which  its  importance  demands. 


28  NAMES    AND    PROPOSITIONS. 

equivalent  in  its  signification  to  a  positive  and  a  negative  name  taken 
togjether ;  being  the  name  of  something  which  has  once  had  a  partic- 
ular attribute,  or  for  some  other  reason  might  have  been  expected  to 
have  it,  but  which  has  it  not.  Such  is  the  word  blind,  which  is  not 
equivalent  to  not  seeing,  or  to  not  Capable  of  seeing,  for  it  would  not, 
except  by  a  poetical  ox  rhetorical  figure,  be  applied  to  stocks  and 
stones.  A  thing  is  not  usually  said  to  be  blind,  unless  the  class  to 
which  it  is  most  famiharly  referred,  or  to  which  it  is  refen-ed  on  the 
particular  occasion,  be  chiefly  composed  of  things  which  can  see,  as 
in  the  case  of  a  blind  man,  or  a  bhnd  horse  ;  or  unless  it  is  supposed 
for  any  reason  that  it  ought  to  see;  as  in  saying  of  a  man,  that  he 
rushed  blindly  ir^  an  abyss,  or  of  philosophers  or  the  clergy  that  the 
greater  part  of  tnem  are  blind  guides.  'The  names  called  privative, 
therefore,  connote  two  things  :  the  absence  of  certain  atti'ibutes,  and 
the  presence  of  others,  from  which  the  presence  also  of  the  former 
might  naturally  have  been  expected. 

§  7.  The  fifth  leading  division  of  names,  is  into  relative  and  absolute, 
or  let  us  rather  say,  relative  and  non-relative ;  for  the  word  absolute 
is  put  upon  much  too  hard  duty  in  metaphysics,  not  to  be  willingly 
spared  when  its  services^  can  be  dispensed  \\'ith.  It  resembles  the 
word  civil  in  the  language  of  jurisprudence,  which  stands  for  the 
opposite  of  criminal,  the  opposite  of  ecclesiastical,  the  opposite  of  mil- 
itary, the  opposite  of  political,  in  short,  the  opposite  of  any  positive 
word  which  wants  a  negative. 

Relative  names  are  such  as  father,  ^on ;  ruler,  subject ;  like  ;  equal ; 
unlike  ;  unequal ;  longer,  shorter ;  cause,  effect.  Theii'  characteristic 
property  is,  that  they  are  always  given  in  pairs.  Every  relative  name 
which  is  predicated  of  an  object,  supposes  another  object  (or  objects), 
of  which  we  may  predicate  either  that  same  name  or  another  relative 
name  which  is  said  to  be  the  correlative  of  the  fonner.  Thus,  when 
we  call  any  person  a  son,  we  suppose  other  persons  who  must  be  called 
'parents.  AVhen  we  call  any  event  a  cause,  we  suppose  another  event 
which  is  an  effect.  A^Hien  we  say  of  any  distance  that  it  is  longer,  we 
suppose  another  distance  which  is  shorter.  Wlien.we  say  of  any  object 
that  it  is  like,  we  mean  that  it  is  like  some  other  object,  which  is  also 
said  to  be  like  the  first.  In  this  case,  both  objects  receive  the  same 
name ;  the  relative  term  is  its  own  con-elative. 

It  is  evident  that  these  words,  when  concrete,  are,  like  other  con- 
crete general  names,  connotative  :  they  denote  a  subject,  and  connote 
an  atti-ibute  :  and  each  of  them  has  or  might  have  a  coiTesponding 
abstr-act  name  to  denote  the  attribute  connoted  by  the  concrete.  Thus 
the  concrete  like  has  its  abstract  likeness  ;  the  concretes,  father  and 
son,  have  the  abstracts,  paternity  and  filiation.  The  concrete  name 
connotes  an  atti'ibute,  and  the  absti-act  name  which  answers  to  it 
denotes  that  attribute.  But  of  what  nature  is  the  attribute  f  Wherein 
consists  the  peculiarity  in  the  connotation  of  a  relative  name  ? 

The  attribute  signified  by  a  relative  name,  say  some,  is  a  relation  ; 
and  this  they  give,  if  not  as  asufficient  explanation,  at  least  as  the  only 
one  attainable.  If  they  are  asked,  What  then  is  a  relation  1  they  do 
not  profess  to  be  able  to  tell.  It  is  generally  regarded  as  something 
peculiarly  recondite  and  mysterious.  I  cannot,  however,  perceive  in 
what  i-espect  it  is  more  so  than  any  other  attribute ;  indeed,  it  appeara 


NAMES.  29 

to  me  to  bo  so  in  a  somcMiat  less  degit;c.  I  conceive,  rather,  that  it 
is  by  exaniinhig  into  the  signification  of  rehitive  names,  or  in  other 
words,  into  the  natm-c  of  the  attribute  which  they  connote,  that  a  clear 
insight  may  best  be  obtained  into  the  nature  of  all  attributes  ,♦  of  all 
that  is  meant  by  an  attribute. 

It  is  obvious,  in  fact,  that  if  we  take  any  two  correlative  names,  j^- 
tlicr  and  son,  fi>r  instance,  although  the  objects  <^enoted  by  the  names  are 
different,  they  both,  in  a  certain  sense,  connote  the  same  thing.  They 
cannot,  indeed;  be  said  to  connote  the  same  attribute  ;  to  be  a  fatlier 
is  not  the  same  thing  as  to  be  a  son.  But  when  we  call  one^  man  a 
father,  another  his  son,  what  we  mean  to  affirm  is  a  set  of  facts,  v<^hich 
are  exactly  the  same  in  both  cases.  To  predicate  of  A  that  he  is  the 
father  of  B,  and  of  B.  that  he  is  the  son  of  A,  is  to  assert  one  and  the 
same  fact  in  ditfcrent  words.  The  two  propositions  are  exactly  equiv- 
alent :  neither  of  them  asserts  more  or  asserts  less  than  the  otlier.  The 
paternity  of  A  and  the  filiation  of  B  are  not  two  facts,  but  two  mode^ 
of  expressing  the  same  fact.  That  fact,  when  analyzed,  consists  of  a 
series  of  physical  events  or  phenometia,  in  whicli  both  A  and  B  are 
parties  concerned,  and  fi-om  which  they  both  derive  names.  What 
those  names  really  connote  is  this  series  of  events  :  that  is  the  meaning 
and  the  whole  meaning,  which  either  of  them  is  intended  to  convey. 
The  series  of  events  may  be  said  to  constitute  the  relatioh  ;  the  school- 
men called  it  the  foundation  of  the  x^dX\oxy,  fundamentum  relationis. 

In  this  manner  any  fact,  or  series  of  facts,  in  which  two  different 
objects  are  implicated,  and  which  is  therefore  predicable  of  both  of 
them,  may  be  either  considered  as  constituting  an  attribute  of  the  one, 
or  an  attribute  of  the  other.  According  as  we  consider  it  in  the  for- 
mer or  in  the  latter  aspect,  it  is  connoted  by  the  one  or  the  other  of  the 
two  con'elative  names.  Father  connotes  the  fact,  regarded  as  consti- 
tuting an  attribute  of  A  :  son  connotes  the  same  fact,  as  constituting  an 
attribute  of  B.  It  may  evidently  be  regarded  with  equal  propriety  in 
either  hght.  And  all  that  appears  necessary  to  account  for  the  exist- 
ence of  relative  names,  is,  that  whenever  there  is  a  fact,  in  which  two ' 
individuals  are  alike  concerned,  an  attribute  gi'ounded  on  that  fact  may 
be  ascribed  to  either  of  these  individuals. 

A  name,  therefore,  is  said  to  be-  relative,  when,  over  and  above  the 
object  which  it  denotes,  it  im.plies  in  its  signification  the  existence  of 
another  object,  also  derivdng  a  denomination  from  the  same  fact  which 
is  thegi'ound  of  the  first  name.  Or  (to  express  the  same  meaning  in 
other  words). a  name  is  relative,  when,  being  the  name  of  one  thing, 
its  signification  eanaot  be  explained  but  by  mentioning  another.  Or 
we  may  state  it  thus  : — when  the  name  cannot  be  employed  in  dis- 
course, so  as  to  have  a  meaning,  unless  the  name  of  some  other  thing 
than  what  it  is  itself  the  name- of,  be  either  expressed  or  understood. 
We  may  take  our  choice  among  these  definitions.  Thoy  are  all,  at 
bottom,  equivalent,  being  modes  of  variously  expressing  this  one  dis- 
tinctive circumstance — that  every  other  attribute  of  an  object  might, 
without  any  contradiction,  be  conceived  still  to  exist  if  all  objects- be- 
sides that  one  were  annihilated  ;*  but  those  of  its  attributes  whidi  aj-e 
expressed  by  relative  names  would  on  that  supposition  be  swept  away. 


*  Or  rather  all  objects,  except  itself  and  the  percipient  mind ;  for,  as  we  shall  S' 
after,  to  ascribe  any  attribute  to  an  object  necessarily  implies  a  mind  to  perceive  it 


see  here- 


30  NAMES    AND    PROPOSITIONS. 

§  S.  Names  liave  been  further  distinguished  into  lodvocal  and  cpquiv- 
ocal :  these,  however,  are  not  two  kinds  of  names,  but  two  different 
modes  of  employing  names.  A  name  is  univocal,  or  appHed,  imivo- 
cally,  with  respect  to  all  things  of  which  it  can  be  precicated  in  the 
same  sense;  but  it  is  Eequivocal,  or  applied  gequivocally,  as  rfespects 
those  things  of  which  it  is  predicated  in  different  senses.  It  is  scai'cely 
necessary  to  giye  instances  of  a  fact  so  familiar  as  the  double  meaning 
of  a  word.  In  reality,  a§  has, been  already  observed,  an  aequivocal  or 
ambiguous  word  is  not  one  name,  but  two  names,  accidentally  coinci- 
ding in, sound.  File  standing  for  an  iron  instrument,  and  Jile  standing 
for  a  line  of  soldiers,  have  no  more  title  to  be  considered  one  word, 
because  ^vTitten  alike,  than  grease  and  Greece  have,  because  they  are 
pronounced  alike.  They  are  one  sound,  appropriated  to  form  two  dif- 
ferent words. 

An  intermediate  case  is  that  of  a  name  used  analogically  or  meta- 
phorically ;  that  is,  a  name  which  is  predicated  of  two  things,  not 
univocally,  or  exactly  in  the  same  signification,  bvit  in  significations 
somewhat  similar,  and  which  being  derived  one  fx-om  the  other,  one  of 
them  may  be  considered  the  jarimary,  and  the  other  a  secondary  .sig- 
nification. As  when  we  speak  of  a  brilliant  light,  and  a  brilliant 
achievement.  The  word  is  not  applied  in  the  same  sense  to  the  light 
and  to  the  achievement ;  but  having  been  applied  to  the  light  in  its 
original  sense,  that  of  brightness  to  the  eye,  it  is  transferred  to  the 
achievement  in  a  derivative  signification,  supposed  to  be  somewhat 
like  the  primitive  one.  The  word,  however,  is  just  as  properly  two 
names  instead  of  one,  in  this  case,  as  in  that  of  the  most  perfect  am- 
biguity. And  one  of  the  commonest  forms  of  fallacious  reasoning 
arising  from  ambiguity,  is  that  of  arguing  fit'om  a  metaphorical  expres- 
sion as  if  it  were  literal ;  that  is,  as  if  a  word,  when  applied  metaphor- 
ically, were  the  same  name  as  when  taken  in  its  original  sense  :  which 
will  be  seen  more  particularly  in  its  place. 


CHAPTER  III. 

OF   THE   THINGS    DENOTED   BY   NAMES. 


§  1.  Looking  back  now  to  the  commeticement  of  our  inquiry,  let  us 
attempt  to  measure  how  far  it  has  advanced..  Logic,  we  found-  is  the 
Theory  of  Proof  But  proof  supposes' something  provable,  Avhich  must 
be  a  Proposition  or  Assertion ;  since  nothing  but  a  Proposition  can  be 
tin  object  of  belief,  or  therefore  of  proof.  A  Proposition  is,  discourse 
which  affinns  or  denies  something  of  some  other  thing.  This  is  one 
step  :  there  must,  it  seems,  be  two  things  concerned  in  every  act  of 
belief  But  what  are  these  Things  %  They  can  be  no  other  than  those 
signified  by  the  two  names,  which  being  joined  together  by  a  copula 
constitute  the  Proposition.  If,  therefore,  Ave  knew  what  all  Names 
signify,  we  should  know  everything  which  is  capable  either  of  being 
made  a  subject  of  affimiation  or  denial,  or  of  being  itself  affinned  or 
denied  of  a  subject.  We  have  accordingly,  in  the  preceding  chapter, 
reviewed  the  various  kinds  of  Names,  in  oz'der  to  ascertain  what  is  sig- 


THINGS  DENOTED  BY   NAMES.  31 

nified  by  each  of  them.  And  we  have  now  canied  this  survey  fai' 
enough  to  be  able  to  take  an  account  of  its  I'eSults,  and  to  exhibit  an 
enumeration  of  all  the  kinds  of  Things  which  are  capable  of  being 
made  predicates,  or  of  having  anything  predicated  of  them :  after 
which  to  determine  the  import  of  Predication,  that  is,  of  Propositions, 
can  be  no  arduous  task. 

The  necessity  of  an  enumeration  of  Existences,  as  the  basis  of  Logic, 
did  not  escape  the  attention  of  the  schoolmen,  and  of  their  master, 
Aristotle,  the  most  comprehensive',  if  not  the  most  sagacious,  of  the 
ancieht  philosophers.  The  Categories,  or  Predicaments — the  former 
a  Greek  word,  the  latter  its  literal  translation  in  the  Latin  language — - 
were  intended  by  him  and  his  followers  as  an  enumeration  of  all  things 
capable  of  being_ named  ;  an  emnncration  by  the  summa  genera,  i.  e. 
the  most  extensive  classes  into  wIiIcIk  things  could  be  distributed ; 
which,  therefore,  were  so  many  highest  Predicates,  one  or  other  of 
which  was  supposed  capable  of  being  affiiTned  with  triith  of  every 
nameable  thing  whatsoever.  The  following  are  the  classes  into  which, 
according  to  this  school  of  philosophy.  Things  in  general  might  be  re- 
duced : — 


'Ovaia, 

Substantia. 

Uoaov, 

Quantitas. 

Uoiov, 

Qualitas. 

Upog  Ti, 

Relatio. 

IIoLelv, 

Actio. 

IlaaxEtv, 

Passio. 

Ugv, 

Ubi. 

Uors, 

Quando. 

Keladai, 

Situs. 

Exscv, 

Habitus. 

The  imperfections  of  this  classification  are  too  obvious  to  require, 
and  its  merits  are  not  sufficient  to  reward,  a  minute  examination.  It 
is  a  mere  catalogue  of  the  distinctions  rudely  marked  out  by  the  lan- 
guage of  familiar  life,  with  little  or  no  attempt  to  penetrate,  by  philo- 
sophic analysis,  to  the  rationale  even  of  those  common  distinctions. 
Such  an  analysis,  however  superficially  conducted,  would  have  shown 
the  enumeration  to  be  both  redundant  and  defective.  Some  objects 
are  omitted,  and  others  repeated  several  times  under  different  heads. 
It  is  like  a  division  of  animals  into  men,  quadrupeds,  horses,  asses,  and 
ponies.  That,  for  instance,  could  not  be  a  very  comprehensive  view 
of  the  nature  of  Relation  which  could  exclude  action,  passivity,  and  lo- 
cal situation  from  that  category.  The  same  observation  applies  to  the 
categories  Quando  (or  position  in  time)  and  Ubi  (or  position  in  space)  ; 
wlxile  the'  distinction  between'  tlie  latter  and  Situs  is  merely  veilsal. 
The  incongruity  of  erecting  into  a  sujnimim  genus  the  class  which  forms 
the  tenth  category  is  manifest.  On  the  other  hand,  the  enumeration 
take.?  no  notice  of  anything  besides  substances  and  atti-ibutes.  In  what 
category  are  we  to  place  sensatipns,  or  any  other  feelings,  and  states 
of  mind ;  as  hope,  joy,  fear  j  sound,  smell,  taste  ;  pain,"  ple,asure ; 
thought,  judgment,  conception,  and  the  like  1  Probably  all-  these 
would  have  been  placed  by  the  Aristotelian  school' in  the  categories  of 
actio  and  2^(iss/o ;  and  the  relation  of  such  of  them  aS  are  active,  to 
their  objects,  and  of  such  of  them  as  are  passive,  to  their  causes,  would 
rightly  be  so  placed  j  but  the  things  themselves,  the  feelings  Or  states 


'32  NAMES    AND   PROPOSITIONS. 

of  mind  wrongly.  Feelings,  or  states-  of  consciousness,  are  assuredly 
to  be  counted  among  realities,  but  they  cannot  be  reckoned  either 
among  substances  or  attributes. 

§  2.  Before  recommeticing,  under  better  auspices,  the  attempt  made 
with  such  imperfect  success  by  the  great  founder  of  the  science  of  logic, 
we  must  take  notice  of  "an  unfortunate  ambiguity  in  all  the  concrete 
names  which  correspond  to  the  most  general  of  all  abstract  terms,  the 
word  Existence.  When  we  have  occasion  for  a  name  which  shall  be 
capable  of  denoting  whatever  exists,  as  contradistinguished  from  non- 
entity or  Nothing,  there  is'  hardly  a  word  applicable  to  the  purpose 
which  is  not  also,  and  even  more  familiarly,  taken  in  a  sense  in  which 
it  denotes  only  substances.  But  substances  are  not  all  that  exist ; 
attributes,  if  such  things  are  to  be  spoken  of,  must  be  said  to  exist ; 
feelings  also  exist.  Yet  when  we  speak  of  an  object,  or  of  a  thing,  we 
are  almost  always  supposed  to  mean  a  substance.  There  seems  a  kind 
of  contradiction  in  using  such  an  expression  as  that  one  thing  is  merely 
an  attribute  of  another  thing.  And  the  announcement  of  a  Classifica- 
tion of  Things  would,  I  believe,  prepare  most  i-eaders  for  an  enumer- 
ation like  those  in  natural  history,  beginning  with  the  great  divisions 
of  animal,  vegetable,  and  mineral,  and  subdividing  them  into  classes 
and  orders.  If,  rejecting  the  word  Thing,-  we  endeavot  to  find  another 
of  a  more  general  import,  or  at  least  more  exclusively  confined  to  that 
general  import,  a  word  denoting  all  that  exists,  and  connoting  only  simple 
existence  ;  no  word  might  be  presumed  fitter  for  such  a  purpose  than 
heing :  originally  the  present  participle  of  a  verb  which  in  one  of  its 
meanings  is  exactly  equivalent  to  the  verb  exist ;  and  therefore  suitable, 
even  by  its  grammatical  formation,  to  be  the  concrete  of  the  abstract  ex- 
istence. But  this  word,  str-ange  as  the  fact  may  appear,  is  still  more  com- 
pletely spoiled  for  the  purpose  which  it  seemed  expressly  made  for, 
than  the  word  Thing.  Being  is,  by  custom,  exactly  synonymous  with 
substance  ;  except  that  it  is  free  fi-om  a  slight  taint  of  a  second  ambigu- 
ity ;  being  applied  impartially  to  matter  and  to  mind,  while  substance, 
though  originally-  and  in  strictness  applicable  to  both,  is  apt  to  suggest 
in  preference  the  idea  of  matter.  Attributes  are  never  called  Beings  ; 
nor  are  Feelings.  A  Being  is  that  which  excites  feelings,  and  which 
possesses  attiibutes.  The  soul  is  called  a  Being ;  God  and  angels  are 
called  Beings ;  but  if  we  were  to  say,  extension,  color,  wisdom,  virtue 
are  beings,  we  should  perhaj^s  be  suspected  of  thinking  with  some  of 
the  ancients,  that  the  cardinal  virtues  are  animals ;  or,  at  the  least,  of 
holding  with  the  Platonic  school  the  doctrine  of  self-existent  Ideas,  or 
witli  the  followers  of  Epicurus  that  of  Sensible  Forms,  which  detach 
themselves  in  every  direction  from  bodies,  and  by  coming  in  contact 
with  our  organs,  cause  our  perceptions.  We  should  be  supposed,  in 
short,  to  believe  that  Attributes  are  Substances. 

In  consequence  of  this  perversion  of  the  word  Being,  philosophers 
looking  about  for  something  to  supply  its  place,  laid  their  hands  upon 
the  word  Entity,  a  piece  of  barbarous  Latin,  invented  by  the  schoolmen 
to  be  used  as  an  absti^act  name,  in  which  class  its  grammatical  foiTU 
would  seem  to  place  it ;  but  being  seized  by  logicians  in  distress  to 
stop  a  leak  in  their  terminology,  it  has  ever  since  been  used  as  a  con- 
crete name.  The  kindred  word  essence,  born  at  the  same  time,  and  of 
the  same  parents,  scarcely  underwent  a  more  complete  transfoi'mation 


THINGS    DENOTED    BY    NAMES.  33 

when,  from  being  the  abstract  of  the  verb  to  he,  it  came  to  denote  some- 
thing sufficiently  concrete  to  be  inclosed  in  a  glass  bottle.  The  word 
Entity,  since  it  settled  down  into  a  c<»ncrete  name,  has  retained  its 
universality  of  signification  somewhat  less  unimpaired  than  any  of  the 
names  before  mentioned.  Yet  the  same  gi'adual  decay  to  which,  after 
a  certain  age,  all  the  language  of  psychology  seems  liable,  has  been  at 
work  even  here.  If  you  call  virtue  an  entity,  you  are  indeed  somewhat 
less  strongly  suspected  of  believing  it  to  be  a  substance  than  if  you 
called  it  a  being ;  but  you  are  by  no  means  free  from  the  suspicion. 
Every  word  which  was  originally  intended  to  connote  mere  existence, 
seems,  after  a  time,  to  enlarge  its  connotation  to  separate  existence,  or 
existence  freed  from  the  condition  of  belonging  So  a  substance;  which 
condition  being  precisely  what  constitutes  an  atti'ibute,  attributes  are 
gradually  shut  out,  aTid  along  with  tlann  feelings,  which,  in  ninety-nine 
cases  out  of  a  hundred,  havt?  no  other  name  than  that  of  the  attribute 
which  is  grounded  upon  them.  Strange  that  when  the  greatest  em- 
ban-assment  felt  by  all  who  have  any  considerable  number  of  thoughts 
to  express,  is  to  find  a  sufficient  variety  of  words  fitted  to  express  them, 
there  should  be  no  practice  to  which  even  philosophers  are  more  ad- 
dicted than  that  of  taking  valuable  words  to  express  ideas  which  are 
sufficiently  expressed  by  other  words  already  appropriated  to  them. 

When  it  is  impossible  to  obtain  good  tools,  the  next  best  thing  is  to 
imderstand  thoroughly  the  defects  of  those  we  have.  I  have  therefore 
warned  the  reader  of  the  ambiguity  of  the  very  names  which,  for  want 
of  better,  I  am  necessitated  to  employ.  It  must  now  be  the  writer's 
endeavor  so  to  employ  them  as  in  no  case  to  leave  his  meaning  doubtful 
or  obscure.  No  one  of  the  above  terms  being  altogether  ambiguous,  I 
shall  not  confine  myself  to  any  one,  but  shall  employ  on  each  occasion 
the  word  which  seems  least  likely  in  the  particular  case  to  lead  to  a 
misunderstanding  of  my  meaning ;  nor  do  I  pretend  to  use  either  these 
or  any  other  words  with  a  rigorous  adherence  to  one  single  sense. 
To  do  so  would  often  leave  us  without  a  word  to  express  what  is  sig- 
nified by  a  known  word  in  some  one  or  other  of  its  senses:  unless 
authors  had  an  unlimited  license  to  coin  new  words,  together  with 
(what  it  would  be  more  difficult  to  assume)  unlimited  power  of  making 
their  readers  adopt  them.  Nor  would  it  be  wise  in  a  wi'iter,  on  a 
subject  involving  so  much  of  abstraction,  to  deny  himself  the  advantage 
derived  from  even  an  improper  use  of  a  term,  when,  by  means  of  it 
some  familiar  association  is  called  up  which  brings  the  meaning  home 
to  the  mind,  as  it  were  by  a  flash. 

The  difficulty,  both  to  the  writer  and  reader,  of  the  attempt  which 
must  be  made  to  use  vague  words  so  as  to  convey  a  precise  meaning, 
is  not  wholly  a  matter  of  regret.  It  is  not  unfitting  that  logical  treatises 
should  affi^rd  an  example  of  that,  to  facilitate  which  is  among  the  most 
impoitaiit  uses  of  logic.  Philosophical  language  will  for  a  long  time, 
and  popular  language  pcrhajjs  always,  retain  so  much  of  vagueness 
and  ambiguity,  that  logic  would  be  of  little  value  if  it  did  not,  among 
its  other  advantages,  exercise  the  understanding  in  doing  its  work 
neatly  and  correctly  with  these  imperfect  tools. 

After  this  preamble  it  is  time  to  proceed  to  our  enumeration.  We 
shall  commence  with  Feelings,  the  simplest  class  of  nameable  things  ; 
the  term  Feeling  being  of  course  understood   in  its  most  enlarged 

E 


34  NAMES    AND    PROPOSITIONS. 

I.  Feelings,  or  States  of  Consciousness. 

§  3.  A  Feeling  and  a  State  of  Consciousness  are,  in  the  language  of 
philosophy,  equivalent  expressions  :  everything  is  a  Feeling,  of  which 
the  mind  is  conscious  :  everything  which  it  feels,  or,  in  other  words, 
which  forms  a  part  of  its  own  sentient  existence.  In  popular  language 
Feeling  is  not  always  synonymous  with  State  of  Consciousness  ;  being 
often  taken  more  peculiarly  for  those  states  which  are  conceived  as 
belonging  to  the  sensitive,  or  to  the  emotional,  phasis  of  our  nature, 
and  sometimes,  with  a  still  naiTower  resti'iction,  to  the  emotional 
alone :  as  distinguished  from  what  are  conceived  as  belonging  to  the 
percipient,  or  intellectual  phasis.  But  this  is  an  admitted  departure 
from  correctness  of  language  ;  just  as,  by  a  popular  perversion  the 
exact  converse  of  this,  the  word  Mind  is  withdrawn  from  its  rightful 
generality  of  signification,  and  restricted  to  the  intellect.  The  still 
gi'eater  perversion  by  which  Feeling  is  sometimes  confined  not  only 
to  bodily  sensations,  but  to  the  sensations  of  a  single  sense,  that  of 
touch,  needs  not  be  more  particulai'ly  adverted  to. 

Feeling,  in  the  proper  sense  of  the  term,  is  a  genus,  of  which 
Sensation,  Emotion,  and  Thought,  are  subordinate  species.  Under  the 
word  Thought  is  here  to  be  included  whatever  we  are  internally  con- 
scious of  when  we  are  said  to  think  ;  from  the  consciousness  we  have 
when  we  think  of  a  red  color  wdthout  having  it  before  our  eyes,  to  the 
most  recondite  thoughts  of  a  philosopher  or  poet.  Be  it  remembered, 
however,  that  by  a  thought  is  to  be  understood  what  passes  in  the  mind 
itself,  and  not  any  object  external  to  the  mind,  which  the  person  is 
commonly  said  to  be  thinking  of  He  may  be  thinking  of  the  sun,  or 
of  God,  but  the  sun  and  God  are  not  thoughts ;  his  mental  image, 
however,  of  the  sun,  and  his  idea  of  God,  are  thoughts ;  states  of  his 
mind,  not  of  the  objects  themselves:  and  so  also' is  his  belief  of  the 
existence  of  the  sun,  or  of  God ;  or  his  disbelief,  if  the  case  be  so. 
Even  imaginary  objects,  (which  are  said  to  exist  only  in  our  ideas,) 
are  to  be  distinguished  from  our  ideas  of  therri.  I  may  think  of  a 
hobgoblin,  as  I  may  think  of  the  loaf  which  was  eaten  yesterday,  or 
of  the  flower  which  will  bloom  to-moiTow.  But  the  hobgoblin  which 
never  existed  is  not  the  same  thing  with  my  idea  of  a  hobgoblin,  any 
more  than  the  loaf  which  once  existed  is  the  same  thing  ^vith  my  idea 
of  a  loaf,  or  the  flower  which  does  not  yet  exist,  but  which  will  exist, 
is  the  same  with  my  idea  of  a-  flower.  They  are  all,  not  thoughts, 
but  objects  of  thought ;  thougli  at  the  present  time  all  the  objects  are 
alik.e  non-existent. 

In  like  manner,  a  Sensation  is  to  be  carefully  distinguished  from 
the  object  which  causes  the  sensation ;  our  sensation  of  white  from  a 
w'hite  object;  nor  is  it  less  to  be  distinguished  fi'om  the  attribute 
whiteness,  which  we  ascribe  to  the  object  in  consequence  of  its  exci- 
ting the  sensation.  Unfortunately  for  clearness  and  due  discrimination 
in  considering  these  subjects,  our  sensations  seldom  receive  separate 
names.  We  have  a  name  for  the  objects  which  produce  in  us  a 
certain  sensation ;  the  word  white.  We  have  a  name  for  the  quality 
in  those  objects,  to  which  we  ascribe  the  sensation;  the  name  tvJiite- 
ness.  But  when  we  speak  of  the  sensation  itself,  (as  we  have  not 
occasion  to  do  this  often  except  in  our  philosophical  speculations,) 
language,  which  adapts  itself  for  the  most  part  only  to  the  common 


rniNGS    DENOTED    BY    NAMES,  35 

uses  of  life,  has  provided  us  with  no  single-worded  or  immediate  desig- 
nation ;  we  nmst  employ  a  circumlocution,  and  say,  The  sensation  of 
white,  or  The  sensation  of  whiteness;  we  must  denominate  the  sensation 
either  from  the  oliject,  or  from  the  attribute,  by  which  it  is  excited. 
Yet  the  sensation,  though  it  never  docs,  might  very  well  be  conceioed  to 
exist,  without  anything  whatever  to  excite  it.  We  can  conceive  it  as 
arising  spontaneously  in  the  mind.  But  if  it  so  arose,  we  should  have 
no  name  to  denote  it  which  would  not  be  a  misnomer.  In  the  case  of 
our  sensations  of  hearing  we  are  better  provided ;  we  have  the  word 
Sound,  and  a  whole  vocabulary  of  words  to  denote  the  various  kinds 
of  sounds.  For  as  we  a,re  often  conscious  of  these  sensations  in  the 
absence  of  any  j^cfcejftible  object,  we  can  more  easily  conceive  having 
them  in  the  absence  of  any  object  whatever.  We  need  only  shut  our 
eyes  and  listen  to  music,  to  have  a  conception  of  a  universe  with 
nothing  in  it  except  sounds,  and  ourselves  hearing  them  ;  and  what  is 
easily  conceived  separately,  easily  obtains  a  separate  name.  But  in 
general  our  names  of  sensations  denote  indiscriminately  the  sensation 
and  the  attribute.  Thus,  color  stands  for  the  sensations  of  white,  red, 
&c.,  but  also  for  the  quality  in  the  colored  object.  We  talk  of  the 
colors  of  things  as  among  their  properties. 

§  4.  In  the  case  of  sensations,  another  distinction  has  also  to  be  kept 
in  view,  which  is  often  confounded,  and  never  without  mischievous 
consequences.  This  is,  the  distinction  between  the  sensation  itself, 
and  the  state  of  the  bodily  organs  which  precedes  the  sensation,  and 
which  constitutes  the  physical  agency  by  which  it  is  produced.  One 
of  the  sources  of  confusion  on  this  subject  is  the  division  commonly 
made  of  feelings  into  Bodily  and  Mental.  Philosophically  speaking, 
there  is  no  foundation  at  all  for  this  distinction :  even  sensations  are 
states  of  the  sentient  mind,  not  states  of  the  body,  as  distinguished 
from  it.  What  I  am  conscious  of  when  I  see  the  color  blue,  is  a  feel- 
ing of  blue  color,  which  is  one  thing ;  the  picture  on  my  retina,  or  the 
phenomenon  of  hitherto  mysterious  nature  which  takes  place  in  my 
optic  nerve  or  in  my  brain,  is  another  thing,  of  which  I  am  not  at  all 
conscious,  and  which  scientific  investigation  alone  could  have  apprised 
me  of.  These  are  states  of  my  body  ;  but  the  sensation  of  blue,  M'hich 
is  the  consequence  of  these  states  of  body,  is  not  a  state  of  body  ;  that 
which  perceives  and  is  conscious  is  called  Mind.  When  sensations 
are  called  bodily  feelings,  it  is  only  as  being  the  class  of  feelings  which 
are  immediately  occasioned  by  bodily  states ;  whereas  the  other  kinds 
of  feelings,  thoughts,  for  instance,  or  emotions,  are  immediately  excited 
not  by  anything  acting  upon  the  bodily  organs,  but  by  sensations,  or 
by  previous  thoughts.  This,  however,  is  a  distinction  not  in  our  feel- 
ings, but  in  the  agency  which  produces  our  feelings ;  all  of  them  when 
actually  pi-oduced  are  states  of  mind. 

Besides  the  affection  of  our  bodily  organs  from  without,  and  the 
sensation  thereby  produced  in  our  minds,  many  waiters  admit  a  third 
link  in  the  chain  of  phenomena,  which  they  term  a  Perception,  and 
which  consists  in  the  recognition  of  an  cxtei-nal  object  as  the  exciting 
cause  of  the  sensation.  This  perception,  they  say,  is  an  act  of  the 
mind,  proceeding  from  its  own  spontaneous  activity,  while  in  sensation 
the  mind  is  passive,  being  merely  acted  upon  by  the  outward  object. 
And  according  to  some  philosophers  it  is  by  an  act  of  the  mind,  similar 


OD  NAMES     AND    PROPOSITIONS. 

to  perception,  except  in  not  being  preceded  by  any  sensation,  that  we 
recognize  the  existence  of  God,  of  the  soul,  and  other  hyperphysical 
reahties. 

These  acts  of  perception,  whatever  be  the  conclusion  ultimately 
come  to  respecting  their  nature,  must,  I  conceive,  take  their  place 
among  the  varieties  of  feelings  or  states  of  mind.  In  so  classing  them, 
I  have  not  the  smallest  intention  of  declaring  or  insinuating  any  theory 
as  to  the  law  of  mind  in  which  these  mental  processes  may  be  supposed 
to  originate,  or  the  conditions  under  which  they  may  be  legitimate  or 
the  reverse.  Far  less  do  I  mean  (as  Mr.  Wliewell  seems  to  suppose 
must  be  meant  in  an  analogous  case*)  to  indicate  that  as  they  are 
^'■merely  states  of  mind,"  it  is  supei-fluous  to  inquire  into  their  distin- 
guishing peculiarities.  I  abstain  from  the  inquiry  as  irrelevant  to  the 
science  of  logic.  In  these  so-called  perceptions,  or  direct  recognitions 
by  the  mind  of  objects,  whether  physical  or  spiritual,  which  are  ex- 
ternal to  itself,  I  can  see  only  cases  of  belief;  but  of  behef  which 
claims  to  be  intuitive,  or  independent  of  external  evidence.  \Mien  a 
stone  lies  before  me,  I  am  conscious  of  certain  sensations  which  I 
receive  from  it;  but  when  I  say  that  these  sensations  come  to  me  from 
an  external  object  which  I  perceive,  the  meaning  of  these  words  is,  that 
receiving  the  sensations,  I  intuitively  helieve  that  an  external  cause  of 
those  sensations  exists.  The  laws  of  intuitive  belief,  and  the  conditions 
under  which  it  is  legitimate,  are  a  subject  which,  as  we  have  already 
so  often  remarked,  belongs  not  to  logic,  but  to  the  higher  or  transcen- 
dental branch  of  metaphysics. 

To  the  same  region  of  speculation  belongs  all  that  can  be  said  re- 
specting the  distinction  which  the  German  metaphysicians  and  their 
French  and  English  followers,  (among  whom  Mr.  Whewell  is  one  of 
the  inost  distinguished,)  so  elaborately  draw  between  the  acts  of  the 
mind  and  its  merely  passive  states ;  between  what  it  receives  from, 
and  what  it  gives  to,  the  crude  materials  of  its  experience.  I  am  aAvare 
that  with  reference  to  the  view  which  those  writers  take  of  the  primary 
elements  of  thought  and  knowledge,  this  distinction  is  fimdamental. 
But  for  our  purpose,  which  is  to  examine  not  the  original  groundwork 
of  our  knowledge,  but  how  we  come  by  that  portion  of  it  which  is  not 
original ;  the  difference  between  active  and  passive  states  of  mind  is  of 
secondary  importance.  For  us,  they  all  are  states  of  mind,  they  all 
are  feelings;  by  which,  let  it  be  said  once  more,  I  mean  to  imply 
nothing  of  passivity,  but  simply  that  they  are  psychological  facts,  facts 
which  take  place  in  the  mind,  and  to  be  carefully  distinguished  from 
the  external  or  physical  facts  with  which  they  may  be  connected,  either 
as  eifects  or  as  causes. 

§  5.  Among  active  states  of  mind',  there  is,  however,  one  species 
which  merits  particular  attention,  because  it  fonns  a  principal  part  of 
the  connotation  of  some  important  classes  of  names.  I  mean  volitions, 
or  acts  of  the  will.  Wlien  we  speak  of  sentient  beings  by  relative 
names,  a  large  portion  of  the  connotation  of  the  name  usually  consists 
of  the  actions  of  those  beings  ;  actions  past,  present,  and  possible  or  pro- 
bable future.  Take,  for  instance,  the  words  Sovereign  and  Subject. 
What  meaning  do  these  words  convey,  but  that  of  innumerable  actions, 

*  Philosophy  of  the  Inductive  Sciences,  vol.  i.  p.  40. 


THINGS    DENOTED    BY    NAMES.  37 

done  oi"  to  be  done  by  the  sovei-eign  and  the  subjects,  to  or  in  regai-d 
to  one  another  reciprocally  I  So  with  the  words  physician  and  patient, 
leader  and  follower,  master  and  servant.  In  many  cases  the  words 
also  connote  actions  which  would  be  done  under  certain  contingencies 
by  persons  other  than  those  denoted  :  as  the  words  mortgagor  and 
mortgagee,  obligor  and  obligee,  and  many  other  words  expressive  of 
legal  relation,  which  connote  what  a  court  of  justice  would  do  to 
enforce  the  legal  obligation  if  not  fuliilled.  There  arc  also  words 
which  connote  actions  previously  done  by  persons  other  than  those 
denoted  either  by  the  name  itself  or  by  its  correlative ;  as  the  word 
brother.  From  these  instances,  it  may  be  seen  how  large  a  portion  of 
the  connotation  of  names  consists  of  actions.  Now,  what  is  an  action  ] 
Not  one  thing,  but  a  series  of  two  things  :  the  state  of  mind  called  a 
volition,  followed  by  an  effect.  The  volition,  or  intention  to  produce 
the  effect,  is  oi^e  thing ;  the  effect  produced  in  consequence  of  the ' 
intention  is  another  thing ;  the  two  together  constitute  the  action.  I 
form  the  pui-pose  of  instantly  moving  my  arm ;  that  is  a  state  of  my 
mind ;  my  arm  (not  being  tied  nor  paralytic)  moves  in  obedience  to  my 
purpose  ;  that  is  a  physical  fact,  consequent  upon  a  state  of  mind. 
The  intention,  when  followed  by  the  fact,  or,  (if  we  prefer  the  expres- 
sion,) the  fact  when  preceded  and  caused  by  the  intention,  is  called  the 
action  of  moving  my  arm. 

§  6.  Of  the  first  leading  division'  of  nameable  things,  viz.,  Feelings 
or  States  of  Consciousness,  we  began  by  recognizing  three  sub-divi- 
sions :  Sensations,  Thoughts,  and  Emotions.  The  first  two  of  these 
we  have  illustrated  at  considerable  length ;  the  third.  Emotions,  not 
being  perplexed  by  similar  ambiguities,  does,  not  require  similar  exem- 
plification. And,  finally,  we  have  found  it  necessary  to  add  to  these 
three  a  fourth  species,  commonly  known  by  the  name  Volitions.  With- 
out seeking  to  prejudge  the  metaphysical  question  whether  any  mental 
state  or  phenomenon  can  be  found  which  is  not  included  in  one  or 
other  of  these  four  species,  it  appears  to  me  that  the  amount  of  illus- 
tration bestowed  upon  these  may,  so  far  as  we  are  concerned,  suffice 
for  the  whole  genus.  We  shall,  thei-efore,  proceed  to  the  two  remain- 
ing classes  of  nameable  things ;  all  things  which  are  external  to  the 
mind  being  considered  as  belonging  either  to  the  class  of  Substances 
or  to  that  of  Attributes. 

II.  Substances. 

Logicians  have  endeavored  to  define  Substance  and  Attribute ; 
but  their  definitions  are  not  so  much  attempts  to  dratw  a  distinction 
between  the  things  themselves,  as  instructions  what  difference  it  is 
customary  to  make  in  the  grammatical  structure  of  the  sentence, 
according  as  you  are  speaking  of  substances  or  of  attributes.  Such 
deSnitions  are  rather  lessons  of  English,  or  of  Greek,  Latin,  or  Ger- 
man, than  of  mental  philosophy.  An  attribute,  say  the  schocjl  logi- 
cians, must  be  the  attribute  o/"  something  :  color,  for  example,  nmst  be 
the  color  of  something  ;  goodness  must  be  the  goodness  of  something  : 
and  if  this  something  should  cease  to  exist,  or  should  cease  to  be  con- 
nected with  the  attribute,  the  existence  of  the  attribute  would  be  at 
an  end,     A  substance,  oft  the  contrary,  is  self-existent ;  in  speaking 


38  NAMES    AND    PROPOSITIONS. 

about  it,  we  need  not  put  o/"  after  its  name.  A  stone  is  not  the  stone 
of  any  thing ;  the  moon  is  not  the  moon  of  anything,  but  simply  the  moon. 
Unless,  indeed,  the  name  which  Ave  choose  to  give  to  the  substance 
be  a  relative  name  ;  if  so,  it  must  be  followed  either  by  oj",  or  by  some 
other  particle,  implying,  as  that  preposition  does,  a  reference  to  some- 
thing else  :  but  then  the  other  characteristic  peculiarity  of  an  attribute 
would  fail ;  the  something  might  be  destroyed,  and  the  substance  might 
still  subsist.  Thus,  a  father  must  be  the  father  of  something,  and  so 
far  resembles  an  attribute,  in  being  refen-ed  to  something  besides  him- 
self: if  there  were  no  child,  there  would  be  no  father :  but  this,  when 
we  look  into  the  matter,  only  means  that  we  should  not  call  him  father. 
The  man  called  father  might  still  exist,  though  the  child  were  annihi- 
lated ;  and  there  would  be  no  contradiction  in  supposing  him  to  exist, 
although  the  whole  universe  except  himself  were  destroyed.  But 
destroy  all  white  substances,  and  where  would  be  the  attribute  Avhite- 
ness  ?     Whiteness,  without  any  white  thing,  is  a  contradiction  in  terms. 

This  is  the  nearest  approach  to  a  solution  of  the  difficulty,  that  will 
be  found  in  the  common  treatises  on  logic.  It  will  scarcely  be  thought 
to  be  a  satisfactoiy  one.  If  an  attribute  is  distinguished  from  a  sub- 
stance by  being  the  attribute  of  something,  it  seems  highly  necessary 
to  understand  what  is  meant  by  of:  a  particle  which  needs  explanation 
too  much  itself  to  be  placed  in  front  of  the  explanation  of  anything 
else.  And  as  for  the  self-existence  of  substances,  it  is  very  true  that  a 
substance  may  be  conceived  to  exist  without  any  other  substance,  but 
so  also  may  an  attribute  without  any  other  atti'ibute :  and  we  can  ik) 
more  imagine  a  substance  without  attributes  than  we  can  imagine 
attributes  without  a  substance. 

Metaphysicians,  however,  have  probed  the  question  deeper,  and  given 
an  account  of  Substance  considerably  more  satisfactory  than  this.  Sub- 
stances are  usually  distinguished  as  Bodies  or  Minds.  Of  each  of  these, 
philosophers  have  at  length  provided  us  with  a  definition  which  seems 
unexceptionable. 

§  7.  A  Body,  according  to  the  received  doctrine  of  modem  metaphy- 
sicians, may  be  defined,  the  external  cause  to  which  we  ascribe  our 
sensations.  When  I  see  and  touch  a  piece  of  gold,  I  am  conscious  of 
a  sensation  of  yellow  color,  and  sensations  of  hardness  and  weight; 
and  by  varying  the  mode  of  handling,  I  may  add  to  these  sensations 
many  others  completely  distinct  from  them.  The  sensations  are  all  of 
which  I  am  directly  conscious ;  but  I  consider  them  as  produced  by 
something  not  only  existing  independently  of  my  will,  but  external  to 
my  bodily  organs  and  to  my  mind.  This  external  something  I  call  a 
Body. 

It  may  be  asked,  how  come  we  to  ascribe  our  sensations  to  any 
external  cause  %  and  is  there  sufficient  ground  for  so  ascribing  them  ? 
It  is  known,  that  there  are  metaphysicians  who  have  raised  a  contro- 
versy on  the  point ;  maintaining  the  paradox,  that  we  are  not  Avarranted 
in  refen-ing  our  sensations  to  a  cause,  such  as  we  understand  by  the 
word  Body,  or  to  any  cause  whatever,  unless,  indeed,  the  First  Cause. 
Though  we  have  no  concern  here  with  this  controversy,  nor  with  the 
metaphysical  niceties  on  which  it  turns,  one  of  the  best  ways  of  showing 
what  is  meant  by  Substance  is,  to  consider  what  position  it  is  necessary 
to  take  up,  in  order  to  maintain  its  existence  against  opponents. 


THINGS    DENOTED    BY    NAMES.  39 

It  is  certain,  then,  that  a  part  of  our  notion  of  a  body  consists  of  the 
notion  of  a  number  of  sensations  of  our  own,  or  of  otlier  sentient  beings, 
habitually  occurring  simultaneously.  My  conception  of  the  table  at 
which  I  am  writing  is  compounded  of  its  visible  form  and  size,  which 
are  complex  sensations  of  sight ;  its  tangible  form  and  size,  which  are 
complex  sensations  of  our  organ  of  touch  and  of  our  muscles ;  its 
weight,  which  is  also  a  sensation  of  touch  and  of  the  muscles  ;  its  color, 
wliich  is  a  sensation  of  sight ;  its  hardness,  which  is  a  sensation  of  the 
muscles ;  its  composition,  which  is  another  word  for  all  the  varieties  of 
sensation  which  we  receive  under  various  circumstances  from  the  wood 
of  which  it  is  made  ;  and  so  forth.  All  or  most  of  these  various  sensa- 
tions frequently  are,  and,  as  we  learn  by  experience,  always  might  be, 
experienced  simultaneously,  or  in  many  differefit  orders  of  succession, 
at  our  own  choice  :  and  hence,  the  thought  of  any  one  of  them  makes 
us  think  bl"  the  others,  and  the  whole  become  mentally  amalgamated  into 
one  mixed  state  of  consciousness,  which,  in  the  language  of  the  school 
of  Locke  and  Hai'tley,  is  termed  a  Complex  Idea. 

Now  there  ai-e  philosophers  who  have  argued  as  follows: — if  we 
take  an  orange,  and  conceive  it  to  be  divested  of  its  natural  color 
without  acquiring  any  new  one ;  to  lose  its  softness  without  becoming 
hard,  its  roundness  without  becoming  square  or  pentagonal,  or  of  any 
other  regular  or  irregular  figure  whatever ;  to  be  deprived  of  size,  of 
weight,  of  taste,  of  smell ;  to  lose  all  its  mechanical  and  all  its  chemical 
properties,  and  acquire  no  new  ones ;  to  become,  in  short,  invisible, 
intangible,  and  imperceptil)le  not  only  by  all  our  senses,  but  by  the 
senses  of  all  other  sentient  beings,  real  or  possible ;  nothing,  say  these 
philosophers,  would  remain.  For  of  what  nature,  they  ask,  could  be 
the  residuum "?  and  by  what  token  could  it  manifest  its  presence  1  To 
the  unreflecting  its  existence  seems  to  rest  on  the  evidence  of  the 
senses.  But  to  the  senses  nothing  is  apparent  except  the  sensations. 
We  know,  indeed,  that  these  sensations  are  bound  together  by  some 
law;  they  do  not  come  together  at  random,  but  according  to  a  systematic 
order,  which  is  part  of  the  order  established  in  the  universe.  When 
we  experience  one  of  these  sensations,  we  usually  experience  the  others 
also,  or  know  that  we  have  it  in  our  power  to  experience  them.  But 
a  fixed  law  of  connexion,  making  the  sensations  occur  together,  does 
not,  say  these  philosophers,  necessarily  require  what  is  called  a  sub- 
stratum to  support  them.  The  conception  of  a  substratum  is  but  one 
of  many  possible  forms  in  which  that  connexion  presents  itself  to  our 
imagination ;  a  mode  of,  as  it  were,  realizing  the  idea.  If  there  be 
such  a  substratum,  suppose  it  this  instant  annihilated  by  the  fiat  of 
Omnipotence,  and  let  the  sensations  continue  to  occur  in  the  same 
order,  and  how  would  the  substratum  be  missed  1  By  what  signs 
should  we  be  able  to  discover  that  its  existence  had  terminated  1  should 
we  not  have  a.s  much  reason  to  believe  that  it  still  existed,  as  we  now 
have  ]  and  if  we  should  not  then  be  wananted  in  believing  it,  how 
can  we  be  so  now?  A  body,  therefore,  according  to  these  meta- 
physicians, is  not  anything  intrinsically  different  from  the  sensations 
which  the  body  is  said  to  produce  in  us  ;  it  is,  in  short,  a  set  of  sensa- 
tions joined  together  according  to  a  fixed  law. 

These  ingenious  speculations  have  at  no  time  in  the  history  of  phi- 
losophy made  many  ])roselyt(!H ;  but  the  controversies  to  which  they 
have  given  rise,  and  the  doctrines  which  have  been  developed  in  the 


40  NAMES    AND    PROPOSITIONS. 

attempt  to  find  a  conclusive  answer  to  them,  have  been  fruitful  of  im- 
portant consequences  to  the  Science  of  Mind.  The  sensations  (it  was 
answered)  which  we  are  conscious  of,  and  which  we  receive  not  at 
random,  but  joined  together  in  a  certain  uniform  manner,  imply  not 
only  a  law  or  laws  of  connexion,  but  a  cause  external  to  our  mind, 
which  cause,  by  its  own  laws,  determines  the  laws  according  to  which 
the  sensations  are  connected  and  experienced.  The  schoolmen  used 
to  call  this  external  cause  by  the  name  we  have  already  employed,  a 
substratum  ;  and  its  attributes  (as  they  expressed  themselves)  inhered, 
literally  stucTi,  in  it.  To  this  substratum  the  name  Matter  is  usually 
given  in  philosophical  discussions.  It  was  soon,  however,  acknowl- 
edged by  all  who  reflected  on  the  subject,  that  the  existence  of  matter 
could  not  be  proved  by  extrinsic  evidence.  The  answer,  therefore, 
now  usually  made  to  Berkeley  and  his  followers  is,  that  the  belief  is 
intuitive ;  that  mankind,  in  all  ages,  have  felt  themselves  compelled,  by 
a  necessity  of  their  nature,  to  refer  their  sensations  to  an  external 
cause  :  that  even  those  who  deny  it  in  theory,  yield  to  the  necessity  in 
practice,  and  both  in  speech,  thought,  and  feeling,  do,  equally  with  the 
vulgar,  acknowledge  their  sensations  to  be  the  effects  of  something  ex- 
ternal to  them  :  this  knowledge,  therefore,  is  as  evidently  intuitive  as 
our  knowledge  of  our  sensations  themselves  is  intuitive.  And  here 
the  question  merges  in  the  fundamental  problem  of  transcendental 
metaphysics ;  to  which  science  we  leave  it. 

But  although  the  extreme  doctrine  of  the  Idealist  metaphysicians, 
that  objects  are  nothing  but  our  sensations  and  the  laws  which  connect 
them,  has  appeared  to  &\v  subsequent  thinkers  to  be  worthy  of  assent ; 
the  only  point  of  much  real  importance  is  one  upon  which  those  meta- 
physicians are  now  very  generally  considered  to  have  made  out  their 
case  :  viz.,  that  all  toe  know  of  objects  is  the  sensations  which  they  give 
us,  and  the  order  of  the  occurrence  of  those  sensations.  Kant  himself, 
on  this  point,  is  as  explicit  as  Berkeley  or  Locke.  However  firmly 
convinced  that  there  exists  an  universe  of  "  Things  in  themselves," 
totally  distinct  fi-om  the  universe  of  phenomena,  or  of  things  as  they 
appear  to  our  senses ;  and  even  when  bringing  into  use  the  technical 
expression  [Noumcnon)  to  denote  what  the  thing  is  in  itself,  as  con- 
trasted with  the  representation  of  it  in  our  minds ;  he  allows  that  this 
representation  (the  matter  of  which,  he  says,  consists  of  our  sensations, 
though  the  form  is  given  by  the  laws  of  the  mind  itself)  is  all  we  know 
of  the  object,  and  that  the  real  nature  of  the  Thing  is,  and  by  the  con- 
stitution of  our  faculties  ever  must  remain,  at  least  in  this  sublunary 
existence,  an  impenetrable  mystery  to  us.*      There  is  not  the  slightest 

*  I  have  much  pleasure  in  quoting  a  passage  in  which  this  doctrine  is  laid  down  in  the 
clearest  and  strongest  terms  by  M.  Cousm,  the  most  distinguished  living  teacher  of  German 
philosophy  out  of  Germany,  whose  authority  on  this  side  of  the  question  is  the  more  valu- 
able, as  his  philosophical  views  are  generally  those  of  the  post-Kantian  movement,  repre- 
sented by  Schelling  and  Hegel,  whose  tendencies  are  much  more  objective  and  ontological 
than  those  of  their  master,  Kant. 

"  Nous  savons  qu'il  existe  quelque  chose  hors  de  nous,  parceque  nous  ne  poavons  expli- 
quer  nos  perceptions  sans  les  rattacher  a  des  causes  distinctes  de  nous-m^mes  ;  nous  savons 
de  plus  que  ces  causes,  dont  nous  ne  connaissons  pas  d'ailleurs  I'essence,  produisent  les 
effets  les  plus  variables,  les  plus  divers,  et  m6me  les  plus  contraires,  selon  qu'elles  rencon- 
trent  telle  nature  ou  telle  disposition  du  sujet.  Mais  savons-nous  quelque  chose  de  plus? 
et  m6me,  vu  le  caractfere  indetermine  des  causes  que  nous  concevons  dans  les  corps,  y  a-t-il 
quelque  chose  de  plus  a  savoir?    Y  a-t-il  lieu  de  nous  enquerir  si  nous  percevons  les  choses 

telles  qu'elles  sont  ?    Non  evidemment Je  ne  dis  pas  que  le  probleme  est  insoluble,  ;9 

dis  qu'il  est  absurde  et  enfcrme  une  contradiction.     Nous  ne  savons  pas  ce  que  ces  causes  sont  en 

elles-m^mes,  et  la  raison  nous  defend  de  chercher  a  le  connaitre :  mais  il  est  bien  evident  ^ 


THINGS    DENOTED    BY   NAMES.  41 

reason  for  believing  that  what  wc  call  the  sensible  qualities  of  the  ob- 
ject are  a  type  of  anything  inherent  in  itself,  or  bear  any  affinity  to  its 
own  nature.  A  cause  does  not,  as  such,  resemble  its  effects ;  an  east 
wind  is  not  like  the  feeling  of  cold,  nor  is  heat  like  the  steam  of  boiling 
^vater  :  why  then  should  matter  resemble  our  sensations  1  Why  should 
the  inmost  nature  of  tire  or  water  resemble  the  impressions  made  by 
these  objects  upon  our  senses  ]*  And  if  not  on  the  principle  of  resem- 
blance, on  what  other  principle  can  the  manner  in  which  objects  affect 
us  through  our  senses  afford  us  any  insight  into  the  inherent  nature  of 
those  objects?  It  may  therefore  safely  be  laid  down  as  a  truth  both 
obvious  in  itself,  and  admitted  by  all  whom  it  is  at  present  necessary 
to  take  into  consideration,  that,  of  the  outward  world,  we  know  and 
can  know  absolutely  nothing,  except  the  sensations  which  we  ex- 
perience from  it.  Those,  however,  who  still  look  upon  Ontology  as 
a  possible  science,  and  think,  not  only  that  bodies  have  an  essen- 
tial constitution  of  their  own,  lying  deeper  than  our  perceptions,  but 
that  this  essence  or  nature  is  not  altogether  inaccessible  to  human  in- 
vestigation, cannot  expect  to  find  their  refutation  here.  The  question 
depends  upon  the  nature  and  laws  of  Intuitive  Knowledge,  and  is  not 
within  the  province  of  logic. 

§  S.  Body  having  now  been  defined  the  external  cause,  and  (accord- 
ing to  the  more  reasonable  opinion)  the  hidden  external  cause,  to  which 
we  refer  our  sensations ;  it  remains  to  frame  a  definition  of  Mind. 
Nor,  after  the  preceding  observations,  will  this  be  difficult.  For,  as 
our  concepti(m  of  a  body  is  that  of  an  unknown  exciting  cause  of 
sensations,  so  our  conception  of  a  mind  is  that  of  an  unknown  recipient, 
or  percipient,  of  them ;  and  not  of  them  alone,  but  of  all  our  other 
feelings.  As  body  is  the  mysterious  something  which  excites  the 
mind  to  feel,  so  mind  is  the  myterious  something  which  feels,  and 

priori,  qu'  elles  ne  sont  pas  en  elles-memes  ce  qu'ellcs  sont  par  rapport  a  nous,  puisque  la  presence 
du  sujet  modifie  necessairement  leur  action.  Suppriinez  tout  siijet  sentant,  il  est  certain 
que  ces  causes  agiraient  encore  puisqu'elles  contiriueraient  d'exister ;  mais  elles  agiraient 
autrement ;  elles  seraient  encore  des  qualites  et  des  proprietes,  mais  qui  ne  resembleraient 
a  rien  de  ce  que  nous  connaissons.  Le  feu  ne  manifesterait  plus  aucune  des  proprietes  que 
nous  lui  connaisons  :  que  serait-il '  C'est  ce  que  nous  ne  saurons  jamais.  C'est  (Tailleurs 
peut-itre  un  probleme  qui  ne  r'epugne  pas  seulement  a  la  nature  de  notre  esprit,  mais  a  I'essence 
mirne  des  choses.  Quand  m6me  en  effet-on  supprimcrait  par  la  pens^e  tous  les  sujetj  sentants, 
il  faudrait  encore  admettre  qye  nul  corps  ne  manifesterait  ses  proprietes  autrement  qu'en 
relation  avec  un  sujet  quelconque,  et  dans  ce  cas  ses  proprietes  ne  seraient  encore  que  relatives  : 
en  sorte  qu'il  me  parait  fort  raisonnable  d'admettre  que  les  proprietes  dcterminees  des  corps 
n'existent  pas  independamment  d'un  sujet  quelconque,  et  que  ciuand  on  demande  si  les  pro- 
prietes de  la  matiere  sont  telles  que  nous  les  percevons,  il  faudrait  voir  auparavant  si  elles 
sont  en  tant  que  determinees,  et  dans  quel  sens  il  est  vrai  de  dire  qu'elles  sont." — Cours 
d'Histoire  de  la  Philosophie  Morale  au  I8me  siecle,  8me  le<;on. 

*  An  attempt,  indeed,  has  been  made  by  Ileid  and  others,  to  establish  that,  although  some 
of  the  properties  we  ascribe  to  objects  exist  only  in  our  sensations,  others  exist  in  the  things 
themselves,  being  such  as  cannot  possibly  be  copies  of  any  impression  upon  the  senses  ;  and 
they  ask,  from  what  sensation  our  notions  of  extension  and  figure  have  been  derived  ?  The 
gauntlet  thrown  down  by  Reid  was  taken  up  by  Brown,  who,  applying  greater  powers  of 
analysis  than  had  previously  been  applied  to  the  notions  of  extension  and  figure,  showed 
clearly  what  are  the  sensations  from  which  those  notions  are  derived,  viz.,  sensations  oi 
touch,  combined  with  sensations  of  a  class  previously  too  little  adverted  to  by  metaphysi- 
cians, those  which  have  their  seat  in  our  muscular  frame.  Whoever  wishes  to  be  more 
particularly  acquainted  with  this  admirable  specimen  of  metaphysical  analysis  may  consult 
the  first  volume  of  Brown's  Lectures,  or  Mill's  Analysis  of  the  Mind. 

On  this  subject  also,  the  authority  of  M.  Cousin  may  be  quoted  in  favor  of  conclusions  re- 
jected by  some  of  the  most  eminent  thinkers  of  the  school  to  which  he  belongs.  M.  Cousin 
recognizes,  in  opposition  to  Reid,  the  esseutial  subjectivity  of  our  conceptions  of  the  primary 
qualities  of  matter,  as  extension,  solidity,  &c.,  equally  with  those  of  color,  heat,  and  the 
remainder  of  what  are  called  secondary  qualities.— Cowrs,  «t  supra,  9ine  leqon. 

F 


42  NAMES    AND    PROPOSITIONS. 

thinks.  It  is  unnecessary  to  give  in  the  case  of  mind,  as  we  gave  in 
the  case  of  matter,  a  particular  statement  of  the  skeptical  system  by 
which  its  existence  as  a  Thing  in  itself,  distinct  from  the  series  of  what 
are  denominated  its  states,  is  called  in  question.  But  it  is  necessary 
to  remark,  that  on  the  inmost  nature  of  the  thinking  principle,  as  well 
as  on  the  inmost  nature  of  matter,  we  are,  and  with  our  human  facul- 
ties must  always  remain,  entirely  in  the  dark.  All  which  we  are 
aware  of,  even  in  our  own  minds,  is  (in  the  words  of  Mr.  Mill)  a  cer- 
tain "thread  of  consciousness;"  a  series  of  feelings,  that  is,  of  sensa- 
tions, thoughts,  emotions,  and  volitions,  more  or  less  numerous  and 
complicated.  There  is  a  something  I  call  Myself,  or,  by  another  form 
of  expression,  my  mind,  which  I  consider  as  distinct  fi-om  these  sensa- 
tions, thoughts,  &c. ;  a  something  which  I  conceive  to  be  not  the 
thoughts,  but  the  being  that  has  the  thoughts,  and  which  I  can  conceive 
as  existing  for  ever  in  a  state  of  quiesence,  without  any  thoughts  at  all. 
But  what  this  being  is,  although  it  is  myself,  I  have  no  knowledge, 
further  than  the  series  of  its  states  of  consciousness.  As  bodies  mani- 
fest themselves  to  me  only  through  the  sensations  of  which  I  regard 
them  as  the  causes,  so  the  thinking  principle,  or  mind,  in  my  own 
nature,  makes  itself  known  to  me  only  by  the  feelings  of  which  it  is  con- 
scious. I  know  nothing  about  myself,  save  my  capacities  of  feeling  or 
being  conscious  (including,  of  course,  thinking  and  wilhng)  :  and  were 
I  to  learn  anything  new  concerning  myself,  I  cannot  with  my  present 
faculties  conceive  this  new  information  to  be  anything  else,  than  that  I 
have  some  additional  capacities,  before  unknown  to  me,  of  feeling, 
thinking,  or  willing. 

Thus,  then,  as  body  is  the  unsentient  cause  to  which  we  are  nat- 
urally prompted  to  refer  a  certain  portion  of  our  feelings,  so  mind  may 
be  described  as  the  sentient  stihject  (in  the  German  sense  of  the  term) 
of  all  feelings ;  that  which  has  or  feels  them.  But  of  the  nature  of 
either  body  or  mind,  liiither  than  the  feelings  which  the  former  excites, 
and  which  the  latter  experiences,  we  do  not,  according  to  the  best 
existing  doctrine,  know  anything ;  and  if  anything,  logic  has  nothing 
to  do  with  it,  or  with  the  manner  in  which  the  knowledge  is  acquired. 
With  this  result  we  may  conclude  this  portion  of  our  subject,  and  pass 
to  the  third  and  only  remaining  class  or  division  of  Nameable  Things. 

III.  Attributes  :  and,  first.  Qualities, 

§  9,  From  what  has  already  been  said  of  Substance,  what  is  to  be 
said  of  Attribute  is  easily  deducible.  For  if  we  know  not,  and  cannot 
know,  anything  of  bodies  but  the  sensations  which  they  excite  in  us  or 
others,  those  sensations  must  be  all  that  we  can,  at  bottom,  mean  by  their 
attributes ;  and  the  distinction  which  we  verbally  make  between  the 
properties  of  things  and  the  sensations  we  receive  from  them,  must 
originate  in  the  convenience  of  discourse  rather  than  in  the  nature  of 
what  is  denoted  by  the  terms. 

Attributes  are  usually  distributed  under  the  three  heads  of  Quality, 
Quantity,  and  Relation.  We  shall  come  to  the  two  latter  presently : 
in  the  first  place  we  shall  confine  ourselves  to  the  former. 

Let  us  take,  then,  as  our  example,  one  of  what  are  termed  the  sen- 
sible qualities  of  objects,  and  let  that  example  be  whiteness.  When 
we  ascribe  whiteness  to  any  substance,  as,  for  instance,  snow ;  when 


THINGS    DENOTED    BY    NAMES.  43 

we  say  that  snow  has  the  quality  whiteness,  what  do  we  really  assert  ] 
Simply,  that  when  snow  is  present  to  our  organs,  we  have  a  particular 
sensation,  which  we  ai'e  accustomed  to  call  the  sensation  of  white.  But 
how  do  I  know  that  snow  is  present  ?  Obviously  by  the  sensations 
which  I  derive  from  it,  and  not  otherwise.  I  hifer  that  the  object  is 
present,  because  it  gives  me  a  certain  assemblage  or  series  of  sensa- 
tions. And  when  I  ascribe  to  it  the  attribute  whiteness,  my  meaning 
is  only,  that,  of  the  sensations  composing  this  group  or  series,  that 
which  I  call  the  sensation  of  white  color  is  one. 

This  is  one  view  which  may  be  taken  of  the  subject.  But  there  is 
also  another,  and  a  different  view.  It  may  be  said,  that  it  is  true  we 
knaio  nothing  of  sensible  objects,  except  the  sensations  they  excite  in 
us ;  that  the  fact  of  our  receiving  from  snow  the  particular  sensation 
which  is  called  the  sensation  of  white,  is  the  ground  on  which  we  as- 
cribe to  that  substance  the  quality  whiteness  ;  the  sole  proof  of  its  pos- 
sessing that  quality.  But  because  one  thing  may  be  the  sole  evidence 
of  the  existence  of  another  thing,  it  does  not  follow  that  the  two  are 
one  and  the  same.  The  attribute  whiteness  (it  may  be  said)  is  not 
the  fact  of  our  receiving  the  sensation,  but  something  in  the  object  it- 
self; a ^.'O^i.Tr  inherent  in  it;  something  ?"«  virtue  of  which  the  object 
produces  the  sensation.  And  when  we  affirm  that  snow  possesses  the 
attribute  whiteness,  we  do  not  merely  assert  that  the  presence  of  snow 
produces  in  us  that  sensation,  buf  that  it  does  so  through,  and  by  rea- 
son of,  that  power  or  quality. 

For  the  puiposes  of  logic  it  is  not  of  material  importance  which  of 
these  views  we  adopt.  The  full  discussion  of  the  subject  behmgs  to 
the  department  of  inquiry  so  often  alluded  to  under  the  name  of  the 
higher  metaphysics  ;  but  it  may  be  said  here,  that  for  the  doctrine  of 
the  existence  of  a  peculiar  species  of  entities  called  qualities,  I  can  see 
no  foundation  except  in  a  tendency  of  the  human  mind  which  is  the 
cause  of  many  delusions.  I  mean,  the  disposition,  wherever  we  meet 
with  two  names  which  are  not  precisely  synonymous,  to  suppose  that 
they  must  be  the  names  of  two  different  things ;  whereas  in  reality 
they  may  be  names  of  the  same  thing  viewed  in  two  different  lights, 
which  is  as  much  as  to  say  under  different  suppositions  as  to  surround- 
ing circumstances.  Because  quality  and  sensation  cannot  be  put  in- 
discriminately one  for  the  other,  it  is  supposed  that  they  cannot  both 
signify  the  same  thing,  namely,  the  im])ression  or  feeling  wth  which 
we  are  affected  through  our  senses  by  the  presence  of  an  object :  al- 
though there  is  at  least  no  absurdity  in  supposing  that  this  identical 
impression  or  feeling  may  be  called  a  sensation  when  considered 
merely  in  itself,  and  a  quality  when  regarded  as  emanating  from  any 
one  of  the  numerous  objects,  the  presence  of  which  to  our  organs  ex- 
cites in  our  minds  that  among  various  other  sensations  or  feelings. 
And  if  this  be  admissible  as  a  supposition,  it  rests  with  those  who  con- 
tend for  an  entity  y;^/-  sc  called  a  quality,  to  show  that  their  opinion  is 
preferable,  or  is  anything  in  fact  but  a  lingering  remnant  of  the  scho- 
lastic doctrine  of  occult  causes ;  the  very  absurdity  which  Moliere  so 
happily  ridiculed  when  he  made  one  of  his  pedantic  physicians  account 
for  the  fact  that  "  I'opium  endormit,"  by  the  maxim  "  parcequ'il  a  une 
vertu  soporifique." 

It  is  evident  that  when  the  physician  stated  that  opium  had  "  une 
vertu  soporifique,"  he  did  not  account  for,  but  merely  asserted  over 


44  NAMES    AND    PROPOSITIONS. 

again,  the  fact  that  it  endormit.  In  like  manner,  when  we  say  that 
snow  is  white  because  it  has  the  quality  of  whiteness,  we  are  only  re- 
asserting in  more  technical  language  the  fact  that  it  excites  in  us  the 
sensation  of  white.  If  it  be  said  that  the  sensation  must  have  some 
cause,  I  answer,  its  cause  is  the  presence  of  the  object.  When  we 
have  asserted  that  as  often  as  the  object  is  present,  and  our  organs  in 
their  normal  state,  the  sensation  takes  place,  we  have  stated  all  that 
we  know  about  the  matter.  There  is  no  need,  after  assigning  a  cer- 
tain and  intelligible  cause,  to  suppose  an  occult  cause  besides,  for  the 
purpose  of  enabling  the  real  cause  to  produce  its  effect.  If  I  am 
asked,  why  does  the  presence  of  the  object  cause  this  sensation  in  me, 
I  cannot  tell :  I  can  only  say  that  such  -is  my  nature,  and  the  nature 
of  the  object :  the  constitution  of  things,  the  scheme  of  the  universe, 
\vill  have  it  so.  And  to  this  we  must  at  last  come,  even  after  interpo- 
lating the  imaginary  entity.  Whatever  number  of  links  the  chain  of 
causes  and  effects  may  .consist  of,  how  any  one  link  produces  the  one 
which  is  next  to  it  remains  equally  inexplicable  to  us.  It  is  as  easy 
to  comprehend  that  the  object  should  produce  the  sensation  directly 
and  at  once,  as  that  it  should  produce  the  same  sensation  by  the  aid 
of  something  else  called  \}(\q  power  of  producing  it. 

But  as  the  difficulties  which  may  be  felt  in  adopting  this  view  of 
the  subject  cannot  be  removed  without  discussions  transcending  the 
bounds  of  our  science,  I  content  myself  with  a  passing  indication,  and 
shall,  for  the  purposes  of  logic,  adopt  a  language  compatible  Avith  either 
view  of  the  nature  of  qualities.  I  shall  say, — what  at  least  admits  of 
no  dispute, — that  the  quality  of  whiteness  ascribed  to  the  object  snow, 
is  grounded  upon  its  exciting  in  us  the  sensation  of  white;  and,  adopt- 
ing the  language  already  used  by  the  school  logicians  in  the  case  of 
the  kind  of  attributes  called  Relations,  I  shall  term  the  sensation  of 
white  the  foundation  of  the  quality  whiteness.  For  logical  purposes 
the  sensation  is  the  only  essential  part  of  what  is  meant  by  the  word ; 
the  only  part  which  we  ever  can  be  concerned  in  proving.  When 
that  is  proved  the  quality  is  proved ;  if  an  object  excites  a  sensation, 
it  has,  of  course,  the  power  of  exciting  it. 

IV.    Relations. 

§  10.  The  qualities  of  a  body,  we  have  said,  are  the  attributes 
grounded  upon  the  sensations  which  the  presence  of  that  particular 
body  to  our  organs  excites  in  our  minds.  But  when  we  ascribe  to  any 
object  the  kind  of  attribute  called  a  Relation,  the  foundation  of  the 
attribute  must  be  something  in  which  other  objects  are  concerned 
besides  itself  and  the  percipient. 

As  there  may  with  propriety  be  said  to  be  a  relation  between  any 
two  things  to  which  two  cori'elative  names  are  or  may  be  given  ;  we 
may  expect  to  discover  what  constitutes  a  relation  in  general,  if  we 
enumerate  the  principal  cases  in  which  mankind  have  imposed  coiTel- 
ative  names,  and  observe  what  all  these  cases  have  in  common. 

What,  then,  is  the  character  which  is  possessed  in  common  by  states 
of  circumstances  so  heterogeneous  and  discordant  as  these  :  one  thing 
like  another ;  one  thing  unlike  another ;  one  thing  near  another ;  one 
thing  for  foam  another ;  one  thing  before,  afoer,  along  with  another ; 
one  thing  greater,  equal,  less,  than  another ;   one  thing  the  cause  of  an- 


THINGS    DENOTED    BY    NAMES.  45 

Other,  the  effect  of  another;  one  person  the  master,  servant,  child, 
parent,  husband,  wife,  sovereign,  subject,  attorney,  client,  of  another,  and 
so  on "? 

Omitting,  for  the  present,  the  case  of  Resemblance  (a  relation  which 
requires  to  be  considered  separately),  there  seems  to  bo  one  thing 
common  to  all  these  cases,  and  only  one;  that  in  each  of  them  there 
exists  or  occurs,  or  has  existed  or  occurred,  some^ac^  or  phenomenon, 
into  which  the  two  things  which  arc  said  to  be  related  to  each  other, 
both  enter  as  parties  concerned.  This  fact,  or  phenomenon,  is  what 
the  Aristotelian  logicians  (^lled  the  fundamcntum  relatjonis.  Thus  in 
the  relation  of  greater  and  less  between  two  magnitudes,  the  funda- 
mentum  relationis  is  the  fact  that  when  one  of  the  two  magnitudes  is 
applied  to  the  other,  it  more  than  covers  it ;  and  cannot,  by  any  new 
arrangement  of  parts,  be  entirely  brought  within  the  boundaries  of  the 
other  object.  In  the  relation  of  master  and  servant,  X\\g  fundamentum 
relationis  is  the  fact  that  the  one  has  undertaken,  or  is  compelled,  to 
perform  certain  senices  for  the  benefit,  and  at  the  bidding,  of  the  other. 
In  that  of  husband  and  wife,  \S\q  fundamentum  relationis  consists  of  the 
facts  that  the  parties  are  a  man  and  a  woman,  that  they  have  promised 
certain  things  with  certain  foniialities,  and  are  in  consequence  invested 
by  the  law  with  certain  rights,  and  subjected  to  certain  duties.  Exam- 
ples might  be  indefinitely  multiplied,  but  it  is  already  obvious  that 
whenever  two  things  are  said  to  be  related,  there  is  some  fact,  or  series 
of  facts,  into  which  they  both  enter ;  and  that  whenever  any  two  things 
are  involved  in  some  one  fact,  or  series  of  facts,  we  may  ascribe  to  those 
two  things  a  mutual  relation  grounded  on  the  fact.  Even  if  they  have 
nothing  in  common  but  what  is  common  to  all  things,  that  they  are 
members  of  the  universe,  we  call  that  a  relation,  and  denominate  them 
fellow-creatures,  fellow-beings,  or  fellow-denizens  of  the  universe.  But 
in  propoi'tion  as  the  fact  into  which  the  two  objects  enter  as  parts  is 
of  a  more  special  and  peculiar,  or  of  a  more  complicated  nature,  so 
also  is  the  relation  grounded  upon  it.  And  there  areas  many  con- 
ceivable relations  as  there  are  conceivable  kinds  of  fact  in  which  two 
things  can  be  jointly  concerned. 

In  the  same  manner,  therefore,  as  a  quality  is  an  attribute  gi'ounded 
upon  the  fact  that  a  certain  sensation  or  sensations  are  produced  in  us 
by  the  object,  so  an  attribute  gi'ounded  upon  some  fact  into  which  the 
object  enters  jointly  with  another  object,  is  a  relation  between  it  and 
that  other  object.  But  the  fact  in  tlie  latter  case  consists  of  the  very 
same  kind  of  elements  as  the  fact  in  the  former  :  namely,  states  of 
consciousness.  In  the  case  last  cited,  for  example,  the  relation  of 
husband  and  wife ;  the  fandamentum  relationis  consists  entirely  of 
thoughts,  emotions,  sensations,  and  volitions  (actual  or  contingent), 
either  of  the  parties  themselves  or  of  other  parties  concerned  in  the 
same  scries  of  transactions,  as,  for  instance,  the  intentions  which  would 
oe  formed  Ijy  a  judge  in  case  a  complaint  were  made  to  his  tribunal 
of  the  infi-ingement  of  any  of  the  legal  obligations  imposed  by  marriage; 
and  the  acts  which  the  judge  would  perform  in  consequence ;  acts 
being  (as  we  have  already  seen)  another  word  for  intentions  followed 
by  an  effect,  and  that  effect  (again)  being  but  another  word  fOr  sensa- 
tions, or  some  other  feelings,  occasioned  cither  to  oneself  or  to  some- 
body else.  There  is  no  part  whatever  of  what  the  names  expressive 
of  the  relation  imply,  that  is  not  resolvable  into  states  of  consciousness ; 


46  NAMES    AND    PROPOSITIOXS. 

outward  objects  being,  no  doubt,  supposed  throughout  as  the  causes 
by  which  some  of  those  states  of  consciousness  are  excited,  and  minds 
as  the  subjects  by  which  all  of  them  are  experienced,  but  neither  the 
external  objects  nor  the  minds  making  their  existence  known  other- 
wise than  by  the  states  of  consciousness. 

Cases  of  relation  are  not  always  so  complicated  as  that  to  which  we 
last  alluded.  The  simplest  of  all  cases  of  relation  are  those  expressed 
by  the  words  antecedent  and  consequent,  and  by  the  word  simultane- 
ous. If  we  say,  for  instance,  that  dawn  preceded  sunrise,  the  fact  in 
which  the  two  things,  dawn  and  sunrise,  wgre  jointly  concerned,  con- 
sisted only  of  the  two  things  themselves  :  no  third  tiling  entered  into 
the  fact  or  phenomenon  at  all ;  unless,  indeed,  we  choose  to  call  the 
succession  of  the  two  objects  a  third  thing;  but  their  succession  is  not 
something  added  to  the  things  themselves ;  it  is  something  involved  in 
them.  Dawn  and  sunrise  announce  themselves  to  our  consciousness 
by  two  successive  sensations  :  our  consciousness  of  the  succession  of 
these  sensations  is  not  a  third  sensation  or  feeling  added  to  them ;  we 
have  not  first  the  two  feelings,  and  then  a  feeling  of  their  succession. 
To  have  two  feelings  at  all,  implies  having  them  either  successively,  or 
else  simultaneously.  Sensations,  or  other  feelings,  being  given,  suc- 
cession and  simultaneousness  are  the  two  conditions,  to  the  alternative 
of  which  they  are  subjected  by  the  nature  of  our  faculties  ;  and  no  one 
has  been  able,  or  needs  expect,  to  analyze  the  matter  any  fmther. 

§  11.  In  a  somewhat  similar  position  are  two  other  sorts  of  relation. 
Likeness  and  Unlikeness.  I  have  two  sensations ;  we  will  suppose 
them  to  be  simple  ones ;  two  seUsEytions  of  Avhite,  or  one  sensation  of 
white  and  another  of  black.  I  call  the  first  two  sensations  li/ce  ;  the  last 
two  unlike.  ^Vliat  is  the  fact  or  phenomenon  constituting  the  funda- 
mentum  of  this  relation  ]  The  two  sensations  first,  and  then  what  we 
call  a  feeling  of  resemblance,  or  a  feeling  of  want  of  resemblance.  Let 
us  confine  ourselves  to  the  fonner  case.  Resemblance  is  evidently  a  feel- 
ing ;  a  state  of  the  consciousness  of  the  observer.  Wliether  the  feeling 
of  the  resemblance  of  the  two  colors  be  a  third  state  of  consciousness, 
which  I  have  after  having  the  two  sensations  of  color,  or  whether  (like 
the  feeling  of  their  succession)  it  is  involved  in  the  sensations  them- 
selves, may  be  a  matter  of  discussion.  But  in  either  ca.se,  these  feel- 
ings of  resemblance,  and  of  its  opposite,  dissimilarity,  are  parts  of  our 
nature ;  and  parts  so  far  from  being  capable  of  analysis,  that  they  are 
pre-supposed  in  every  attempt  to  analyze  any  of  our  other  feelings. 
Likeness  and  unlikeness,  therefore,  as  well  as  antecedence,  sequence, 
and  simultaneousness,  must  stand  apart  among  relations,  as  things  sui 
generis.  They  are  attributes  grounded  on  facts,  that  is,  on  states  of 
consciousness,  but  on  states  which  ai'e  peculiar,  unresolvable,  and 
inexplicable. 

But,  although  likeness  or  unlikeness  cannot  be  resolved  into  any- 
thing else,  complex  cases  of  likeness  or  unlikeness  can  be  I'esolved  into 
simpler  ones.  AVlien  we  say  of  two  things  whidi  consist  of  parts,  that 
they  are  like  one  another,  the  likeness  of  the  whole  does  admit  of  analy- 
sis; it  is  compounded  of  likenesses  between  the  various  parts  respec- 
tively. Of  how  vast  a  variety  of  resemblances  of  parts  must  that  re- 
semblance be  composed,  which  induces  us  to  say  that  a  portrait,  or  a 
landscape,  is  like  its  original.     If  one  person  mimics  another  with  any 


THINGS    DENOTED    BY    NAMES.  17 

success,  of  how  many  simple  likcucsst'S  must  the  general  or  complex 
likeness  be  compounded:  likeness  in  ii  suocessioji  of  bodily  i)ostures; 
likeness  in  voiee,  or  in  the  accents  and  intonations  of  the  voice;  like- 
ness in  the  choice  of  Avoids,  and  in  the  thoughts  or  sentiments  express- 
ed, whether  by  word,  countenance,  or  gesture. 

All  likeness,  and  unlikeness  of  which  wo  have  any  cognizance,  re- 
solve themselves  into  likeness  and  unlikeness  between  states  of  our 
own,  or  some  other  mind.  AVlien  we  say  that  one  body  is  like  another, 
(since  we  know  nothing  of  bodies  but  the  sensations  which  they  ex- 
cite,) we  mi>an  really  that  there  is  a  resemblance  between  the  sensa- 
tions excited  by  the  two  bodies,  or  between  some  portion  at  least  of 
those  sensations.  If  we  say  that  two  attributes  are  like  one  another, 
(since  we  know  nothing  of  attributes  except  the  sensations  or  states  of 
feeling  on  which  they  are  grounded,)  we  mean  really  tluiX  those  sensa- 
tions, or  states  of  feeling,  resemble  each  other.  We  may  also  say  that 
two  relations  are  alike.  The  fact  of  resemblance  between  relations  is 
sometimes  called  analogy,  forming  one  of  the  numerous  meanings  of 
that  word.  The  relation  in  which  Priam  stood  to  Hector,  namely,  that 
of  father  and  son,  resembles  the  relation  in  which  Philip  stood  to  Alex- 
ander ;  resembles  it  so  closely  that  they  are  called  the  same  relation. 
The  relation  in  which  Cromwell  stood  to  England  resembles  the  rela- 
tion in  which  Napoleon  stood  to  Franco,  thougli  not  so  closely  as  to  be 
called  the  same  relation.  The  meaning  in  both  these  instances  must 
be,  that  a  resemblance  existed  between  the  facts  which  constituted  the 
fundament um  relationis. 

This  resemblance  may  exist  in  all  conceivable  gi-adations,  from 
perfect  undistinguishableness  to  sometliing  very  slight  indeed.  When 
we  say,  that  a  thought  suggested  to  the  mind  of  a  person  of  genius  is 
like  a  seed  cast  into  the  gi-ound,  because  the  former  jiroduces  a  multi- 
tude of  other  thoughts,  and  the  latter  a  multitude  of  other  seeds,  this  is 
saying  that  between  the  relation  of  an  inventive  mind  to  a  thought 
contained  in  it,  and  the  relation  of  a  fertile  soil  to  a  seed  contained  in 
it,  there  exists  a  resemblance  :  the  real  resemblance  being  in,  the  two 
fundamcnta  relationis,  m  each  of  which  there  occurs  a  germ,  producing 
by  its  development  a  multitude  of  other  things  similar  to  itself.  And 
as,  whenever  two  objects  are  jointly  concerned  in  a  phenomenon,  this 
constitutes  a  relation  between  those  objects ;  so,  if  wo  suppose  a  second 
pair  of  objects  concerned  in  a  second  phenomenon,  the  slightest  resem- 
blance between  the  two  phenomena  is  sufficient  to  admit  of  its  being 
said  that  the  two  relations  resemble ;  provided,  of  coiu'se,  the  points 
of  resemblance  are  found  in  those  portions  of  the  two  phenomena 
respectively  which  are  connoted  by  the  relative  names. 

While  speaking  of  resemblance,  it  is  necessary  to  take  notice  of  an 
ambiguity  of  language,  against  which  scarcely  any  one  is  sufficiently 
on  his  guard.  Resemblance,  when  it  exists  in  the  highest  degree  of 
all,  amounting  to  undistinguishableness,  is  often  called  identity,  and 
the  two  similar  things  are  said  to  be  the  same.  I  say  often,  not  always ; 
for  we  do  not  say  that  two  visible  objects,  two  persons  for  instance, 
are  the  same,  because  they  are  so  much  alike  that  one  might  be  mis- 
taken for  the  other :  but  W£  constantly  use  this  mode  of  expression 
Avhen  speaking  of  fijelings ;  as  when  I  say  that  the  sight  of  any  object 
gives  me  the  same  sensation  or  emotion  to-day  that  it  did  yesterday,  or 
the  sa7ne  wliich  it  gives  to  some  other  person.     This  is  evidently  an 


48  NAMES    AND    PROPOSITIONS. 

incorrect  application  of  the  word  same ;  for  the  feehng  which  I  had 
yesterday  is  gone,  never  to  return  ;  what  I  have  to-day  is  another  feel- 
ing, exactly  like  the  fomier  perhaps,  but  distinct  from  it;  and  it  is 
evident  that  two  different  persons  cannot  be  experiencing  the  same 
feeling,  in  the  sense  in  which  we  say  that  they  are  both  sitting  at  the 
same  table.  By  a  similar  ambiguity  we  say,  that  two  persons  are  ill 
of  the  sa7}ie  disease ;  that  two  people  hold  the  same  office  ;  not  in  the 
sense  in  which  we  say  that  they  are  engaged  in  the  same  adventure, 
or  sailing  in  the  same  ship,  but  in  the  sense  that  they  fill  offices  exactly 
similar,  though,  perhaps,  in  distant  places.  Great  confusion  of  ideas 
is  often  produced,  and  many  fallacies  engendered,  in  otherwise  enlight- 
ened understandings,  by  not  being  sufficiently  alive  to.  the  fact  (in 
itself  not  always  to  be  avoided),  that  they  use  the  same  name  to  express 
ideas  so  different  as  those  of  identity  and  undistinguishable  resemblance. 
Among  modem  writers.  Archbishop  Whately  stands  almost  alone  in 
having  drawn  attention  to  this  distinction,  and  to  the  ambiguity  con- 
nected with  it.* 

Several  relations,  generally  called  by  other  names,  are  really  cases 
of  resemblance.  As  for  example,  equality  ;  which  is  but  another  word 
for  the  exact  resemblance  commonly  called  identity,  considered  as 
subsisting  between  things  in  respect  of  their  quantity.  And  this  ex- 
ample foniis  a  suitable  transition  to  the  third  and  last  of  the  three  heads, 
under  Avhich,  as  already  remarked.  Attributes  are  commonly  aiTanged. 

V.  Quantity. 

§  12.  Let  us  imagine  two  things,  between  which  there  is  no  differ- 
ence (that  is,  no  dissimilarity),  except  in  quantity  alone  :  for  instance, 
a  gallon  of  water,  and  more  than  a  gallon  of  water.  A  gallon  of  water, 
like  any  other  external  object,  makes  its  presence  known  to  us  by  a 
set  of  sensations  which  it  excites.  Ten  gallons  of  water  are  also  an 
external  object,  making  its  presence  known  to  us  in  a  similar  manner ; 
and  as  we  do  not  mistake  ten  gallons  of  water  for  a  gallon  of  water, 

*  "  Same  (as  well  as  '  One,' '  Identical,'  and  other  words  derived  from  them)  is  used  fre- 
quently in  a  sense  very  different  from  its  primary  one,  as  applicable  to  a  single  object,  being 
employed  to  denote  great  similarity.  When  several  objects  are  undistinguishably  alike,  one 
single  description  will  apply  equally  to  any  of  them  ;  and  thence  they  are  said  to  be  all  of  one 
and  the  same  nature,  appearance,  &c.,  as,  e.  g.,  when  we  say  '  this  house  is  built  of  the  same 
stone  with  such  another,'  we  only  mean  that  the  stones  are  undistinguishable  in  their  qual- 
ities; not  that  the  one  building  was  pulled  down,  and  the  other  constructed  with  the  ma- 
terials. Whereas  sameness,  in  the  primary  sense,  does  not  even  necessarily  imply  similar- 
ity ;  for  if  we  say  of  any  man,  that  he  is  greatly  altered  since  such  a  time,  we  understand, 
and,  indeed,  imply  by  the  very  expression,  that  he  is  one  person,  though  different  in  several 
qualities.  It  is  worth  observing,  also,  that  Same,  in  the  secondary-  sense,  admits,  accord- 
ing to  popular  usage,  of  degrees.  We  speak  of  two  things  being  tiearty  the  same,  but 
not  entirely  ;  personal  identity  does  not  admit  of  degrees.  Nothing,  perhaps,  has  contribu- 
ted more  to  the  error  of  Realism  than  inattention  to  this  ambiguity.  WTien  several  persons 
are  said  to  have  One  and  the  Sa?7ie  opinion,  thought,  or  idea,  men,  overlooking  the  true  simple 
statement  of  the  case,  which  is,  that  they  are  all  thinking  alike,  look  for  something  more 
abstruse  and  mystical,  and  imagine  there  must  be  some  Otie  Thing,  in  the  primary  sense, 
though  not  an  individual,  which  is  present  at  once  in  the  mind  of  each  of  these  persons  ; 
and  thence  readily  sprung  Plato's  Theory  of  Ideas,  each  of  which  was,  according  to  him, 
one  real,  eternal  object,  existing  entire  and  complete  in  each  of  the  individual  objects  that 
are  known  by  one  name.  .  .  .  The  Hindoos  of  the  present  day,  from  observing  the  similar 
symptoms  which  are  known  by  the  name  of  small-pox,  and  the  communication  of  the  like 
from  one  patient  to  another,  do  not  merely  call  it  (as  we  do)  one  disease,  but  believe  (if  we 
may  credit  the  accounts  given)  that  the  small-pox  is  a  goddess,  who  becomes  incarnate  in 
each  infected  patient."— l*^^c  ;  Appendix  on  Ambiguous  Terms,  p.  298.  My  references  to 
this  work  are  always  to  the  first  edition. 


THINGS    DENOTED   BY    NAMES.  49 

it  is  plain  that  tlie  set  of  sensations  is  more  or  less  difTcrent  in  the  two 
cases.  In  Uke  manner,  a  jrallon  of  water,  and  a  gallon  of  Madeira, 
are  two  external  objects,  making  their  presence  known  by  two  sets  of 
sensations,  which  sensations  are  different  from  each  other.  In  the  first 
case,  however,  we  say  that  the  difference  is  in  quantity ;  in  the  last 
there  is  a  difference  in  quality,  while  the  quantity  of  the  water  and  of 
the  Madeira  is  tlie  same.  What  is  the  rt;al  distinction  between  the 
two  cases  ?  It  is  not  the  province  oi'  Logic  to  analyze  it ;  nor  to  decide 
whether  it  is  susceptible  of  analysis  or  not.  For  us  the  following  con- 
siderations are  sufficient.  It  is  evident  that  the  sensations  I  receive 
from  the  gallon  of  water,  and  those  I  receive  from  the  gallon  of 
Madeira,  are  not  the  same,  that  is,  not  precisely  alike ;  neither  are 
they  altogether  unlike:  they  are  partly  similar,  partly  dissimilar;  and 
that  in  which  they  resemble  is  precisely  that  in  which  alone  the  gallon 
of  water  and  the  ten  gallons  do  not  resemble.  That  in  which  the 
gallon  of  water  and  the  gallon  of  wine  arc  like  each  other,  and  in 
which  the  gallon  and  the  ten  gallons  of  water  are  imlike  each  other,  is 
called  their  quantity.  This  likeness  and  unlikeness  I  do  not  pretend 
to  explain,  no  more  than  any  other  kind  of  likeness  or  unlikeness. 
But  my  object  is  to  show,  that  when  we  say  of  two  things  that  they 
differ  in  quantity,  just  as  when  we  say  that  they  differ  in  quality,  the 
assertion  is  always  grounded  upon  a  difference  in  the  sensations  which 
they  excite.  Nobody,  I  presume,  will  say,  that  to  see,  or  to  lift,  or  to 
drink,  ten  gallons  of  water,  does  not  include  in  itself  a  different  set  of 
sensations  from  those  of  seeing,  lifting,  or  drinking  one  gallon  ;  or  that 
to  see  or  handle  a  foot-rule,  and  to  see  or  handle  a  yard-measure  made 
exactly  like  it,  are  the  same  sensations.  I  do  not  undertake  to  say 
what  the  difference  in  the  sensations  is.  Everybody  knows,  and 
nobody  can  tell ;  no  more  than  any  one  could  tell  what  white  is,  to  a 
person  who  had  never  had  the  sensation.  But  the  difference,  so  far  as 
cognizable  by  our  faculties,  lies  in  the  sensations.  Whatever  difference 
we  say  there  is  in  the  things  themselves,  is,  in  this  as  in  all  other  cases, 
gromided,  and  gx-ounded  exclusively,  on  a  difference  in  the  sensations 
excited  by  them. 

VI.  Attributes  Concluded. 

§  13.  Thus,  then,  all  the  attrilnitcs  of  bodies  which  are  classed  under 
Quality  or  Quantity,  are  gi-oundcd  upon  the  sensations  which  we 
receive  from  those  bodies,  and  may  be  defined,  the  powers  which  the 
bodies  have  of  exciting  those  sensations.  And  the  same  general 
explanation  has  been  found  to  apply  to  most  of  the  attributes  usually 
classed  under  the  head  of  Relatiijn.  They,  too,  are  gi'ounded  upon 
some  fact  or  phenomenon  into  which  the  related  objects  enter  as  parts  ; 
that  fact  or  phenomenon  having  no  meaning  and  no  existence  to  us, 
except  the  series  of  sensations  or  other  states  of  consciousness  by 
which  it  makes  itself  known  :  and  the  relation  being  simply  the  power 
or  capacity  which  the  object  possesses,  of  taking  part  along  with  the 
correlated  object  in  the  production  of  that  series  of  sensations  or  states 
of  consciousness.  We  have  been  obliged,  indeed,  to  recognize  a 
somewhat  different  character  in  certain  peculiar  relations,  tiiose  of 
succession  and  simultaneity,  of  likeness  and  unlikeness.  These,  not 
being  grounded  on  any  fact  or  phenomenon  distinct  from  the  related 
G 


50  NAMES    AND    PROPOSITIONS. 

objects  themselves,  do  not  admit  of  the  same  kind  of  ginalysis.  But 
these  relations,  though  not,  like  other  relations,  grounded  upon  states 
of  consciousness,  are  themselves  states  of  consciousness  :  resemblance 
is  nothing  but  our  feeling  of  resemblance ;  succession  is  nothing  but 
our  feeling  of  succession.  Or,  if  this  be  disputed,  (and  we  cannot, 
without  transgressing  the  bounds  of  our  science,  discuss  it  here,)  at 
least  om-  knowledge  of  these  relations,  and  even  our  possibility  of 
knowledge,  is  confined  to  those  which  subsist  between  sensations  or 
other  states  of  consciousness  :  for,  though  we  ascribe  resemblance,  or 
succession,  or  simultaneity,  to  objects  and  to  attributes,  it  is  always  in 
^^rtue  of  resemblance  or  succession  or  simultaneity  in  the  sensations 
or  states  of  consciousness  which  those  objects  excite,  and  on  which 
those  attributes  are  grounded. 

§  14.  In  the  preceding  investigation  we  have,  for  the  sake  of  sim- 
plicity, considered  bodies  only,  and  omitted  minds.  But  what  we 
have  said  is  applicable,  mutatis  mutandis,  to  the  latter.  The  attributes 
of  minds,  as  well  as  those  of  bodies,  are  grounded  upon  states  of  feel- 
ing or  consciousness.  But  in  the  case  of  a  mind,  we  have  to  consider 
its  own  states,  as  well  as  those  which  it  produces  in  other  minds. 
Every  attribute  of  a  mind  consists  either  in  being  itself  affected  in  a 
certain  way,  or  affecting  other  minds  in  a  certain  way.  Considered 
in  itself,  we  can  predicate  nothing  of  it,  but  the  series  of  its  own  feel- 
ings. When  we  say  of  any  mind,  that  it  is  devout,  or  superstitious,  or 
meditative,  or  cheerful,  we  mean  that  the  ideas,  emotions,  or  volitions 
implied  in  those  words,  form  a  frequently  recurring  part  of  the  series 
of  feelings,  or  states  of  consciousness,  which  fill  up  the  sentient  exist- 
ence of  that  mind. 

In  addition,  however,  to  those  attributes  of  a  mind,  which  are 
grounded  upon  its  own  states  of  feeling,  attributes  may  also  be  ascribed 
to  it,  in  the  same  manner  as  to  a  body,  grounded  on  the  feelings  which 
it  excites  in  other  minds.  A  mind  does  not,  indeed,  like  a  body,  excite 
sensations,  but  it  inay  excite  thoughts  or  emotions.  The  most  important 
example  of  attributes  ascribed  on  this  ground  is,  the  employment  of 
terms  expressive  of  approbation  or  blame.  When,  for  example,  we 
say  of  any  character,  or  (in  other  words)  of  any  mind,  that  it  is 
admirable,  we  mean  that  the  contemplation  of  it  excites  the  sentiment 
of  admiration ;  and  indeed  somewhat  more,  for  the  word  implies  that 
we  not  only  feel  admiration,  but  approve  that  sentiment  in  ourselves. 
In  some  cases,  under  the  semblance  of  a  single  attribute,  two  are 
really  predicated :  one  of  them,  a  state  of  the  mind  itself;  the  other, 
a  state  with  which  other  minds  are  affected  by  thinking  of  it :  as  when 
we  say  of  any  one  that  he  is  generous.  The  word  generosity  ex- 
presses a  certain  state  of  mind,  but  being  a  term  of  praise,  it  also 
expresses  that  this  state  of  mind  excites  in  us  another  mental  state, 
called  approbation.  The  assertion  made,  therefore,  is  two-fold,  and 
of  the  following  purport :  Certain  feelings  form  habitually  a  part  of 
this  person's  sentient  existence  ;  and,  moreover,  the  idea  of  those  feel- 
ings of  his  excites  the  sentiment  of  approbation  in  ourselves  or  others. 

As  we  thus  ascribe  attributes  to  minds  on  the  ground  of  ideas  and 
emotions,  so  may  we  to  bodies  on  similar  grounds,  and  not  solely  on 
the  ground  of  sensations  :  as  in  speaking  of  the  beauty  of  a  statue  ; 
since  tliis  attribute  is  gi-ounded  upon  the  peculiar  feeling  of  pleasure 


THINGS    DENOTED    BY    NAMES.  51 

which  the  statue  prodiicos  in  our  minds,  and  whicli  is  not  a  sensation, 
but  an  emotion. 

VII.  General  Result. 

§  15.  Our  survey  of  the  varieties  of  Things  whicli  have  been,  or 
which  are  capable  of  being,  named — which  have  been,  or  are  capable 
of  being,  either  predicated  of  other  Things,  or  made  themselves  the 
subject  of  predications — is  now  complete. 

Our  enumeration  commenced  with  Feelings.  These  we  scrupulously 
<listinguished  from  the  objects  which  excite  them,  and  from  the  organs 
by  which  they  are,  or  may  be  supposed  to  be,  conveyed.  Feelings  are 
of  four  sorts  :  Sensations,  Thoughts,  Emotions,  and  Volitions.  What 
are  called  perceptions  are  merely  a  particular  case  of  Belief,  and  be- 
lief is  a  kind  of  thought.  Actions  are  merely  volitions  followed  by  an 
ctlect.  If  there  be  any  other  kind  of  mental  state  not  included  under 
these  subdivisions,  we  did  not  think  it  necessary  or  proper  in  this  place 
to  discuss  its  existence,  or  the  rank  which  ought  to  be  assigned  to  it. 

After  Feelings  we  proceeded  to  Substances.  These  are  either 
Bodies  or  Minds.  Without  entering  into  the  gi'ounds  of  the  meta- 
physical doubts  which  have  been  raised  conceniing  the  existence  of 
Matter  and  Mind  as  objective  realities,  we  stated  as  sufficient  for  us 
the  conclusion  in  which  the  best  thinkers  are  now  very  generally 
agreed,  that  all  we  can  know  of  Matter  is  the  sensations  which  it  gives 
us,  and  the  order  of  occuri-ence  of  those  sensations  ;  and  that  while  the 
substance  Body  is  the  unknown  cause  of  our  sensations,  the  substance 
Mind  is  the  unknown  percipient. 

The  only  remaining  class  of  Nameable  Things  is  Attributes ;  and 
these  are  of  three  kinds,  Quality,  Relation,  and  Quantity.  Qualities, 
like  substances,  are  knoAvn  to  us  no  otherwise  than  by  the  sensations 
or  other  states  of  consciousness  Avhich  they  excite ;  and  while,  in 
compliance  with  common  usage,  we  have  continued  to  speak  of  them 
as  a  distinct  class  of  Things,  we  showed  that  in  predicating  them  no 
one  means  to  predicate  anything  but  those  sensations  or  states  of 
consciousness,  on  which  they  may  bo  said  to  be  gi'ounded,  and  by 
which  alone  they  can  be  defined.  Relations,  except  the  simple  cases 
of  likeness  and  unlikeness,  succession  and  simultaneity,  are  similarly 
grounded  upon  some  fact,  or  phenomenon,  that  is,  upon  some  series  of 
sensations  or  states  of  consciousness,  more  or  less  complicated.  The 
third  species  of  attribute,  Quantity,  is  also  manifestly  grounded  upon 
something  in  our  sensations  or  states  of  feeling,  since  there  is  an  indu- 
bitable difference  in  the  sensations  excited  by  a  larger  and  a  smaller 
bulk,  or  by  a  greater  or  a  less  degi-ee  of  intensity,  in  any  object  of 
sense  or  of  consciousness.  All  attributes,  therefore,  are  to  us  nothing 
but  either  our  sensations  and  other  staWs  of  feeling,  or  something  inex- 
tricably involved  therein  ;  and  to  this  even  the  peculiar  and  simple 
relations  just  adverted  to  are  not  exceptions.  Those  peculiar  rela- 
tions, however,  are  so  important,  and,  even  if  they  might  in  strictness 
be  classed  among  our  states  of  consciousness,  are  so  fundamentally 
distinct  from  any  other  of  those  states,  that  it  would  be  a  vain  subtlety 
to  confound  them  under  that  common  head,  and  it  is  necessary  that 
they  should  be  classed  apart. 

As  the  result,  therefore,  of  our  analysis,  we  obtain  the  following  as 
an  enumeration  and  classification  of  all  Nameable  Things  : — 


52  NAMES    AND   PROPOSITIONS. 

1st.  Feelings,  or  States  of  Consciousness. 

Snd.   The  Minds  which  experience  those  feehngs. 

3rd.  The  Bodies,  or  external  objects,  which  excite  certain  of  those 
feelings,  together  with  the  powers  or  properties  whereby  they  excite 
them ;  these  last  being  included  rather  in  compliance  with  common 
opinion,  and  because  their  existence  is  taken  for  gi-anted  in  the  com- 
mon language  from  which  I  cannot  prudently  deviate,  than  because  the 
recognition  of  such  powers  or  properties  as  real  existences  appears  to 
me  warranted  by  a  sound  philosophy. 

4th,  and  last.  The  Successions  and  Co-existences,  the  Likenesses 
and  Unlikenesses,  between  feelings  or  states  of  consciousness.  Those 
relations,  when  considered  as  subsisting  between  other  things,  exist  in 
reality  only  between  the  states  of  consciousness  which  those  things,  if 
bodies,  excite,  if  minds,  either  excite  or  experience. 

This,  until  a  better  can  be  suggested,  must  serve  us  as  a  substitute 
for  the  abortive  Classification  of  Existences,  termed  the  Categories  of 
Aristotle.  The  practical  application  of  it  will  appear  when  we  com- 
mence the  inquiiy  into  the  Import  of  Propositions ;  in  other  words, 
when  we  inquire  what  it  is  which  the  mind  actually  believes,  when  it 
gives  what  is  called  its  assent  to  a  proposition. 

These  four  classes  comprising,  if  the  classification  be  correct,  all 
Nameable  Things,  these  or  some  of  them  must  of  covirse  compose  the 
signification  of  all  names;  and  of  these  or  some  of  them  is  made  up 
whatever  we  call  a  fact. 

For  distinction's  sake,  every  fact  which  is  solely  composed  of  feel- 
ings or  states  of  consciousness  considered  as  such,  is  often  called  a 
Psychological  or  Subjective  fact;  while  every  fact  which  is  composed, 
either  wholly  or  in  part,  of  something  different  from  these,  that  is,  of 
substances  and  attributes,  is  called  an  Objective  fact.  We  may  say, 
then,  that  every  objective  fact  is  gi'ounded  on  a  cori'esponding  subjec- 
tive one ;  and  has  no  meaning  to  us  (apart  from  the  subjective  fact 
which  corresponds  to  it),  except  as  a  name  for  the  unknown  and  in- 
scrutable process  by  which  that  subjective  or  psychological  fact  is 
brought  to  pass. 


CHAPTER  IV. 

OP  PROPOSITIONS, 

§  1.  In  treating  of  Propositions,  as  already  in  treating  of  Names, 
some  considerations  of  a  comparatively  elementary  nature  respecting 
their  form  and  varieties  must  be  premised,  before  entering  upon  that 
analysis  of  the  import  conveyed  by  tliem,  which  is  the  real  subject  and 
purpose  of  this  preliminary  book. 

A  proposition,  we  have  before  said,  is  a  portion  of  discourse  in  which 
a  predicate  is  affirmed  or  denied  of  a  subject.  A  predicate  and  a  sub- 
ject are  all  that  is  necessarily  required  to  make  vip  a  proposition :  but 
as  we  cannot  conclude  from  merely  seeing  two  names  put  together, 
that  they  are  a  predicate  and  a  subject,  that  is,  that  one  of  them  is  in- 
tended to  be  affirmed  or  denied  of  the  other,  it  is  necessary  that  there 


PROPOSITIONS.  53 

should  be  some  mode  or  form  of  indicating  that  such  is  the  intention ; 
some  sign  to  distinguish  a  predication  from  any  other  kind  of  discourse. 
This  is  sometimes  done  by  a  shght  alteration  of  one  of  the  words,  called 
an  hijlection ;  a,s  when  we  say,  Fire  burns ;  the  change  of  the  second 
word  fiom  burn  to  burns  showing  that  we  mean  to  affirm  the  predicate 
burn  of  the  subject  fire.  But  this  function  is  more  commonly  fulfilled 
by  the  word  is,  when  an  affii'mation  is  intended ;  is  not,  when  a  nega- 
tion; or  by  some  other  part  of  the  verb  to  be.  Tlie  word  which  thus 
serves  the  pui^jiose  of  a  sign  of  predication  is  called,  as  wc  formci-ly 
observed,  the  copula.  It  is  of  the  utmost  importance  that  there  should 
be  no  indistinctness  in  our  conception  of  the  nature  and  office  of  the 
copula;  for  confused  notions  respecting  it  are  among  the  causes  which 
have  spread  mysticism  over  the  field  of  logic,  and  perverted  its  specu- 
lations into  logomachies. 

It  is  apt  to  be  supposed  that  the  copula  is  much  more  than  a  mere 
sign  of  predication;  that  it  also  signifies  existence.  In  the  proposition, 
Socrates  is  just,  it  may  seem  to  be  implied  not  only  that  the  quality 
just  can  be  affirmed  of  Socrates,  but  moreover  that  Socrates  is,  that  is 
to  say,  exists.  This,  however,  only  shows  that  there  is  an  ambiguity  in 
the  word  is;  a  word  which  not  only  perfoiTns  the  function  of  the  copula 
in  affirmations,  but  has  also  a  meaning  of  its  own,  in  virtue  of  which  it 
may  itself  be  made  the  predicate  of  a  proposition.  That  the  employ- 
ment of  it  as  a  copula  does  not  necessarily  include  the  affirmation  of 
existence,  appears  fi'om  such  a  proposition  as  this,  A  centaur  is  a  fiction 
of  the  poets ;  where  it  cannot  possibly  be  implied  that  a  centaur  exists, 
since  the  proposition  itself  expressly  asserts  that  the  thing  has  no  real 
existence. 

Many  volumes  might  be  filled  with  the  frivolous  speculations  con- 
cerning the  nature  of  Being  (ro  bv,  ovaia,  Ens,  Entitas,  Essentia,  and 
the  like),  which  have  arisen  fi-om  overlooking  this  double  meaning  of 
the  words  to  be ;  from  supposing  that  when  it  signifies  to  exist,  and 
when  it  signifies  to  be  some  specified  thing,  as  to  be  a  man,  to  be  Soc- 
rates, to  be  seen  or  spoken  of,  to  be  a  phantom,  even  to  be  a  nonentity, 
it  must  still,  at  bottom,  answer  to  the  same  idea ;  and  that  a  meaning 
must  be  found  for  it  which  shall  suit  all  these  cases.  The  fog  which 
rose  from  this  naiTow  spot  diffused  itself  at  an  early  period  over  the 
whole  surface  of  metaphysics.  Yet  it  becomes  us  not  to  triumph  over 
the  gigantic  intellects  of  Plato  and  Aristotle  because  we  are  now  able 
to  presence  ourselves  from  many  ciTors  into  which  they,  perhaps  inev- 
itably, fell.  The  fire-teazer  of  a  modern  steam-engine  produces  by  his 
exertions  far  greater  effects  than  Milo  of  Crotono  could,  but  he  is  not 
therefore  a  stronger  man.  The  Greeks  seldom  knew  any  language 
but  their  own.  This  rendered  it  far  more  difficult  for  them  than  it  is 
for  us,  to  acquire  a  readiness  in  detecting  ambiguities.  One  of  the 
advantages  of  having  systematically  studied  a  plurality  of  languages, 
especially  of  those  languages  which  philosophers  have  used  as  the 
vehicle  of  their  thoughts,  is  the  practical  lesson  we  learn  respecting 
the  ambiguities  of  words,  by  finding  that  the  same  word  in  one  language 
corresponds,  on  different  occasions,  to  different  words  in  another. 
^Vhen  not  thus  exercised,  even  the  strongest  understandings  find  it 
difficult  to  believe  that  things  which  have  a  common  name,  have  not  in 
some  respect  or  other  a  common  nature ;  and  often  expend  much  labor 
not  only  unprofitably  but  mischievously  (as  was  frequently  done  by 


54  NAMES    AND    PROPOSITIONS. 

the  two  philosophers  just  mentioned),  on  vain  attempts  to  discover  in 
what  this  common  nature  consists.  But,  the  habit  once  formed,  intel- 
lects much  inferior  are  capable  of  detecting  even  ambiguities  which 
are  common  to  many  languages :  and  it  is  sui'prising  that  the  one  now 
under  consideration,  though  it  exists  in  the  modern  languages  as  well 
as  in  the  ancient,  should  have  been  overlooked  by  almost  all  authors. 
The  quantity  of  futile  speculation  which  had  been  caused  by  a  mis- 
apprehension of  the  nature  of  the  copula,  was  hinted  at  by  Hobbes ; 
but  Mr.  Mill*  was,  I  believe,  the  first  who  distinctly  characterized  the 
ambiguity,  and  pointed  out  how  many  errors  in  the  received  systems  of 
philosophy  it  has  had  to  answer  for.  It  has  indeed  misled  the  modems 
scarcely  less  than  the  ancients,  though  their  mistakes,  because  our  un- 
derstandings are  not  yet  so  completely  emancipated  from  their  influ- 
ence, do  not  appear  equally  ridiculous. 

We  shall  now  briefly  review  the  principal  distinctions  which  exist 
among  propositions,  and  the  technical  terms  most  commonly  in  use  to 
express  those  distinctions 

§  2.  A  proposition  being  a  portion  of  discourse  in  which  something 
is  affirmed  or  denied  of  something,  the  first  division  of  propositions  is 
into  affirmative  and  negative.  An  affirmative  proposition  is  that  in 
which  the  predicate  is  affirmed  of  the  subject ;  as  Caesar  is  dead.  A 
negative  proposition  is  that  in  which  the  predicate  is  denied  of  the 
subject;  as,  Caesar  is  not  dead.  The  copula  in  this  last  species  of 
proposition,  consists  of  the  words  is  not,  which  are  the  sign  of  negation ; 
is  being  the  sign  of  affirmation. 

Some  logicians,  among  whom  may  be  mentioned  Hobbes,  state  this 
distinction  differently ;  they  recognize  only  one  form  of  copula,  is,  and 
attach  the  negative  sign  to  the  predicate.  "  Caesar  is  dead,"  and 
"  Caesar  is  not  dead,"  according  to  these  writers,  are  propositions 
agreeing  not  in  the  subject  and  predicate,  but  in  the  subject  only. 
They  do  not  consider  "  dead,"  but  "  not  dead,"  to  be  the  predicate  of 
the  second  proposition,  and  they  accordingly  define  a  negative  proposi- 
tion to  be  one  in  which  the  predicate  is  a  negative  name.  The  point, 
though  not  of  much  practical  moment,  deserves  notice  as  an  example 
(not  unfi-equent  in  logic)  where  by  means  of  an  apparent  simplification, 
but  which  is  merely  verbal,  matters  are  made  more  complex  than  before. 
The  idea  of  these  writers  was,  that  they  could  get  rid  of  the  distinction 
between  affirming  and  denying,  by  treating  every  case  of  denying  as 
the  affirming  of  a  negative  name.  But  what  is  meant  by  a  negative 
name  %  A  name  expressive  of  the  absence  of  an  attribute.  So  that 
when  we  affirm  a  negative  name,  what  we  are  really  predicating  is 
absence  and  not  presence  :  we  are  asserting  not  that  anything  is,  but 
that  something  is  nM ;  to  express  which  operation  no  word  seems  so 
proper  as  the  word  denying.  The  fundamental  distinction  is  between 
a  fact  and  the  non-existence  of  that  fact ;  between  seeing  something  and 
not  seeing  it,  between  Caesar's  being  dead  and  his  not  being  dead ; 
and  if  this  were  a  merely  verbal  distinction,  the  generalization  which 
brings  both  within  the  same  form  of  assertion  would  be  a  real  simpli- 
fication :  the  distinction,  however,  being  real,  and  in  the  facts,  it  is 
the  generalization  confounding  the  distinction  that  is  merely  verbal; 

'^Analysis  of  the  Phenomena  of  the  Human  Mind^i.  126  et  seqq. 


PROPOSITIONS.  55 

and  tends  to  obsciire  the  subject,  by  treating  the  difference  between 
two  kinds  of  truths  as  if  it  were  only  a  difference  between  two  kinds  of 
words.  To  put  things  together,  and  to  put  tlieni  or  keep  them  asunder, 
will  remain  different  operations,  whatever  tricks  we  may  play  with 
language.  ♦*--.- 

remark  of  a  similar  nature  may  be  apjilied  to  most  of  those  dis- 
tinctions among  propositions  which  are  said  to  have  reference  to  their 
modality :  as,  difference  of  tense  or  time  ;  the  sun  did  rise,  the  sun  is 
rising,  the  sun  will  rise.  All  these  differences,  like  that  between  affinn- 
ation  and  negation,  might  be  glossed  over  by  considering  the  incident 
of  time  as  a  mere  modification  of  the  predicate  :  thus,  The  sun  is  an 
object  having  risen.  The  sun  is  an  uhjcct  now  rising,  The  sun  is  an  object 
to  rise  kcrea/fcr.  But  the  simplification  would  be  merely  verbal.  Past, 
present,  or  future,  do  not  constitute  so  many  different  kinds  of  rising ; 
they  are  designations  belonging  to  the  event  asserted,  to  the  sun's  rising 
to-day.  They  affect,  not  the  predicate,  but  the  applicability  of  the 
predicate  to  the  particular  subject.  That  which  w^e  affirm  to  be  past, 
present,  or  future,  is  not  what  the  subject  signifies,  nor  what  the  pre- 
dicate signifies,  but  specifically  and  expressly  what  the  predication 
signifies ;  what  is  expressed  only  by  the  proposition,  as  such,  and  not 
by  either  or  both  of  the  terms.  Therefore  the  circumstance  of  time  is 
properly  considered  as  attaching  to  the  copida,  which  is  the  sign  of 
predication,  and  not  to  the  predicate.  If  the  same  cannot  be  said  of 
such  modifications  as  these,  Caesar  may  be  dead ;  Csesar  is  perhajJS 
dead ;  It  is  j^ossihle  that  Ca?sar  is  dead  ;  it  is  only  because  these  fall 
altogether  under  another  head,  being  properly  assertions  not  of  any- 
thing relating  to  the  fact  itself,  but  of  the  state  of  our  own  mind  in 
regard  to  it;  namely,  our  absence  of  disbelief  of  it.  Thus,  "Caesar 
may  be  dead  "  means  "  I  am  not  sure  that  Caesar  is  alive." 

§  3.  The  next  division  of  propositions  is  into  Simple  and  Complex. 
A  simple  proposition  is  that  in  which  one  predicate  is  affirmed  or 
denied  of  one  subject.  A  complex  proposition  is  that  in  which  there 
is  more  than  one  predicate,  or  more  than  one  subject,  or  both. 

At  first  sight  this  decision  has  the  air  of  an  absurdity;  a  solemn  dis- 
tinction of  things  into  one  and  more  than  one  ;  as  if  we  were  to  divide 
horses  into  single  horses  and  teams  of  horses.  And  it  is  true  that  what 
is  called  a  complex  proposition  is  often  not  a  proposition  at  all,  but 
several  propositions,  held  together  by  a  conjunction.  Such,  for  exam- 
ple, is  this,  Caesar  is  dead,  and  Brutus  is  alive :  or  even  this,  Caesar  is 
dead,  hut  Brutus  is  alive.  There  are  here  two  distinct  assertions  ;  and 
we  might  as  well  call  a  street  a  complex  house,  as  these  two  propo- 
sitions a  complex  proposition.  It  is  true  that  the  syncategorematic 
words  and  and  but  have  a  meaning,  but  that  meaning  is  so  far  from 
making  the  two  propositions  one^  that  it  adds  a  third  j)roposition  to 
them.  All  particles  are  abbreviations,  and  generally  abbreviations  of 
propositions  ;  a  kind  of  short-hand,  whereby  that  which,  to  be  expressed 
fully,  would  have  required  a  proposition  or  a  series  of  propositions,  is 
suggested  to  the  mind  at  once.  Thus  the  words,  Caesar  is  dead  and 
Brutus  is  alive,  are  equivalent  to  these:  Caisar  is  dead;  Brutus  is 
alive ;  it  is  my  wish  that  the  two  preceding  propositions  should  be 
thought  of  together.  If  the  words  were,  Caesar  is  dead  hut  Bi-utus  is 
alive,  the  sense  would  be  equivalent  to  the  same  three  propositions 


56  NAMES    AND    PROPOSITIONS. 

together  with  a  fourth ;  "  between  the  two  preceding  propositions 
there  exists  a  contrast :"  viz.,  either  between  the  two  facts  themselves, 
or  between  the  feehngs  with  which  it  is  my  wish  that  they  should  be 
regarded. 

In  the  instances  cited<Hhe  two  propositions  are  kept  visibly  distinct, 
each  subject  having  its  separate  predicate,  and  each  predicate  its  sepa- 
rate subject.  For  brevity,  however,  and  to  avoid  repetition,  the  pro- 
positions are  often  blended  together :  as  in  this,  "  Peter  and  James 
preached  at  Jerusalem  and  in  Galilee,"  which  contains  four  propo- 
sitions :  Peter  preached  at  JeiTisalem,  Peter  preached  in  Galilee, 
James  preached  at  Jerusalem,  James  preached  in  Galilee. 

We  have  seen  that  when  the  two  or  more  propositions  comprising 
what  is  called  a  complex  proposition,  are  stated  absolutely,  and  not 
under  any  condition  or  proviso,  it  is  not  a  proposition  at  all,  but  a  plu- 
rality of  pi'opositions  ;  since  what  it  expresses  is  not  a  single  assertion, 
but  several  assertions,  which,  if  true  when  joined,  are  true  also  when 
separated.  But  there  is  a  kind  of  proposition  which,  although  it  con- 
tains a  plurality  of  subjects  and  of  predicates,  and  may  be  said  in  one 
sense  of  the  word  to  consist  of  several  propositions,  contains  but  one 
assertion  ;  and  its  truth  does  not  at  all  imply  that  of  the  simple  propo- 
sitions which  compose  it.  An  example  of  this  is,  when  the  simple 
propositions  are  connected  by  the  particle  or  ;  as,  either  A  is  B  or  C 
is  D  ;  or  by  the  particle  if;  as  A  is  B  //"C  is  D.  In  the  former  case, 
the  proposition  is  called  disjmictive,  in  the  latter  conditional :  the  name 
liypothctical  was  originally  common  to  both.  As  has  been  well 
remarked  by  Archbishop  Whately  and  others,  the  disjunctive  form  is 
resolvable  into  the  conditional;  every  disjunctive  proposition  being 
equivalent  to  two  or  more  conditional  ones.  "  Either  A  is  B  or  C  is 
D,"  means,  "  if  A  is  not  B,  C  is  D  ;  and  if  C  is  not  D,  A  is  B."  All 
hyjiothetical  propositions,  therefore,  though  (disjunctive  in  fonn,  are 
conditional  in  meaning ;  and  the  words  hypothetical  and  conditional 
may  be,  as  indeed  they  generally  are,  used  synonymously.  Propo- 
sitions in  which  the  assertion  is  not  dependent  upon  a  condition,  are 
said,  in  the  language  of  logicians,  to  be  categorical. 

An  hypothetical  proposition  is  not,  hke  the  pretended  complex  pro- 
positions which  we  previously  considered,  a  mere  aggi'egation  of 
simple  propositions.  The  simple  propositions  which  form  part  of  the 
words  in  which  it  is  couched,  form  no  part  of  the  assertion  which  it 
conveys.  When  we  say.  If  the  Koran  comes  fi-om  God,  Mahomet  is 
the  prophet  of  God,  we  do  not  intend  to  affirm  either  that  the  Koran 
does  come  from  God,  or  that  Mahomet  is  really  his  prophet.  Neither 
of  these  simple  propositions  may  be  true,  and  yet  the  truth  of  the 
hypothetical  proposition  may  be  indisputable.  "WHiat  is  asserted  is 
not  the  truth  of  either  of  the  propositions,  but  the  inferribility  of  the 
one  from  the  other.  Wliat,  then,  is  the  subject,  and  what  the  predi- 
cate of  the  hypothetical  proposition  %  "  The  Koran  "  is  not  the  subject 
of  it,  nor  is  "  Mahomet :"  for  nothing  is  affirmed  or  denied  either  of 
the  Koran  or  of  Mahomet.  The  real  subject  of  the  predication  is  the 
entire  proposition,  "  Mahomet  is  the  prophet  of  God;"  and  the  affirm- 
ation is,  that  this  is  a  legitimate  inference  from  the  proposition,  "  The 
Koran  comes  from  God."  The  subject  and  predicate,  therefore,  of  an 
hypothetical  proposition  are  names  of  propositions.  The  subject  is 
some  one  proposition.     The  predicate  is  a  general  relative   name 


PR0P0SITI0N3.  57 

applicable  to  propositions ;  of  this  foma — "  an  inference  from  so  anJ 
so."  A  fresh  instance  is  hero  aflordod  of  the  remark,  tliat  all  particles 
are  abbre\'iations ;  since  "Z/"  A  is  J3,  C  is  D,"  is  found  to  be  an  abbre- 
\-iation  of  the  following :  "  Tlie  proposition  C  is  D,  is  a  legitimate 
inference  from  the  proposition  A  is  B." 

The  distinction,  therefore,  between  hypothetical  and  categorical 
propositions  is  not  so  great  as  it  at  first  appears.  In  the  conditional, 
as  well  as  in  the  categorical  form,  one  predicate  is  affirmed  of  one  sub- 
ject, and  no  more  :  but  a  conditional  propositicm  is  a  proposition  con- 
cerning a  proposition  ;  the  subject  of  the  assertion  is  itself  an  assertion. 
Nor  is  this  a  property  peculiar  to  hypothetical  propositions.  There 
are  other  classes  of  assertions  concerning  propositions.  Like  other 
things,  a  proposition  has  attributes  which  may  be  predicated  of  it. 
The  attribute  predicated  of  it  in  an  hypothetical  propasition,  is  that 
of  being  an  inference  from  a  certain  other  proposition.  But  this  is 
only  one  of  many  attributes  that  might  be  predicated.  We  may  say, 
That  the  wliole  is  gi-eater  than  its  part,  is  an  axiom  in  mathematics : 
That  the  Holy  Ghost  proceeds  from  the  Father  alone,  is  a  tenet  of 
the  Greek  Church  :  The  doctrine  of  the  divine  right  of  kings  was  re- 
nounced by  Parliament  at  the  Revolution  :  The  infallibility  of  the  Pope 
has  no  countenance  from  Scripture.  In  all  these  cases  the  subject  of 
the  predication  is  an  entire  proposition.  That  which  these  difterent 
predicates  are  affiiTned  of,  is  the  proposition,  "  the  whole  is  greater 
than  its  part;"  the  proposition,  "the  Holy  Ghost  proceeds  fi'om  the 
Father  alone:"  the  proposition,  "  kings  have  a  divine  right;"  tJie  prop- 
osition, "  the  Pope  is  infallible." 

Seeing,  then,  that  there  is  much  less  difference  between  hypotheti- 
cal propositions  and  any  others,  than  one  might  be  led  to  imagine 
fi-om  their  form,  we  should  be  at  a  loss  to  account  for  the  conspicuous 
position  which  they  have  been  selected  to  fill  in  treatises  on  Logic,  if 
we  did  not  remember  that  what  they  predicate  of  a  proposition,  namely, 
its  being  an  inference  fi'om  something  else,  is  precisely  that  one  of  its 
attributes  with  which  most  of  all  a  logician  is  concerned. 

§  4.  The  next  of  the  common  divisions  of  Pi-opositions  is  into  Uni- 
versal, Particular,  Indefinite,  and  Singular  :  a  distinction  founded 
upon  the  degree  of  generality  in  which  the  name,  which  is  the  subject 
of  the  proposition,  is  to  be  understood.     The  following  are  examples: 

All  men  are  mortal —  Universal. 

So)ne  men  are  moital —  Particular. 

Man  is  mortal —  Indefinite. 

Julius  Ccesar  is  mortal —  Singular. 

The  proposition  is  Singular,  when  the  subject  is  an  individual  name. 
The  individual  name  needs  not  be  a  proper  name.  "  The  Founder  of 
Christianity  was  crucifieH,"  is  as  much  a  singular  proposition  as 
"  Christ  was  crucified." 

AVTien  the  name,  which  is  the  subject  of  the  proposition,  is  a  general 
name,  we  may  intend  to  affiiTn  or  deny  the  predicate,  either  of  all  the 
things  that  the  subject  denotes,  or  only  of  some.  When  the  predicate 
is  affirmed  or  denied  of  all  and  each  of  the  things  denoted  by  the  sub- 
ject, the  proposition  is  universal;  when  of  some  non-assignable  portion 
of  them  only,  it  is  particular.  Thus,  All  men  are  mortal;  l^^vcry  man 
is  mortal ;  are  universal  propositions.  No  man  is  immortal,  is  also  an 
H 


58  NAMES    AND    PROPOSITIONS. 

universal  proposition,  since  the  predicate,  immortal,  is  denied  of  each 
and  every  individual  denoted  by  the  term  man ;  the  negative  propo- 
sition being  exactly  equivalent  to  the  following,  Evei-y  man  is  not-im- 
mortal. But  "  some  men  are  wise,"  "  some  men  are  not  wise,"  are 
particular  propositions  ;  the  predicate  wise  being  in  the  one  case 
affirmed  and  in  the  other  denied  not  of  each  and  every  individual  de- 
noted by  the  term  man,  but  only  of  each  and  every  one  of  some  por- 
tion of  those  individuals,  without  specifying  what  portion  ;  for  if  this 
were  specified,  the  proposition  would  be  changed  either  into  a  singu- 
lar proposition,  or  into  an  universal  proposition  with  a  different  subject; 
as,  for  instance,  "  all  instructed  men  are  wise."  There  are  other  forms 
of  particular  propositions:  as,  "ikZos^men  are  incapable  of  self-govem- 
ment :"  it  being  immaterial  how  large  a  portion  of  the  subject  the 
predicate  is  asserted  of,  as  long  as  it  is  left  uncertain  how  that  portion 
is,  to  be  distinguished  from  the  rest. 

When  the  form  of  the  expression  does  not  clearly  show  whether  the 
general  name  which  is  the  subject  of  the  proposition  is  meant  to  stand 
for  all  the  individuals  denoted  by  it,  or  only  for  some  of  them,  the 
proposition  is  commonly  called  Indefinite  ;  but  this,  as  Archbishop 
Wliately  obsei-ves,  is  a  solecism,  of  the  same  nature  as  that  committed 
by  some  gi-ammarians  when  in  their  list  of  genders  they  enumerate  the 
doubtful  gender.  The  speaker  must  mean  to  assert  the  proposition 
either  as  an  universal  or  as  a  particular  proposition,  though  he  has 
failed  to  declare  which :  and  it  often  happens  that  though  the  words 
do  not  show  which  of  the  two  he  intends,  the  context,  or  the  custom 
of  speech,  supplies  the  deficiency.  Thus,  when  it  is  affirmed  that 
"  Man  is  mortal,"  nobody  doubts  that  the  assertion  is  intended  of  all 
human  beings,  and  the  word  indicative  of  universality  is  commonly 
omitted  only  because  the  meaning  is  evident  without  it. 

When  a  general  name  stands  for  each  and  every  individual  which  it 
is  a  name  of,  or  in  other  words,  which  it  denotes,  it  is  said  by  logicians 
to  be  distribzited,  or  taken  distributively.  Thus,  in  the  proposition, 
All  men  are  mortal,  the  subject,  Man,  is  distributed,  because  mortality 
is  affirmed  of  each  and  every  man.  The  predicate  Mortal,  is  not  dis- 
tributed, because  the  only  mortals  who  are  spoken  of  in  the  proposition 
are  those  who  happen  to  be  men ;  while  the  word  may,  for  aught  that 
appears  (and  in  fact  does),  comprehend  under  it  an  indefinite  number 
of  objects  besides  men.  In  the  proposition,  Some  men  are  mortal, 
both  the  predicate  and  the  subject  are  undistributed.  In  the  following, 
No  men  are  perfect,  both  the  predicate  and  subject  are  distributed. 
Not  only  is  the  attribute  perfection  denied  of  the  entire  class  Man, 
but  that  class  is  severed  and  cast  out  from  the  whole  of  the  class  Per- 
fect, and  not  merely  from  some  part  of  that  class. 

This  phraseology,  which  is  of  great  service  in  stating  and  demon- 
strating the  rules  of  the  syllogism,  enables  us  to  express  very  con- 
cisely the  definitions  of  an  universal  and  a  particular  proposition.  An 
universal  proposition  is  that  of  which  the  subject  is  distributed ;  a  par- 
ticular proposition  is  that  of  which  the  subject  is  vmdistributed. 

There  are  many  more  distinctions  among  propositions  than  those  we 
have  here  stated,  some  of  them  of  considerable  importance.  But,  for 
explaining  and  illustrating  these,  more  suitable  opportunities  will  occiir 
in  the  sequel. 


IMPORT    OF    PROrOSITIONS.  59 

CHAPTER  V. 

OF  THE  LMPORT  OF  PROPOSITIONS. 

§  1.  An  inquiry  into  tlie  nature  of  Propositions  must  have  one  of 
two  objects  :  to  analyze  the  state  of  mind  called  Belief,  or  to  analyze 
what  is  believed.  AH  language  recognizes  a  difference  between  a  doc- 
trine or  opinion,  and  the  act  of  entertaining  the  opinion ;  between  as- 
sent, and  what  is  assented  to. 

Logic,  according  to  the  conception  here  formed  of  it,  has  no  con- 
cern with  the  nature  of  the  act  of  judging  or  bcheving;  the  considera- 
tion of  that  act,  as  a  phenomenon  of  the  mind,  belongs  to  another 
science.  Philosophers,  however,  from  Descartes  downwards,  and  es- 
pecially from  the  era  of  Leibnitz  and  Locke,  have  by  no  means  ob- 
served this  distinction ;  and  would  have  treated  with  gi-eat  disrespect 
any  attempt  to  analyze  the  import  of  Propositions,  unless  founded 
upon  an  analysis  of  the  act  of  Judgment.  A  Proposition,  they  would 
have  said,  is  but  the  expression  in  words  of  a  Judgment.  The  thingr 
expressed,  not  the  mere  verbal  expression,  is  the  important  matter. 
When  the  mind  assents  to  a  proposition,  it  judges.  Let  us  find  out 
what  the  mind  does  when  it  judges,  and  we  shall  know  what  proposi- 
tions mean,  and  not  otherwise. 

Conformably  to  these  views,  almost  all  the  writers  on  Logic  in  the 
last  two  centuries,  whether  English,  Gennan,  or  French,  have  made 
their  theory  of  Propositions,  from  one  end  to  the  other,  a  tlieory  ot 
Judgments.  They  considered  a  Proposition,  or  a  Judgment,  for  they 
used  the  two  words  indiscriminately,  to  consist  in  affirming  or  denying^ 
one  idea  of  another.  To  judge,  was  to  put  two  ideas  together,  or  to 
bring  one  idea  under  another,  or  to  compare  tAVO  ideas,  or  to  perceive 
the  agreement  or  disagi-eement  between  two  ideas :  and  the  whole 
doctrine  of  Propositions,  together  with  the  theory  of  Ileasoning  (always 
necessarily  founded  upon  the  theory  of  Propositions),  was  stated  as  if 
Ideas,  or  Conceptions,  or  whatever  other  term  the  ^vriter  preferred  as 
a  name  for  mental  representations  generally,  constituted  essentially  the 
subject  matter  and  substance  of  those  operations. 

It  is,  of  course,  true,  that  in  any  case  of  judgment,  as  for  instance 
when  wo  judge  that  gold  is  yellow,  a  process  takes  place  in  our  minds 
of  which  some  one  or  other  of  these  theories  is  a  partially  coiTect  ac- 
count. We  must  have  the  idea  of  gold  and  the  idea  of  yellow,  and 
these  two  ideas  must  be  brought  together  in  our  mind.  But  in  the 
first  place,  it  is  evident  that  this  is  only  a  part  of  what  takes  place  ;  for 
we  may  put  two  ideas  together  without  any  act  of  belief ;  as  when  we 
merely  imagine  something,  such  as  a  golden  mountain ;  or  when  we 
actually  disbelieve :  for  in  order  even  to  disbelieve  that  Mahomet  was 
an  apostle  of  God,  we  must  put  the  idea  of  Mahomet  and  that  of  an 
apostle  of  God  together.  To  determine  what  it  is  that  happens  in  the 
case  of  assent  or  dissent  besides  putting  two  ideas  together,  is  one  of 
the  most  intricate  of  metaphysical  problems.  But  whatever  the  solu- 
tion may  be,  we  may  venture  to  assert  that  it  can  have  nothing  what 
ever  to  do  with  the  import  of  propositions  ;  for  this  reason,  that  propo- 
sitions (except  where  the  mind  itself  is  the  subject  treated  of)  are  not 
assertions  respecting  our  ideas  of  things,  but  assertions  respecting  the 


60  NAMES   AND   PROPOSITIONS. 

things  tliemselves.  In  order  to  believe  that  gold  is  yellow,  I  must, 
indeed,  have  the  idea  of  gold  and  the  idea  of  yellow^,  and  something 
having  reference  to  those  ideas  must  take  place  in  my  mind ;  but  my 
belief  has  not  reference  to  the  ideas,  it  has  reference  to  the  things. 
What  I  believe  is  a  fact  relating  to  the  outward  thing,  gold,  and  to  the 
impression  made  by  that  outward  thing  upon  the  human  organs;  not 
a  fact  relating  to  my  conception  of  gold,  which  would  be  a  fact  in  my 
mental  history,  not  a  fact  of  external  nature.  It  is  true,  that  in  order  to 
believe  this  fact  in  external  nature,  another  fact  must  take  place  in  my 
mind,  a  process  must  be  performed  upon  my  ideas;  but  so  it  must  in 
everything  else  that  I  do.  I  cannot  dig  the  ground  unless  I  have  the 
idea  of  the  ground,  and  of  a  spade,  and  of  all  the  other  things  I  am 
operating  upon,  and  unless  I  put  those  ideas  together.  But  it  would 
be  a  very  ridiculous  description  of  digging  the  gi'ound  to  say  that  it  is 
putting  one  idea  into  another.  Digging  is  an  operation  which  is  per- 
formed upon  the  things  themselves,  although  it  cannot  be  performed 
unless  I  have  in  my  mind  the  ideas  of  them.  And  so  in  like  manner, 
believing  is  an  act  which  has  for  its  subject  the  facts  themselves, 
although  a  previous  mental  conception  of  the  facts  is  an  indispensable 
condition.  When  I  say  that  fire  causes  heat,  do  I  mean  that  my  idea 
of  fire  causes  my  idea  of  heat]  No:  I  mean  that  the  natural  pheno- 
menon, fire,  causes  the  natural  phenomenon,  heat.  When  I  mean  to 
assert  anything  respecting  the  ideas,  I  give  them  their  proper  name,  I 
call  them  ideas  :  as  when  I  say,  that  a  child's  idea  of  a  battle  is  unlike 
the  reality,  or  that  the  ideas  entertained  of  the  Deity  have  a  great 
effect  on  the  characters  of  mankind. 

The  notion  that  what  is  of  primary  importance  to  the  logician  in  a 
proposition,  is  the  relation  between  the  two  ideas  corresponding  to 
the  subject  and  predicate  (instead  of  the  relation  between  the  two 
plienomena  which  they  respectively  express),  seems  to  me  one  of  the 
most  fatal  errors  ever  introduced  into  the  philosophy  of  L  ogic ;  and 
the  principal  cause  why  the  theory  of  the  science  has  made  such  incon- 
siderable progress  during  the  last  two  centuries.  The  treatises  on 
Logic,  and  on  the  branches  of  Mental  Philosophy  coimected  with 
Logic,  which  have  been  produced  since  the  intrusion  of  this  cardinal 
error,  though  sometimes  written  by  men  of  extraordinary  abilities  and 
attainments,  almost  always  tacitly  imply  a  theory  that  the  investigation 
of  truth  consists  in  contemplating  and  handling  our  ideas,  or  concep- 
tions of  things,  instead  of  the  things  themselves  :  a  process  by  which, 
I  will  venture  to  affirm,  not  a  single  truth  ever  was  amved  at,  except 
truths  of  psychology,  a  science  of  which  Ideas  or  Conceptions  are 
avowedly  (along  with  other  mental  phenomena)  the  subject-matter. 
Meanwhile,  inquiries  into  every  kind  of  natural  phenomena  were 
incessantly  establishing  gi-eat  and  fruitful  truths  on  the  most  important 
subjects,  by  processes  upon  which  these  views  of  the  nature  of  Judg- 
ment and  Reasoning  threw  no  light,  and  in  which  they  afforded  no 
assistance  whatever.  No  wonder  that  those  who  knew  by  practical 
experience  how  truths  are  come  at,  should  deem  a  science  futile,  which 
consisted  chiefly  of  such  speculations.  Wliat  has  been  done  for  the 
advancement  of  Logic  since  these  doctrines  came  into  vogue,  has  been 
done  not  by  professed  logicians,  but  by  discoverers  in  the  other  sci- 
ences ;  in  whose  methods  of  investigation  many  gi-eat  principles  of 
logic,  not  previously  thought  of,  have  successively  come  forth  into  light, 


IMPORT    OF    PROPOSITIONS.  CI 

but  who  have  generally  committed  tlie  eiTor  of  supposing  lliat  notliin'T 
whatever  was  known  of  the  art  of  philosopliizing  by  the  old  logicians, 
because  their  modem  interpreters  have  written  to  so  little  purpose 
respecting  it. 

We  have  to  inquire,  then,  on  the  present  occasion,  not  into  Judg- 
ment, but  judgments ;  not  into  the  act  of  belic\'ing,  but  into  the  thing 
believed.  What  is  the  immediate  object  of  belief  in  a  Proposition  J 
"Wliat  is  the  matter  of  fact  signified  by  it  I  AVliat  is  it  to  whi'ch,  when 
I  assert  the  proposition,  I  give  my  assent,  and  call  u])()n  others  to  give 
theirs  I  Wliat  is  that  which  is  expressed  by  the  fonn  of  discourse 
called  a  Proposition,  and  the  conformity  of  which  to  fact  constitutes 
the  truth  of  the  jjroposition  ? 

§  2.  One  of  the  clearest  and  most  consecutive  thinkers  whom  this 
country  or  the  world  has  produced,  I  mean  Hobbes,  has  given  the  fol- 
lowing answer  to  this  question.  In  every  proposition  (says  he),  what 
is  signified  Ls,  the  belief  of  the  speaker  that  the  predicate  is  a  name  of 
the  same  thing  of  which  the  subject  is  a  name ;  and  if  it  really  is  so, 
the  proposition  is  true.  Thus  the  proposition.  All  men  are  living  be- 
ings (he  would  say),  is  true,  because  living  being  is  a  name  of  every- 
thing of  wliich  man  is  a  name.  All  men  are  six  feet  high  is  not  true, 
because  six  feet  high  is  not  a  name  of  everything  (though  it  is  of  some 
things)  of  which  man  is  a  name. 

What  is  stated  by  Hobbes  as  the  definition  of  a  true  proposition, 
must  be  allowed  to  be  a  property  which  all  tiaie  propositions  possess. 
The  subject  and  predicate  being  both  of  them  names  of  things,  if  they 
were  names  of  quite  different  things  the  one  name  could  not,  consist- 
ently with  its  signification,  be  predicated  of  the  other.  If  it  be  true 
that  some  men  are  copper-colored,  it  must  be  true — and  the  proposi- 
tion does  really  assert — that  among  the  individuals  denoted  by  the 
name  man,  there  are  some  who  are  also  among  those  denoted  by  the 
name  copper-colored.  If  it  be  true  that  all  oxen  ruminate,  it  must 
be  true  that  all  the  individuals  denoted  by  the  name  ox  are  also  among 
those  denoted  by  the  name  ruminating ;  and  whoever  asserts  that  all 
oxen  ruminate,  undoubtedly  does  assert  that  this  relation  subsists  be- 
tween the  two  names. 

The  assertion,  therefore,  which,  according  to  Hobbes,  is  the  only 
one  made  in  any  proposition,  really  is  made  in  every  proposition  :  and 
his  analysis  has  consequently  one  of  the  requisites  for  being  the  true 
one.  We  may  go  a  step  further ;  it  is  the  only  analysis  that  is  rigor- 
ously true  of  all  propositions  without  exception.  Wliat  he  gives  as 
the  meaning  of  projjositions,  is  part  of  the  meaning  of  all  propositions, 
and  the  whole  meaning  of  some.  This,  however,  only  shows  what  an 
extremely  minute  fragment  of  meaning  it  is  quite  possible  to  include 
wthin  the  logical  fonnula  of  a  proposition.  It  does  not  show  that  no 
proposition  means  more.  To  warrant  us  in  putting  together  two  words 
with  a  copula  between  them,  it  is  really  enough  that  the  thing  or  things 
denoted  by  one  of  the  names  should  be  capable,  without  violation  of 
usage,  of  being  called  by  the  other  name  also.  If  then  this  be  all  the 
meaning  necessarily  implied  in  the  foi-m  of  discourse  called  a  Proposi- 
tion, why  do  I  object  to  it  as  the  scientific  definition  of  what  a  propo- 
sition means  ?  Because,  though  the  mere  collocation  which  makes  the 
proposition  a  proposition,  conveys  no  more  meaning  than  Hobbes  con- 


62  NAMES    AND    PROPOSITIONS. 

tends  for,  that  same  collocation  combined  with  other  circumstances, 
that  form  combined  with  other  matter,  does  convey  more,  and  much 
more. 

The  only  propositions  of  which  Hobbes'  principle  is  a  sufficient  ac- 
count, are  that  limited  and  vmimportant  class  in  which  both  the  predi- 
cate and  the  subject  are  proper  names.  For,  as  has  akeady  been 
remarked,  proper  names  have  strictly  no  meaning;  they  are  mere 
marks  for  indi\ddual  objects :  and  when  a  proper  name  is  predi- 
cated of  another  proper  name,  all  the  signification  conveyed  is,  that 
both  the  names  are  marks  for  the  same  object.  But  this  is  precisely 
what  Hobbes  produces  as  a  theory  of  predication  in  general.  His 
doctrine  is  a  full  explanation  of  such  predications  as  these  :  Hyde  was 
Clarendon,  or,  Tully  is  Cicero.  It  exhausts  the  meaning  of  those 
propositions.  But  it  is  a  sadly  inadequate  theory  of  any  others.  That 
it  should  ever  have  been  thought  of  as  such,  can  be  accounted  for  only 
by  the  fact,  that  Hobbes,  in  common  with  the  other  Nominalists,  be- 
stowed little  or  no  attention  upon  the  connotation  of  words  ;  and  sought 
for  their  meaning  exclusively  in  what  they  denote :  as  if  all  names  had 
been  (what  none  but  proper  names  really  are)  marks  put  upon  indi- 
viduals ;  and  as  if  there  were  no  difference  between  a  proper  and  a 
general  name,  except  that  the  first  denotes  only  one  individual,  and  the 
last  a  greater  number. 

It  has  been  seen,  however,  that  the  meaning  of  all  names,  except 
proper  names  and  that  portion  of  the  class  of  abstract  names  which  are 
not  connotative,  resides  in  the  connotation.  When,  therefore,  we  are 
analyzing  the  meaning  of  any  proposition  in  which  the  predicate  and 
the  subject,  or  either  of  them,  are  connotative  names,  it  is  to  the  con- 
notation of  those  teiTns  that  we  mus'  exclusively  look,  and  not  to  what 
they  denote,  or  in  the  language  of  Hobbes  (language  so  far  coiTect)  are 
names  of. 

In  asserting  that  the  truth  of  a  proposition  depends  upon  the  con- 
formity of  import  between  its  temis,  as,  for  instance,  that  the  proposi- 
tion, Socrates  is  wise,  is  a  true  px'oposition,  because  Socrates  and  wase 
are  names  applicable  to,  or,  as  he  expresses  it,  names  of  the  same  per- 
son ;  it  is  very  remarkable  that  so  powerful  a  thinker  should  not  have 
asked  himself  the  question,  But  how  came  they  to  be  names  of  the  same 
person"?  Surely  not  because  such  was  the  intention  of  those  who  in- 
vented the  words.  Wlien  mankind  fixed  the  meaning  of  the  word 
wise,  they  were  not  thinking  of  Socrates,  nor  when  his  parents  gave 
him  the  name  Socrates,  were  they  thinking  of  wisdom.  The  names 
happen  to  fit  the  same  person  because  of  a  certainyhc;;,  which  fact  was 
not  known,  nor  in  being,  when  the  names  were  invented.  If  we  want 
to  know  what  the  fact  is,  we  shall  "find  the  clue  to  it  in  the  connotation 
of  the  names. 

A  bird,  or  a  stone,  a  man,  or  a  wise  man,  means  simply,  an  object 
having  such  and  such  attiibutes.  The  real  meaning  of  the  word  man, 
is  those  attributes,  and  not  John,  Peter,  Thomas,  &c.  The  word 
mortal,  in  like  manner  connotes  a  certain  attribute  or  attributes ;  and 
when  we  say,  All  men  are  mortal,  the  meaning  of  the  proposition  is, 
that  all  beings  which  possess  the  one  set  of  attributes,  possess  also  the 
other.  If,  in  our  experience,  the  attributes  connoted  by  7nan  are 
always  accompanied  by  the  attribute  connoted  by  7n ortaJ,  it  will  follow 
as  a  consequence,  that  the  class  fiian  will  be  v/holly  included  in  the 


IMPORT    OF    PROPOSITIONS.  63 

class  mortal,  and  that  mortal  \\\\\  be  a  name  of  all  things  of  which  man 
is  a  name  :  but  why  I  Those  objects  are  brought  under  the  name,  by- 
possessing  the  attributes  connoted  by  it :  but  their  possession  of  the 
atti-ibutes  is  the  real  condition  on  which  the  truth  of  the  proposition 
depends  ;  not  their  being  called  by  the  name.  Connotative  names  do 
not  precede,  but  follow,  the  attributes  Avhich  they  connote.  If  one 
attribute  happens  to  be  always  found  in  conjunction  with  another 
attribute,  the  concrete  names  which  answer  to  those  attributes  will  of 
course  be  predicable  of  the  same  subjects,  and  may  be  said,  in  Hobbes' 
language  (in  the  propriety  of  which  on  this  occasion  I  fully  concur),  to 
be  two  names  for  the  same  things.  But  the  possibility  of  a  concun'ent 
application  of  the  two  names,  is  a  mere  consequence  of  the  conjunction 
between  the  two  attributes,  and  was,  in  most  cases,  never  thought  of 
when  the  names  were  invented  and  their  signification  fixed.  That  the 
diamond  is  combustible,  was  a  proposition  certainly  not  dreamed  of 
when  the  words  Diamond  and  Combustible  received  their  present 
meaning ;  and  could  not  have  been  discovered  by  the  most  ingenious 
and  refined  analysis  of  the  signification  of  those  words.  It  was  found 
out  by  a  very  different  process,  namely,  by  exerting  the  five  senses, 
and  learning  from  them,  that  the  attribute  of  combustibility  existed  in 
all  those  diamonds  upon  which  the  experiment  was  tried ;  these  being 
60  numerous,  and  the  circumstances  of  the  experiments  such,  that  what 
was  true  of  those  individuals  might  be  concluded  to  be  true  of  all  sub- 
stances "  coming  within  the  name,"  that  is,  of  all  substances  possessing 
the  attributes  which  the  name  connotes.  The  assertion,  therefore, 
when  analyzed,  is,  that  wherever  we  find  certain  attributes,  there  will 
be  found  a  certain  other  attribute  :  which  is  not  a  question  of  the  sig- 
nification of  names,  but  of  the  laws  of  nature  ;  the  order  existing:  amono: 
phenomena. 

§  3.  Although  Hobbes'  theory  of  Predication  has  not,  in  the  terms 
in  which  he  stated  it,  met  with  a  very  favorable  reception  from  philos- 
ophers, a  theory  virtually  identical  with  it,  and  not  by  any  means  so 
perspicuously  expressed,  may  almost  be  said  to  have  taken  the  rank  of 
an  established  opinion.  The  most  generally  received  notion  of  Predi- 
cation decidedly  is,  that  it  consists  in  referring  something  to  a  class,  i.  e., 
either  placing  an  indi\adual  under  a  class,  or  placing  one  class  under 
another  class.  Thus,  the  proposition,  Man  is  mortal,  asserts,  according 
to  this  view  of  it,  that  the  class  man  is  included  in  the  class  mortal. 
"  Plato  is  a  philosopher,"  asserts  that  the  individual  Plato  is  one  of 
those  who  compose  the  class  philosopher.  If  the  proposition  is  nega- 
tive, then  instead  of  placing  something  in  a  class,  it  is  said  to  exclude 
something  from  a  class.  Thus,  if  the  following  be  the  proposition, 
The  elephant  is  not  carnivorous ;  what  is  asserted  (according  to  this 
thfeory)  is,  that  the  elephant  is  excluded  from  the  class  carnivorous,  or 
is  not  numbered  among  the  things  comprising  that  class.  There  is  no 
real  difference  except  in  language,  between  this  tlieoiy  of  Predication 
and  the  theory  of  Hobbes.  For  a  class  is  absolutely  nothing  but  an 
indefinite  number  of  individuals  denoted  by  a  general  name.  The 
name  given  to  them  in  common,  is  what  makes  them  a  class.  To  refer 
anything  to  a  class,  therefore,  is  to  look  upon  it  as  one  of  the  things 
which  are  to  be  called  by  that  common  name.  To  exclude  it  from  a 
class,  is  to  say  that  the  common  name  is  not  applicable  to  it. 


64  NAMES    AND    PROPOSITIONS. 

How  widely  these  views  of  predication  have  prevailed,  is  evident 
from  this,  that  they  are  the  basis  of  the  celebrated  Dictum  de  omni  et 
nullo.  When  the  syllogism  is  resolved,  by  all  who  treat  of  it,  into  an 
inference  that  what  is  true  of  a  class  is  tnie  of  all  things  whatever  that 
belong  to  the  class  ;  and  when  this  is  laid  down  by  almost  all  professed 
logicians  as  the  ultimate  principle  to  which  all  reasoning  owes  its 
validity ;  it  is  clear  that  in  the  general  estimation  of  logicians,  the 
propositions  of  which  reasonings  are  composed  can  be  the  exj^ression 
of  nothing  but  the  process  of  dividing  things  into  classes,  and  referring 
everything  to  its  proper  class. 

This  theory  appears  to  me  a  signal  example  of  a  logical  error  very 
often  committed  in  logic,  that  of  varepov  Trporepov,  or  explaining  a 
thing  by  something  which  presupposes  it.  When  I  say  that  snow  is 
white,  I  may  and  ought  to  be  thinking  of  snow  as  a  class,  because  I 
am  asserting  a  proposition  as  true  of  all  snow  :  but  I  am  certainly  not 
thinking  of  white  objects  as  a  class;  I  am  thinking  of  no  white  object 
whatever  except  snow,  but  only  of  that,  and  of  the  sensation  of  white 
which  it  gives  me.  AVlien,  indeed,  I  have  judged,  or  assented  to  the 
propositions,  that  snow  is  white,  and  that  several  other  things  also  are 
white,  I  gradually  begin  to  think  of  white  objects  as  a  class,  including 
snow  and  those  other  things.  But  this  is  a  conception  which  followed, 
not  preceded,  those  judgments,  and  therefore  cannot  be  given  as  an 
explanation  of  them.  Instead  of  explaining  the  effect  by  the  cause, 
this  doctrine  explains  the  cause  by  the  effect,  and  is,  I  conceive,  founded 
upon  a  latent  misconception  of  the  nature  of  classification. 

There  is  a  sort  of  language  very  generally  prevalent  in  these  dis- 
cussions, which  seems  to  suppose  that  classification  is  an  aiTangement 
and  grouping  of  definite  and  knovra  individuals  :  that  when  names 
were  imposed,  mankind  took  into  consideration  all  the  individual  ob- 
jects in  the  universe,  made  them  up  into  parcels  or  lists,  and  gave  to 
the  objects  of  each  list  a  common  name,  repeating  this  operation  toties 
quoties  until  they  had  invented  all  the  general  names  of  which  language 
consists ;  which  having  been  once  done,  if  a  question  subsequently 
arises  whether  a  certain  general  name  can  be  truly  predicated  of  a 
certain  particular  object,  we  have  only  (as  it  were)  to  read  the  roll  of 
the  objects  upon  which  that  name  was  confeiTed,  and  see  whether  the 
object  about  which  the  question  arises,  is  to  be  found  among  them. 
The  framers  of  language  (it  would  seem  to  be  supposed)  have  prede- 
termined all  the  objects  that  are  to  compose  each  class,  and  we  have 
only  to  refer  to  the  record  of  an  antecedent  decision. 

So  absurd  a  doctrine  will  be  owned  by  nobody  when  thus  nakedly 
stated  ;  but  if  the  commonly  received  explanations  of  classification  and 
naming  do  not  imply  this  theory,  it  requires  to  be  shown  how  they  ad- 
mit of  being  reconciled  with  any  other. 

General  names  are  not  marks  put  upon  definite  objects ;  classes  are 
not  made  by  drawing  a  line  round  a  given  number  of  assignable  indi- 
viduals. The  objects  which  compose  any  given  class  are  peiq^etually 
fluctuating.  We  may  fi-ame  a  class  without  knowing  the  individuals, 
or  even  any  of  the  individuals,  of  which  it  will  be  composed  :  we  may 
do  so  while  belie-sdng  that  no  such  individuals  exist.  If  by  the  meaning 
of  a  general  name  are  to  be  understood  the  things  which  it  is  the  name 
of,  no  general  name,  except  by  accident,  has  a  fixed  meaning  at  all,  or 
ever  long  retains  the  same  meaning.     The  only  mode  in  Avhich  any 


IMPORT    OF   PROrOSITIOXS.  65 

general  name  has  a  definite  meaning,  is  hy  being  a  name  of  an  iudofi- 
nite  variety  of  things,  namely,  of  all  things,  known  or  unknown,  past, 
present,  or  future,  which  possess  certain  definite  attributes.  WHien, 
by  studying  not  the  meaning  of  words,  but  the  phenomena  of  nature, 
we  discover  that  these  attributes  are  jiossesscd  by  some  object  not  pre- 
viously known  to  possess  them,  (as  wlieu  chemists  found  that  the  dia- 
mond was  combustible),  we  include  this  new  object  in  die  class;  but 
it  did  not  already  belong  to  the  class.  We  place  the  individual  in  the 
class  because  the  proposition  is  true ;  the  2)roposition  is  not  true  be- 
canfie  the  object  is  placed  in  the  class. 

It  will  appear  hereafter  in  treating  of  reasoning,  how  much  the 
theory  of  that  intellectual  process  Ikls  been  vitiated  by  the  influence 
of  tliese  erroneous  views,  and  by  the  habit  which  they  exemplify  of 
assimilating  all  the  operations  of  the  human  understanding  which  have 
truth  for  thoir  object,  to  processes  of  mere  classification  and  naming. 
Unfortunately,  the  minds  which  have  been  entangled  in  this  net  are 
precisely  those  which  have  escaped  the  other  cardinal  error  commented 
upon  in  the  beginning  of  the  present  chaptei'.  Since  the  revolution 
which  dislodged  Aristotle  from  the  schools,  logicians  may  almost  be 
diN-ided  into  those  who  have  looked  upon  reasoning  as  essentially  an 
•  affair  of  Ideas,  and  those  who  have  looked  upon  it  as  essentially  an 
affair  of  Names. 

One  thing  it  is  but  just  to  remark.  Although  Hobbes'  theory  of 
Predication,  according  to  the  well  known  remark  of  Leibnitz,  and  the 
avowal  of  Hobbes  himself,*  renders  truth  and  falsity  completely  arbi- 
trary, with  no  standard  but  the  will  of  men,  it  must  not  be  concluded 
that  either  Hobbes,  or  any  of  the  other  philosophers  who  have  in  the 
main  agreed  with  him,  did,  in  fact,  consider  the  distinction  between 
truth  and  eiTor  as  less  real,  or  attached  one  jot  less  of  importance  to  it, 
than  other  people.  To  suppose  that  they  did  so  ^vould  argue  total 
imacquaintance  with  their  other  speculations.  But  this  shows  how 
little  hold  their,  docti-ine  possessed  over  their  own  minds.  No  person 
at  bottom  ever  imagined  that  there  was  nothing  more  in  truth  than 
]>ropriety  of  expression ;  than  using  language  in  conformity  to  a  pre- 
vious convention.  With  whatever  illusions  even  profound  thinkers 
may  have  satisfied  themselves  when  engaged  in  finding  a  general  solu- 
tion for  a  metaphysical  problem ;  when  they  came  to  the  practical  ap- 
plication of  their  doctrines,  they  were  always  prepared  with  some 
means  of  explaining  the  solution  away.  When  the  inquiry  was 
brought  down  from  generals  to  a  particular  case,  it  has  always  been 
acknowledged  that  there  is  a  distinction  between  verbal  and  real  ques- 
tions ;  that  some  false  propositions  are  uttered  from  ignorance  of  the 
meaning  of  words,  but  that  in  others  the  source  of  the  error  is  a  mis- 
apprehension of  things;  that  a  person  who  has  not  the  use  of  language 
at  all  may  foiTn  propositions  mentally,  and  that  they  may  be  untrue, 
that  is,  he  may  believe  as  matters  of  fact  what  are  not  really  so.  This 
last  admission  cannot  be  made  in- stronger  terms  than  it  is  by  Hobbes 
himself  ;t  though  he  will  not  allow  such  eiToneous  belief  to  be  called 

*  "  From  hence  also  this  may  he  deduced,  that  the  first  truths  were  arbitrarily  made  by 
those  that  first  of  all  imposed  names  upon  things,  or  received  them  from  the  imposition  of 
others.  For  it  is  true  (for  example)  that  rrean  is  a  living  creature,  but  it  is  for  this  reason, 
that  it  pleased  men  to  impose  both  these  names  on  the  same  thing."— Computation  or  Logic, 
ch.  iii.,  sect.  8. 

t  "  Men  are  subject  to  err  not  only  in  affirming  and  denying,  but  also  in  perception,  and 


66  NAMES    AND    PROPOSITIONS. 

falsity,  but  only  eiTor.  And,  moreover,  he  has  himself  laid  down,  In 
other  places,  doctrines  in  which  the  true  theory  of  predication  is  by 
implication  contained.  He  distinctly  says  that  general  names  are  given 
to  things  on  account  of  their  attributes,  and  that  abstract  names  are  the 
names  of  those  attributes.  "  Abstract  is  that  which  in  any  subject  de- 
notes the  cause  of  the  concrete  name.  ....  And  these  causes  of  names 
are  the  same  with  the  causes  of  our  conceptions,  namely,  some  power 
of  action,  or  affection,  of  the  thing  conceived,  which  some  call  the  man- 
ner by  which  anything  works  upon  ovu-  senses,  but  by  most  men  they 
are  called  accidents^*  It  is  strange  tliat  having  gone  so  far,  he  should 
not  have  gone  one  step  farther,  and  seen  that  what  he  calls  the  cause 
of  the  concrete  name,  is  in  reality  the  meaning  of  it ;  and  that  when  we 
predicate  of  any  subject  a  name  which  is  given  hecavse  of  an  attribute 
(or,  as  he  calls  it,  an  accident),  our  object  is  not  to  affimi  the  name,  but, 
by  means  of  the  name,  to  affirm  the  attribute. 

§  4.  Let  the  predicate  be,  as  we  have  said,  a  connotative  term;  and 
to  take  the  simplest  case  first,  let  the  subject  be  a  proper  name:  "The 
summit  of  Chimborazo  is  white."  The  word  white  connotes  an  attri- 
bute which  is  possessed  by  the  individual  object  designated  by  the 
words,  "summit  of  Chimborazo,"  which  attribute  consists  in  the  phys- 
ical fact  of  its  exciting  in  human  beings  the  sensation  which  we  call  a 
sensation  of  white.  It  will  be  admitted  that,  by  asserting  the  propo- 
sition, we  wish  to  communicate  information  of  that  physical  fact,  and 
are  not  thinking  of  the  names,  except  as  the  necessary  means  of  ma- 
king that  communication.  The  meaning  of  the  proposition,  therefore, 
is,  that  the  indixddual  thing  denoted  by  the  subject,  has  the  attiibutes 
connoted  by  the  predicate. 

If  we  now  suppose  the  subject  also  to  be  a  connotative  name,  the 
meaning  expressed  by  the  proposition  has  advanced  a  step  further  in 
complication.  Let  us  first  suppose  the  proposition  to  be  universal,  as 
well  as  affirmative :  "  All  men  are  mortal."  In  this  case,  as  in  the 
last,  what  the  proposition  asserts  (or  expresses  a  belief  in),  is,  ot 
course,  that  the  objects  denoted  by  the  subject  (man)  possess  the 
attributes  connoted  by  the  predicate  (mortal).  But  the  characteristic 
of  this  case  is,  that  the  objects  are  no  longer  individually  designated. 
They  are  pointed  out  only  by  some  of  their  attributes  :  they  are  the 
objects  called  men,  that  is,  the  beings  possessing  the  attributes  con- 
noted by  the  name  man;  and  the  only  thing  known  of  them  may  be 
those  atti-ibutes  :  indeed,  as  the  proposition  is  general,  and  the  objects 
denoted  by  the  subject  are  therefore  indefinite  in  number,  most  of  them 
are  not  known  individually  at  all.  The  assertion,  therefore,  is  not,  as 
before,  that  the  atti-ibutes  which  the  predicate  connotes  are  possessed 
by  any  given  individual,  or  by  any  number  of  individuals  previously 
known  as  John,  Thomas,  Richard,  &c.,  but  that  those  attributes  are 
possessed  by  each  and  every  individual  possessing  certain  other  attri- 

in  silent  cogitation Tacit  errors,  or  the  errors  of  sense  and  cogitation,  are  made  by 

passing  from  one  imagination  to  the  imagination  of  another  diflerent  thing ;  or  by  feigning 
that  to  be  past,  or  future,  which  never  was,  nor  ever  shall  be;  as  when,  by  seeing  the  im- 
age of  the  sun  in  water,  we  imagine  the  sun  itself  to  be  there;  or  by  seeing  swords,  that 
there  has  been,  or  shall  be,  fighting,  because  it  uses  to  be  so  for  the  most  part;  or 
when  from  promises  we  feign  the  mind  of  the  promiser  to  be  such  and  such  ;  or,  lastly, 
when  from  any  sign  we  vainly  imagine  something  to  be  signified  which  is  not.  And  errors 
of  this  sort  are  common  to  all  thmgs  that  have  sense." — Computatian  or  Logic,  ch.  v.,  sect.  1. 
*  lb.,  ch.  iii.,  sect.  3. 


IMPORT    OF    PROPOSITIONS.  G7 

butes ;  that  whatever  has  the  attributes  connoted  by  the  suDJcct,  has 
also  those  connoted  by  the  predicate ;  that  the  latter  set  of  attxibutes 
constanlhj  accompanij  the  foiiner  set.  Wliatever  has  the  attributes  of 
man  has  the  atti-ibute  of  mortality ;  mortality  constantly  accompanies 
the  attributes  of  man. 

If  it  be  remembered  tliat  every  attiibute  is  grounded  upon  some  fact 
or  phenomenon,  either  of  outwai'd  sense  or  of  inward  consciousness, 
and  that  to  possess  an  attinbute  is  another  phrase  for  being  the  cause 
of,  or  fonnuig  part  of,  the  fact  or  phenomenon  upon  which  the  attribute 
is  grounded ;  we  may  add  one  more  step  to  complete  the  analysis. 
The  proposition  which  asserts  that  one  attribute  always  accompanies 
another  attribute,  does  really  assert  thereby  no  other  thing  than  this, 
that  one  phenomenon  alway*  accompanies  another  phenomenon  ;  inso- 
much that  where  we  find  the  one,  we  have  assurance  of  the  existence 
of  the  other.  Thus,  in  the  proposition.  All  men  are  mortal,  the  word 
man  connotes  the  attributes  which  we  ascribe  to  a  certain  kind  of  living 
creatures,  on  the  ground  of  certain  phenomena  which  they  exhibit, 
and  which  are  partly  physical  phenomena,  namely  the  impressions 
made  on  our  senses  by  their  bodily  form  and  structure,  and  partly 
mental  phenomena,  namely  the  sentient  and  intellectual  life  which  they 
have  of  their  o^vn.  All  this  is  understood  when  we  utter  the  word 
man,  by  any  one  to  whom  the  meaning  of  the  word  is  known.  Now, 
when  we  say,  Man  is  mortal,  we  mean  that  wherever  these  various 
physical  and  mental  phenomena  are  all  found,  there  we  have  assurance 
that  the  other  physical  and  mental  phenomenon,  called  death,  will  not  fail 
to  take  place.  The  proposition  does  not  affirm  when  ;  for  the  connota- 
tion of  the  word  mortal  goes  no  further  than  to  the  occurrence  of  the  phe- 
nomenon at  some  time  or  other,  leaving  the  precise  time  undecided. 

§  5.  We  have  already  proceeded  far  enough  not  only  to  demonstrate 
the  error  of  Hobbes,  but  to  ascertain  the  real  import  of  by  far  the 
most  numerous  class  of  propositions.  The  object  of  belief  in  a  propo- 
sition, when  it  asserts  anything  more  than  the  meaning  of  words,  is 
generally,  as  in  the  cases  which  we  have  examined,  either  the  coexist- 
ence or  the  sequence  of  two  phenomena.  At  the  very  commencement 
of  our  inquiry,  we  found  that  every  act  of  belief  implied  two  Things  ; 
we  have  now  ascertained  what,  in  the  most  frequent  case,  these  two 
things  are,  namely  two  Phenomena,  in  other  words,  two  states  of 
consciousness  ;  and  what  it  is  which  the  proposition  affirms  (or  denies) 
to  subsist  between  them,  namely  either  succession,  or  coexistence. 
And  this  case  includes  innumerable  instances  which  no  one,  previous 
to  reflection,  would  think  of  refeiTing  to  it.  Take  the  following 
example  :  A  generous  person  is  worthy  of  honor.  "VTho  would  expect 
to  recognize  here  a  case  of  coexistence  between  phenomena  ?  But  so 
it  is.  The  attribute  which  causes  a  person  to  be  termed  generous,  is 
ascribed  to  him  on  the  ground  of  states  of  his  mind,  and  particulars  of 
his  conduct :  both  are  phenomena ;  the  former  are  facts  of  internal 
consciousness,  the  latter,  so  far  as  distinct  from  the  fonner,  are  physical 
facts,  or  perceptions  of  the  senses.  Worthy  of  honor,  admits  of  a 
similar  analysis.  Honor,  as  here  used,  means  a  state  of  approving 
and  admiring  emotion,  followed  upon  occasion  by  corresponding  out- 
ward acts.  "  Worthy  of  honor"  connotes  all  this,  together  with  our 
approval  of  the   act  of  shoAving  honor.     All  these  are  j^hcnomenaj 


68  NAMES    AND    PROPOSITIONS. 

States  of  internal  coixsciousness,  accompanied  or  followed  by  physical 
facts.  When  we  say,  A  generous  person  is  worthy  of  honor,  we  affinn 
coexistence  between  the  two  complicated  phenomena  connoted  by  the 
two  terms  respectively.  We  affirm,  that  wherever  and  whenever  the 
inward  feelings  and  outward  facts  implied  in  the  word  generosity, 
have  place,  then  and  there  the  existence  and  manifestation  of  an  inward 
feeling,  honor,  would  be  followed  in  our  minds  by  another  inward 
feeling,  approval. 

After  the  analysis  in  a  former  chapter  of  the  import  of  names,  many 
examples  are  not  needed  to  illustrate  the  import  of  propositions. 
When  there  is  any  obscurity  or  difficulty,  it  does  not  lie  in  the  mean- 
ing of  the  proposition,  but  in  the  meaning  of  the  names  which  compose 
it ;  in  the  complicated  nature  of  the  connotation  of  many  words ;  the 
immense  multitude  and  prolonged  series  of  facts  which  often  constitute 
the  phenomenon  connoted  by  a  name.  But  where  it  is  seen  what  the 
phenomenon  is,  there  is  seldom  any  difficulty  in  seeing  that  the  asser- 
tion conveyed  by  the  proposition  is,  the  coexistence  of  one  such 
phenomenon  with  another ;  or  the  succession  of  one  such  phenomenon 
to  another :  their  conjunction ,  in  short,  so  that  where  the  one  is  found, 
we  may  calculate  on  finding  both. 

This,  however,  though  the  most  common,  is  not  the  only  meaning 
which  propositions  are  ever  intended  to  convey.  In  the  first  place, 
sequences  and  coexistences  are  not  only  asserted  respecting  Phe- 
nomena ;  we  make  propositions  also  respecting  those  hidden  causes  of 
phenomena  which  ai"e  named  substances  and  attributes.  A  substance, 
however,  being  to  us  nothing  but  either  that  which  causes,  or  that 
which  is  conscious  of,  phenomena ;  and  the  same  being  ti-ue,  mutatis 
mutandis,  of  attributes ;  no  assertion  can  be  made,  at  least  with  a 
meaning,  concerning  these  unknown  and  unknowable  entities,  (beyond 
their  mere  existence),  except  in  virtue  of  the  Phenomena  by  which 
alone  they  manifest  themselves  to  our  faculties.  When  we  say,  Socrates 
was  contemporary  with  the  Peloponnesian  war,  the  foundation  of  this 
assertion,  as  of  all  assertions  concerning  substances,  is  an  assertion 
concerning  the  phenomena  which  they  exhibit, — namely,  that  the  series 
of  facts  by  which  Socrates  manifested  himself  to  mankind,  and  the 
series  of  mental  states  which  constituted  his  earthly  existence,  went 
on  simultaneously  with  the  series  of  facts  known  by  the  name  of  the 
Peloponnesian  war.  Still,  the  proposition  does  not  assert  that  alone  ; 
it  asserts  that  the  Thing  in  itself,  the  noumcnon  Socrates,  was  existing, 
and  doing  or  experiencing  those  various  facts,  during  the  same  time. 
Coexistence  and  sequence,  therefore,  may  be  affimied  or  denied  not 
only  between  phenomena,  but  between  noumena,  or  between  a  noume- 
non  and  phenomena.  And  there  is  one  kind  of  assertion  which  may 
be  made  respecting  noumena,  independently  of  the  phenomena  which 
are  their  sensible  m8.nifestation ;  the  assertion  of  their  simple  exist- 
ence. But  what  is  a  uoumenon  1  an  unknown  cause.  In  affirming, 
therefore,  the  existence  of  a  noumenon,  we  affirm  causation.  Here, 
therefore,  are  two  additional  kinds  of  fact,  capable  of  being  asserted 
in  a  proposition.  Besides  t\ie  propositions  which  assert  Sequence  or 
Coexistence,  there  are  some  which  assert  simple  Existence  ;  and 
others  assert  Causation,  which,  subject  to  the  explanations  which  will 
follow  in  the  Third  Book,  must  be  considered  provisionally  as  a  distinct 
and  peculiar  kind  of  assertion. 


IMPORT    OF    PROPOSITIONS.  69 

§  6.  To  these  four  kinds  of  matter-of-fact  or  assertion,  must  be 
added,  a  fifth,  Resemblance.  This  was  a  species  of  attribute  which 
we  found  it  impossible  to  analyze  ;  for  which  wo  fundament  um,  distinct 
fi-om  the  objects  themselves,  could  be  assigned.  In  addition  to  prop- 
ositions which  assert  a  secpience  or  coexistence  between  two  phenom- 
ena, there  arc  therefore,  also,  propcjsitions  which  assert  resemblance 
between  them  :  as.  This  color  is  like  that  color ; — The  heat  of  to-day  is 
equal  to  the  heat  of  yesterday.  It  is  tnle  that  such  an  assertion  might 
with  some  plausibility  be  brought  within  the  description  of  an  affirma- 
tion of  sequence,  by  considering  it  as  an  assertion  that  the  simulta- 
neous contemplation  of  the  two  colors  is  Jhllowcd  by  a  specific  feeling 
termed  the  feeling  of  resemblance.  But  tliere  would  be  nothing 
gained  by  encumbering  ourselves,  especially  in  this  place,  with  a 
generalization  which  may  be  looked  upon  as  strained.  Logic  does 
not  undertake  to  analyze  things  into  their  ultimate  elements.  Resem- 
blance between  two  phenomena  is  more  intelligible  in  itself  than  any 
explanation  could  make  it,  and  under  any  classification  must  remain 
specifically  distinct  from  the  ordinary  cases  of  sequence  and  coexistence. 

It  is  sometimes  said  that  all  propositions  whatever,  of  which  the 
predicate  is  a  general  name,  do,  in  point  of  fact,  affirm  or  deny  resem- 
blance. All  such  propositions  affirm  that  a  thing  belongs  to  a  class  ; 
but  things  being  classed  together  according  to  their  resemblance, 
everything  is  of  course  classed  with  the  things  which  it  resembles 
most ;  and  thence,  it  may  be  said,  when  we  affirm  that  gold  is  a 
metal,  or  that  Socrates  is  a  man,  the  affirmation  intended  is,  that  gold 
resembles  other  metals,  and  Socrates  other  men,  more  nearly  than 
they  resemble  the  objects  contained  in  any  other  of  the  classes  co- 
ordinate with  these. 

There  is  some  slight  degree  of  foundation  for  this  remark,  but  no 
more  than  a  slight  degree.  The  arrangement  of  things  into  classes, 
such  as  the  class  metal,  or  the  class  7na7i,  is  grounded  indeed  upon  a 
resemblance  among  the  things  which  are  placed  in  the  same  class,  but 
not  upon  a  mere  general  resemblance  :  the  resemblance  it  is  grounded 
upon  consists  in  the  possession  by  all  those  things,  of  certain  common 
peculiarities ;  and  those  peculiarities  it  is  which  the  terms  connote, 
and  which  the  propositions  consequently  assert ;  not  the  resemblance  : 
for  though  when  I  say.  Gold  is  a  metal,  I  say  by  implication  that  if 
there  be  any  other  metals  it  must  resemble  them,  yet  if  there  were  no 
other  metals  1  might  still  assert  the  proposition  \vith  the  same  mean- 
ing as  at  present,  namely,  that  gold  has  the  various  properties  implied 
in  the  word  metal ;  just  as  it  might  be  said.  Christians  are  men,  even 
if  there  were  no  men  who  were  not  Christians ;  or  as  the  expression, 
Jehovah  is  God,  might  be  used  by  the  firmest  believer  in  the  unity  of 
the  godhead.  Propositions,  therefore,  in  which  objects  are  refeiTed  to 
a  class  because  they  possess  the  attributes  constituting  the  class,  are 
so  far  from  asserting  nothing  but  resemblance,  that  they  do  not,  prop- 
erly speaking,  assert  resemblance  at  all 

But  we  remarked  some  time  ago  (and  tho  reasons  of  the  remark 
will  be  more  fully  entered  into  in  a  subsequent  Book),  that  there  is  some- 
times a  convenience  in  extending  the  bound.aries  of  a  class  so  as  to 
include  things  which  possess  in  a  very  inferior  degree,  if  in  any,  the 
characteristic  properties  of  the  class, — provided  they  resemble  that 
class  more  than  any  other,  insomuch  that  the  general  propositions 


70  NAMES    AND    PROPOSITIONS. 

which  are  true  of  the  class  will  be  nearer  to  being  true  of  those  things 
than  any  other  equally  general  propositions.  As,  for  instance,  there 
are  substances  called  metals  which  have  very  few  of  the  properties  by 
which  metals  are  commonly  recognized  ;  and  almost  every  great  family 
of  plants  or  animals  has  a  few  anomalous  genera  or  species  on  its 
borders,  which  are  admitted  into  it  by  a  sort  of  courtesy,  and  concern- 
ino-  which  it  has  been  matter  of  discussion  to  what  family  they  properly 
belonged.  Now  when  the  class-name  is  predicated  of  any  object  of 
this  description,  we  do,  by  so  predicating  it,  affirm  resemblance  and 
nothing  more.  And  in  order  to  be  scrupulously  correct,  it  ought  to 
be  said,  that  in  eveiy  case  in  which  we  jjredicate  a  general  name,  we 
affirm,  not  absolutely  that  the  object  possesses  the  properties  designa- 
ted by  the  name,  but  that  it  either  possesses  those  properties,  or  if  it 
does  not,  at  any  rate  resembles  the  things  which  do  so,  more  than  it 
resembles  any  other  things.  In  most  cases,  however,  it  is  unnecessary 
to  suppose  any  such  alternative,  the  latter  of  the  two  grounds  being 
very  seldom  that  on  which  the  assertion  is  made  :  and  when  it  is,  there 
is  generally  some  slight  difference  in  the  form  of  the  expression,  as, 
This  species  (or  genus)  is  considered,  or  may  be  ranl<ed,  as  belonging 
to  such  and  such  a  family  :  we  should  hardly  say  positively  that  it 
does  belong  to  it,  vmless  it  possessed  unequivocally  the  properties  of 
which  the  class-name  is  scientifically  significant. 

There  is  still  another  exceptional  case  in  which,  although  the  predi- 
cate is  a  name  of  a  class,  yet  in  predicating  it  we  affirm  nothing  but 
resemblance,  the  class  being  founded  not  upon  resemblance  in  any 
particular  respect,  but  upon  general  unanalyzable  resemblance.  The 
classes  in  question  are  those  into  which  our  simple  sensations,  or 
other  simple  feelings,  are  divided.  Sensations  of  white,  for  instance, 
are  classed  together,  not  because  we  can  take  them  to  pieces,  and  say 
they  are  alike  in  this,  and  not  alike  in  that,  but  because  we  feel  them 
to  be  alike  altogether,  although  in  different  degi'ees.  When,  there- 
fore, I  say.  The  color  I  saw  yesterday  was  a  white  color,  or,  The 
sensation  I  feel  is  one  of  tightness,  in  both  cases  the  attribute  I  affirm 
of  the  color  or  of  the  other  sensation  is  mere  resemblance, — simple 
likeness  to  sensations  which  I  have  had  before,  and  which  have  had 
those  names  bestowed  upon  them.  The  names  of  feelings,  like  other 
concrete  general  names,  are  connotative  ;  but  they  connote  a  mere 
resemblance.  When  predicated  of  any  individual  feeling,  the  infor- 
mation they  convey  is  that  of  its  likeness  to  the  other  feelings  which 
we  have  been  accustomed  to  call  by  the  same  name.  And  thus  much 
may  suffice  in  illustration  of  the  kind  of  Propositions  in  whicli  the 
matter-of-fact  asserted  (or  denied)  is  simple  Resemblance. 

Existence,  Coexistence,  Sequence,  Causation,  Resemblance  :  one  or 
other  of  these  is  asserted  (or  denied)  in  every  proposition,  without  ex- 
ception. This  five-fold  di\-ision  is  an  exhaustive  classification  of  mat- 
ters-of-fact ;  of  all  things  that  can  be  believed  or  tendered  for  belief; 
of  all  questions  that  can  be  propounded,  and  all  answers  that  can  be 
retui-ned  to  them.  Instead  of  Coexistence  and  Sequence,  we  shall 
sometimes  say,  for  greater  particularity.  Older  in  Place,  and  Order  in 
Time  :  Order  in  Place  being  one  of  the  modes  of  coexistence,  not  ne- 
cessary to  be  more  particularly  analyzed  here ;  while  the  mere  fact  of 
coexistence,  or  simultaneousness,  may  be  classed,  together  with  Se- 
quence, under  the  head  of  Order  in  Time. 


IMPORT    OF    PROPOSITIONS.  71 

§  7.  In  the  foregoing  incjuiry  into  the  import  of  Propositions,  we 
have  thought  it  necessai'y  to  analyze  directly  those  ah)ne,  in  which  the 
tenus  of  the  proposition  (or  the  predicate  at  least)  ai'e  concrete  terms. 
But,  in  doing  so,  we  have  indirectly  iuialyzed  those  in  which  the  terms 
are  abstract.  The  distinction  between  an  abstract  term  and  its  cor- 
responding concrete,  is  no  difference  in  what  they  are  appointed  to  sig- 
nify ;  fur  the  real  signification  of  a  concrete  general  name  is,  as  we 
have  so  often  said,  its  connation ;  and  what  the  concrete  term  con- 
notes, forms  the  entire  meaning  of  the  abstract  name.  Since  there  is 
nothing  in  the  import  of  an  absti'act  name  which  is  not  in  the  impoi't 
of  the  corresponding  concrete,  it  is  natural  to  suppose  that  neither  can 
there  be  anything  in  the  import  of  a  pi'oposition  of  which  the  terms  are 
abstract,  but  what  there  is  in  some  proposition  which  can  be  framed  of 
concrete  terms. 

And  this  presumption  a  closer  examination  will  confirm.  An  ab- 
stract name  is  the  name  of  an  attiibute,  or  combination  of  attributes. 
The  coiTesponding  concrete  is  a  name  given  to  things,  because  of,  and 
in  order  to  express,  their  possessing  that  attribute,  or  that  combination 
of  attributes.  \Vlien,  therefore,  we  predicate  of  anything  a  concrete 
name,  the  attribute  is  what  we  in  reality  predicate  of  it.  But  it 
has  now  been  shown  that  in  all  propositions  of  which  the  predicate  is 
a  concrete  name,  what  is  really  predicated  is  one  of  five  things :  Ex- 
istence, Coexistence,  Causation,  Sequence,  or  Resemblance.  An 
attribute,  therefore,  is  necessarily  either  an  existence,  a  coexistence, 
a  causation,  a  sequence,  or  a  resemblance.  Wlien  a  proposition  con- 
sists of  a  subject  and  predicate  which  are  abstract  terms,  it  consists  of 
terms  which  must  necessarilly  signify  one  or  other  of  these  things. 
When  we  predicate  of  any  thing  an  abstract  name,  we  affirm  of  the 
thing  that  it  is  one  or  other  of  these  five  things ;  that  it  is  a  case  of 
Existence,  or  of  Coexistence,  or  of  Causation,  or  of  Sequence,  or  of 
Resemblance. 

It  is  impossible  to  imagine  any  proposition  expressed  in  abstract 
terras,  which  cannot  be  transformed  into  a  precisely  equivalent  propo- 
sition in  which  the  terms  are  concrete,  namely,  either  the  concrete 
names  Avhich  connote  tlie  attributes  themselves,  or  the  names  of  the 
fundamcnta  of  those  attributes,  the  facts  or  phenomena  on  which  they 
are  grounded.  To  illustrate  the  latter  case,  let  us  take  this  propo- 
sition, of  which  only  the  subject  is  an  abstract  name, — "  Thoughtless- 
ness is  dangerous."  Thoughtlessness  is  an  attribute  grounded  on  the 
facts  which  we  call  thoughtless  actions  ;  and  the  proposition  is  equiva- 
lent to  this,  Thoughtless  actions  are  dangerous.  In  the  next  example 
the  predicate  as  well  as  the  subject  are  abstract  names  :  "  Wliiteness 
is  a  color;"  or  "  The  color  of  snow  is  a  whiteness."  These  attributes 
being  grounded  upon  sensations,  the  equivalent  propositions  in  the 
concrete  would  be.  The  sensation  of  white  is  one  of  the  sensations 
called  those  of  color, — The  sensation  of  sight,  caused  by  looking  at 
snow,  is  one  of  the  sensations  called  sensations  of  white.  In  these 
propositions,  as  we  have  before  seen,  the  matter-of-fact  asserted  is  a 
Resemblance.  In  the  following  examples,  the  concrete  terms  are 
those  which  directly  coiTespond  to  the  abstract  names ;  connoting  the 
attribute  which  these  denote.  "Prudence  is  a  virtue:"  this  may  be 
rendered,  "  All  prudent  persons,  in  so  far  an  prudent,  are  virtuous  :" 
"  Courage  is  deserving  of  honor"  thits,  "  All  courageous  persons  are 


72  NAMES    AND    PROPOSITIONS. 

deserving  of  honor  so  far  forth  as  they  are  courageous;"  which  is 
equivalent  to  this — "  All  courageous  persons  deserve  an  addition  to  the 
honor,  or  a  diminution  of  the  disgi-ace,  which  would  attach  to  them  on 
other  grounds." 

In  order  to  throw  still  further  light  upon  the  import  of  propositions 
of  which  the  terms  are  abstract,  we  will  subject  one  of  the  examples 
given  above  to  a  minuter  analysis.      The  proposition  we  shall  select  is 
the  following — "  Prudence   is   a  virtue."     Let   us   substitute  for  the 
word  virtue  an  equivalent  but  more  definite  expression,  such  as  "  a 
mental  qviality  beneficial  to  society,"  or  "  a  mental  quality  pleasing  to 
God,"  or  whichever  other  of  the  definitions  of  virtue  we  prefer.     What 
the  proposition   asserts  is   a  sequence,  accompanied  with  causation, 
namely,  that  benefit  to  society,  or  that  the  approval  of  God,  is  consequent 
upon,  and  caused  by,  prudence.     Here  is  a  sequence  ;  but  between 
what  %     We  understand  the  consequent  of  the  sequence,  but  we  have 
yet  to  analyze  the  antecedent.     Prudence  is  an  attiibute  ;   and,  in  con- 
nexion with  it,  two  things  besides  itself  are  to  be  considered  ;  prudent 
persons,  who  are  the  svbjecis  of  the  attribute,  and  prudential  conduct, 
which  may  be  called  Xhe  foundation  of  it.     Now,  is  either  of  these  the 
antecedent  %  and,  first,  is  it  meant,  that  the  approval  of  God,  or  benefit 
to  society,  is  attendant  upon  all  prudent  2>crsons  ?     No  ;   except  in  so 
far  forth  as  they  are  prudent ;  for  prudent  persons  who  are  scoundrels 
can  seldom  on  the  whole  be  beneficial  to  society,  nor  acceptable  to 
even  finite  wisdom.     Is  it  upon  prudential  conduct,  then,  that  divine 
approbation  and  benefit  to  mankind  are  invariably  consequent  ]     Nei- 
ther is  this  the  assertion  meant  when  it  is  said  that  prudence   is   a 
virtue ;  except  with  the  same  reservation  as  before,  and  for  the  same 
reason,  namely,  that  j^rudential  conduct,  although  in  so  far  as  it  is  pru- 
dential it  is  beneficial  to  society,  may  yet,  by  reason  of  some  other  of 
its  qualities,  be  productive  of  an  injury  outweighing  the  benefit,  and  of 
a  divine  displeasure  exceeding  the  approbation  which  would  be  due 
to  the  prudence.     Neither  the  substance,  therefore  (viz.,  the  person), 
nor  the  phenomenon  (the  conduct),  is  an  antec-edent  upon  which  the 
other  tenn  of  the  sequence  is  universally  consequent.     But  the  propo- 
sition, "  Prudence  is  a  virtue,"  is  an  universal  proposition.     What  is  it, 
then,  upon  which  the  proposition  aflSrms  the  effects  in  question  to  be 
universally  consequent  ]     Upon  that  in  the  person,  and  in  the  conduct, 
which  causes  them  to  be  called  prudent,  and  which  is  equally  in  them 
when  the  action,  though  prudent,  is  wicked ;  namely,  a  coiTect  fore- 
sight of  consequences,  a  just  estimation  of  their  importance  to  the  object 
in  view,  and  repression  of  any  unreflecting  impulse  at  vai'iance  with 
the  deliberate  purpose.     These,  which  are  states  of  the  person's  mind, 
are  the  real  antecedent  in  the  sequence,  the  real  cause  in  the  causation, 
which  are  asserted  by  the  proposition.     But  these  are  also  the  real 
ground,  or  foundation,  of  the  attribute  Prudence  ;  since  wherever  these 
states  of  mind  exist  we  may  predicate  prudence,  even  before  we  know 
whether  any  conduct  has  followed.     And  in  this  manner  every  asser- 
tion respecting  an  attribute  may  be  transformed  into  an  assertion  exactly 
equivalent  respecting  the  fact  or  phenomenon  which  is  the  grotmd  of 
the  attribute.     And  no  case  can  be  assigned,  where  that  which  is  pre- 
dicated of  die  fact  or  phenomenon,  does  not  belong  to  one  or  other  of 
the  five  species  formerly  enumerated :   it  is  either  simple  Existence,  or 
it  is  some  Sequence,  Coexistence,  Causation,  or  Resemblance, 


VERBAL    AND    REAL    PROTOSITIONS.  73" 

And  as  these  five  9,re  the  bnly  things  which  can  be  affirmed,  so  arc 
they  the  only  things  which  can  be  denied.  '.'  No  horses  are  web- 
footed,"  denies  that  the  attributes  of  a  horse  ever  coexist  \vith  web-feet. 
It  is  scarcely  necessary  to  apply  the  same  analysis  to  Particular  affirm- 
ations and  negations.  "  Some  birds  are  web-footed,"  affirms  that,  \vith 
the  atti-ibutes  connoted  by  bird,  the  phenomenon  web-fcet  is  sometimes 
coexistent :  "  Some  birds  are  not  web-footed,"  asserts  that  there  are 
other  instances  in  which  this  coexistence  does  not  have  place.  Any 
farther  explanation  of  a  thing  which,  if  the  previous  exposition  has 
been  assented  to,  is  so  obvious,  may  well  be  spared. 


CHAPTER  VI. 

OF  PROPOSITIONS  BIERELY  VERBAL. 


§  1.  As  a  preparation  for  the  inquiiy  which  is  the  proper  object  of 
Logic,  namely,  in  what  manner  propositions  are  to  be  proved,  we  have 
found  it  necessary  to  inquire  what  they  contain  which  requires,  or  is 
susceptible  of,  proof;  or  (which  is  the  same  thing)  what  they  assert. 
In  the  course  of  this  preliminary  investigation  into  the  import  of  Prop- 
ositions, we  examined  the  opinion  of  the  Conceptualists,  that  a  propo- 
sition is  the  expression  of  a  relation  between  two  ideas ;  and  the  doc- 
tiine  of  the  Nominalists,  that  it  is  the  expression  of  an  agreement  or 
disagi-eement  between  the  meanings  of  two  names.  We  decided  that, 
as  general  theories,  both  of  these  are  erroneous ;  and  that,  although 
propositions  may  be  made  both  respecting  names  and  respecting  ideas, 
neither  the  one  nor  the  other  are  the  subject-matter  of  Propositions 
considered  generally.  AVe  then  examined  the  different  kinds  of  prop- 
ositions, and  we  found  that,  w\x\\  the  exception  of  those  which  are 
merely  verbal,  they  assert  five  different  kinds  of  matters  of  fact,  name- 
ly. Existence,  Order  in  Place,  Order  in  Time,  Causation,  and  Resem- 
blance ;  that  in  every  proposition  one  of  these  five  is  either  affirmed,  or 
denied,  of  some  fact  or  phenomenon,  or  of  some  object  the  unknown 
source  of  a  fact  or  phenomenon. 

In  distinguishing,  however,  the  different  kinds  of  matters  of  fact  as- 
serted in  propositions,  we  reserved  one  class  of  propositions,  which  do 
not  relate  to  any  matter  of  fact,  in  the  proper  sense  of  the  term,  at  all, 
but  to  the  meaning  of  names.  Since  names  and  their  signification  are 
entirely  arbitrary,  such  propositions  are  not,  strictly  speaking,  suscep- 
tible of  tnith  or  falsity,  but  only  of  conformity  or  disconformity  to  usage 
or  convention  ;  and  all  the  proof  they  are  capable  of,  is  proof  of  usage  ; 
proof  that  the  words  have  been  employed  by  others  in  the  acceptation 
in  which  the  speaker  or  writer  desires  to  use  them.  These  propositions 
occupy,  however,  a  conspicuous  place  in  philosophy  ;  and  their  nature 
and  characteristics  are  of  as  much  importance  in  logic,  as  those  of  any 
of  the  other  classes  of  propositions  previously  adverted  to. 

If  all  propositions  respecting  the  signification  of  words,  were  as  sim- 
ple and  unimportant  a.s  those  which  served  as  for  examples  when  ex- 
amining Hobbes'  theory  of  predication,  viz.,  those  of  which  the  subject 
and  predicate  are  proper  names,  and  which  assert  only  that  those  names 
K 


74  NAMES    AND    PROPOSITIONS. 

have,  or  that  they  have  not,  been  conventionally  assigned  to  the  same 
individual ;  there  would  be  little  to  attract  to  such  propositions  the 
attention  of  philosophers.  But  the  class  of  merely  verbal  propositions 
embraces  not  only  much  more  than  these,  but  much  more  than  any 
propositions  which  at  first  sight  present  themselves  as  verbal ;  compre- 
hending a  kind  of  assertions  which  have  been  regarded  not  only  as 
relating-  to  things,  but  as  having  actually  a  more  intimate  relation  with 
them  than  any  other  propositions  whatever.  The  student  in  philosophy 
will  perceive  that  I  allude  to  the  distinction  on  which  so  much  stress 
was  laid  by  the  schoolmen,  and  which  has  been  retained  either  under 
the  same  or  under  other  names  by  most  metaphysicians  to  the  present 
day,  viz.,  between  what  were  called  essential,  and  what  were  called 
accidental  propositions,  and  between  essential  and  accidental  properties 
or  attributes. 

§  2.  Almost  all  metaphysicians  prior  to  Locke,  as  well  as  many  since 
his  time,  have  made  a  great  mystery  of  Essential  Predication,  and  of 
predicates  which  were  said  to  be  of  the  essence  of  the  subject.  The 
essence  of  a  thing,  they  said,  was  that  without  which  the  thing  could 
neither  be,  nor  be  conceived  to  be.  Thus,  rationality  was  of  the  es- 
sence of  man,  becalise  without  rationality,  man  could  not  be  conceived 
to  exist.  The  different  attributes  which  made  up  the  essence  of  the 
thing,  were  called  its  essential  properties ;  and  a  proposition  in  which 
any  of  these  were  predicated  of  it,  was  called  an  Essential  Proposi- 
tion, and  was  considered  to  go  deeper  into  the  nature  of  the  thing,  and 
to  convey  more  important  information  respecting  it,  than  any  other 
proposition  could  do.  All  properties,  not  of  the  essence  of  the  thing, 
were  called  its  accidents ;  were  supposed  to  have  nothing  at  all,  or 
nothing  comparatively,  to  do  with  its  inmost  nature ;  and  the  proposi- 
tions in  which  any  of  these  were  predicated  of  it  were  called  Acciden- 
tal Propositions.  A  connexion  may  be  traced  between  this  distinction, 
which  originated  with  the  schoolmen,  and  the  well  knoA\-n  dogmas  of 
substanticE  secundce,  or  general  substances,  and  substantial  forms,  doc- 
trines which  under  varieties  of  language  pervaded  alike  the  Aristote- 
lian and  the  Platonic  schools,  and  of  which  more  of  the  spirit  has  come 
down  to  modern  times  than  might  be  conjectured  from  the  disuse  of 
the  phraseology.  The  false  ^-iews  of  the  nature  of  classification  and 
generalization  which  prevailed  among  the  schoolmen,  and  of  which 
these  dogmas  were  the  technical  expression,  afford  the  only  explanation 
which  can  be  given  of  their  ha\"ing  misunderstood  the  real  nature  of 
those  Essences  which  held  so  conspicuous  a  place  in  their  philosophy. 
They  said,  truly,  that  man  cannot  be  conceived  without  rationality. 
But  though  man  cannot,  a  being  may  be  conceived  exactly  like  a  man 
in  all  points  except  that  one  quality,  and  those  others  which  are  the 
conditions  or  consequences  of  it.  All  therefore  winch  is  really  true  in 
the  assertion  that  man  cannot  be  conceived  without  rationality,  is  only, 
that  if  he  had  not  rationality,  he  would  not  be  reputed  a  man.  There 
is  no  impossibility  in  conceiving  the  thing,  nor,  for  aught  we  know,  in 
its  existing  :  the  impossibility  is  in  the  conventions  of  language,  which 
will  not  allow  the  thing,  even  if  it  exist,  to  be  called  by  the  name  which 
is  reserved  for  rational  beings.  Rationality,  in  short,  is  involved  in  the 
meaning  of  the  word  man ;  it  is  one  of  the  attributes  connoted  by  the 
name.     The  essence  of  man,  simply  means  the  whole  of  the  attributes 


VERBAL    AND    REAL    PROPOSITIONS.  75 

connoted  by  the  word  ;  and  any  one  of  those  attributes  taken  singly,  is 
an  essential  property  of  man. 

The  doctiines  which  prevented  the  real  meaning  of  Essences  from 
being  understood,  not  having  assumed  so  settled  a  shape  in  the  time  of 
Aristotle  and  his  immediate  followers  as  was  afterwards  given  to  them 
by  the  Realists  of  the  middle  ages,  we  find  a  nearer  approach  to  tiiie 
views  of  the  subject  in  the  writings  of  the  ancient  Aristotelians  than  in 
their  more  modem  followers.  Poi-phyry,  in  his  Lsagoge,  approached  so 
near  to  the  true  conception  of  essences,  that  only  one  step  remained  to 
be  taken,  but  this  stej?,  so  easy  in  appearance,  was  reserved  for  the 
Nominalists  of  modern  times.  By  altering  any  property,  not  of  the 
essence  of  the  thing,  you  merely,  according  to  Poq>hyry,  made  a  differ- 
ence in  it ;  you  made  it  dXXolov :  but  by  altering  any  property  which 
was  of  its  essence,  you  made  it  another  thing,  aXko*  To  a  modei-n  it 
is  obvious  that  between  the  change  which  only  makes  a  thing  diiferent, 
and  the  change  which  makes  it  another  thing,  the  only  distinction  is 
that  in  the  one  case,  though  changed,  it  is  still  called  by  the  same  name. 
Thus,  pound  ice  in  a  mortar,  and  being  still  called  ice,  it  is  only  made 
aXXolov :  melt  it,  and  it  becomes  aXXo,  another  thing,  namely,  water. 
Now  it  is  really  the  same  thing,  i.  e.,  the  same  paiticles  of  matter,  in 
both  cases ;  and  you  cannot  so  change  an\1;hing  that  it  shall  cease  to  be 
the  same  tiling  in  this  sense.  The  identity  which  it  can  be  deprived 
of  is  merely  that  of  the  name  :  when  the  thing  ceases  to  be  called  ice, 
it  becomes  another  thing,  its  essence,  what  constitutes  it  ice,  is  gone; 
while,  so  long  as  it  continues  to  be  so  called,  nothing  is  gone  except 
some  of  its  accidents.  But  these  reflections,  so  easy  to  us,  would  have 
been  difficult  to  persons  who  thought,  as  most  of  the  AristoteliaiLS  did, 
that  objects  were  made  what  they  were  called,  that  ice  (for  instance) 
was  made  ice,  not  by  the  possession  of  certain  properties  to  which 
mankind  have  chosen  to  attach  that  name,  but  by  participation  in  the 
nature  of  a  certain  general  substance,  called  Ice  in  general,  which  sub- 
stance, together  with  all  the  propoities  that  belonged  to  it,  inhered  in 
every  indi\-idual  piece  of  ice.  As  they  did  not  consider  these  univei-sal 
substances  to  be  attached  to  all  general  names  but  only  to  some,  they 
thought  that  an  object  boiTowed  only  a  part  of  its  properties  fi'om  an 
universal  substance,  and  that  the  rest  belonged  to  it  individually :  the 
fonner  they  called  its  essence,  and  the  latter  its  accidents.  The  scho- 
lastic doctrine  of  essences  long  sur%'ived  the  theory  on  which  it  rested, 
that  of  the  existence  of  real  entities  corresponding  to  general  terras ; 
and  it  was  reserved  for  Locke,  at  the  end  of  the  seventeenth  century, 
to  convince  philosoj^hers  that  the  supposed  essences  of  classes  were 
merely  the  signification  of  their  names;  nor,  among  the  signal  services 
which  that  great  man  rendered  to  philosophy,  was  there  one  more 
needful  or  more  valuable.! 

♦  KaQolov  /isv  ovv  rruaa  (Jta^opri  vpoiryivo/xhfT)  rivl  irepoiov  ttoieV  ulV  a!  fiiv  kocvu^ 
re  Kai  I6iu^  (differences  in  the  accidental  properties)  uM.oiov  noiovGiv  al  6e  idiairara, 
(differences  in  the  essential  properties)  uX?m. — Porph.,  Isag.,  cap.  iii. 

t  Few  among  the  great  names  in  philosophy  have  met  with  a  harder  measure  of  justice 
from  the  present  generation  than  Locke;  the  unquestioned  founder  of  the  analytic  philos- 
ophy of  mind,  but  whose  doctrines  were  first  caricatured,  then,  when  the  reaction  arrived, 
ca^t  off"  by  the  prevailing  school  even  with  contumely,  and  who  is  now  regarded  by  one  of 
the  conflicting  parties  in  philosophy  as  an  apostle  of  heresy  and  sophistry,  while  among 
those  who  still  adhere  to  the  standard  which  he  raised,  there  has  been  a  disposition  in  later 
times  to  sacrifice  his  reputation  in  favor  of  Hobbes  ;  a  great  writer,  and  a  great  thinker  for 
his  lime,  but  inferior  to  Locke  not  only  in  sober  judgment  but  even  in  profundity  and  origi- 


76  NAMES    AND    PROPOSITIONS. 

Now,  as  the  most  familiar  of  the  general  names  predicable  of  an 
object  usually  connotes  not  one  only,  but  several  attributes  of  the  object, 
each  of  which  atti'ibutes  separately  forms  also  the  bond  of  union  of  some 
class,  and  the  meaning  of  some  general  name ;  we  may  predicate  of  a 
name  which  connotes  a  variety  of  attributes,  another  name  which  con- 
notes only  one  of  these  atti-ibutes,  or  some  smaller  number  of  them  than 
all.  In  such  cases,  the  universal  affiiTuative  proposition  will  be  true  ; 
since  whatever  possesses  the  whole  of  any  set  of  attributes,  must  pos- 
sess any  part  of  that  same  set.  A  proposition  of  this  sort,  however, 
conveys  no  information  to  any  one  who  previously  understood  the  whole 
meaning  of  the  terms.  The  propositions,  Eveiy  man  is  a  corporeal 
being.  Every  man  is  a  li\'ing  creature,  Every  man  is  rational,  convey 
no  knowledge  to  any  one  who  was  already  aware  of  the  entire  meaning 
of- the  word  man,  for  the  meaning  of  the  word  includes  all  this:  and^ 
that  every  man  has  the  attributes  connoted  by  all  these  predicates,  is 
already  asserted  when  he  is  called  a  man.  Now,  of  this  nature  are  all 
the  propositions  which  have  been  called  essential ;  they  are,  in  fact, 
identical  propositions. 

It  is  true  that  a  proposition  which  predicates  any  attribute,  even 
though  it  be  one  implied  in  the  name,  is  in  most  cases  understood  to 
involve  a  tacit  assertion  that  there  exists  a  thing  coiTesponding  to  the 
name,  and  possessing  the  attributes  connoted  by  it ;  and  this  implied 
assertion  may  convey  information,  even  to  those  who  understood  the 
meaning  of  the  name.  But  all  information  of  this  sort,  conveyed  by 
all  the  essential  propositions  of  which  man  can  be  made  the  subject,  is 
included  in  the  assertion,  Men  exist.  And  this  assumption  of  real  ex- 
istence is  after  all  only  the  result  of  an  imperfection  of  language.  It 
arises  from  the  ambiguity  of  the  copula,  which,  in  addition  to  its  proper 
office  of  a  mark  to  shoAV  that  an  assertion  is  made,  is  also,  as  we  have 
formerly  remarked,  a  concrete  word  connoting  existence.  The  actual 
existence  of  the  subject  of  the  proposition  is  therefore  only  apparently, 
not  really,  implied  in  the  predication,  if  an  essential  one :  we  may 
say,  A  ghost  is  a  disembodied  spirit,  without  believing  in  ghosts.  But 
an  accidental,  or  non-essential,  affirmation,  does  imply  the  real  exist- 
ence of  the  subject,  because  in  the  case  of  a  non-existent  subject  there 
is  nothing  for  the  proposition  to  assert.  Such  a  proposition  as.  The 
ghost  of  a  murdered  person  haunts  the  couch  of  the  murderer,  can 
only  have  a  meaning  if  understood  as  implying  a  belief  in  ghosts  ;  for 
since  the  signification  of  the  word  ghost  implies  nothing  of  the  kind, 
the  speaker  either  means  nothing,  or  means  to  assert  a  thing  which 
he  -vrishes  to  be  believed  really  to  have  taken  place. 

It  will  be  hereafter  seen  that  when  any  important  consequences 
seem  to  follow,  as  in  mathematics,  from  an  essential  proposition,  or,  in 
other  words,  from  a  proposition  involved  in  the  rneaning  of  a  name, 
what  they  really  flow  from  is  tlie  tacit  assumption  of  the  real  existence 

nal  genius.  Locke,  the  most  candid  of  philosophers,  and  one  whose  speculations  bear  on 
every  subject  the  strongest  marks  of  having  been  wrought  out  from  the  materials  of  his 
own  mind,  has  been  mistaken  for  an  unworthy  plagiarist,  while  Hobbes  has  been  extolled 
as  having  anticipated  many  of  his  leading  doctrines.  He  did  anticipate  many  of  them,  and 
the  present  is  an  instance  in  what  manner  it  was  generally  done.  They  both  rejected  the 
scholastic  doctrine  of  essences  ;  but  Locke  understood  and  explained  what  these  supposed 
essences  really  were  ;  Hobbes,  instead  of  explaining  the  distinction  between  essential  and 
accidental  properties,  and  between  essential  and  accidental  propositions,  jumped  over  it, 
and  gave  a  definition  which  suits  at  most  only  essential  propositions,  and  scarcely  those,  as 
the  definition  of  Proposition  in  general. 


VERBAL    AND    UEAL    mOPOSITIONS.  77 

of  the  object  so  named.  Apart  from  this  assmnption  of  real  existence, 
the  class  of  propositions  in  which  the  predicate  is  of  the  essence  of  the 
subject  (that  is,  in  which  the  ])redicate  connotes  the  whole  or  j)art  of 
Avhat  the  subject  connotes,  but  nothing  besides),  answers  no  purpose 
but  that  of  unfolding  the  whole  or  sonae  part  of  the  meaning  of  the 
name,  to  those  \vho  did  not  previously  know  it.  Accordingly,  tlu;  most 
useful,  and  in  strictness  the  only  useful,  kind  of  essential  propositions, 
are  Definitions :  which,  to  be  complete,  should  unfold  the  whole  of 
what  is  involved  in  the  meaning  of  the  word  defined ;  that  is  (when  it 
is  a  connotative  word),  the  whole  of  what  it  connotes.  In  defining  a 
name,  however,  it  is  not  usual  to  specify  its  entire  connotation,  but  so 
much  only  as  is  sufficient  to  mark  out  the  objects  usually  denoted  by 
it  from  all  other  known  objects.  And  sometimes  a  merely  accidental 
property,  not  involved  in  the  meaning  of  the  name,  answers  this  pur- 
pose equally  well.  The  various  kinds  of  definition  which  these  dis- 
tinctions give  rise  to,  and  the  pui-poses  to  which  they  are  respectively 
subservient,  will  be  minutely  considered  in  the  proper  place. 

§  3.  According  to  the  above  view  of  essential  propositions,  no  prop- 
osition can  be  reckoned  such  which  relates  to  an  individual  by  name, 
that  is,  in  which  the  subject  is  a  proper  name.  Individuals  have  no 
essences.  When  the  schoolmen  talked  of  the  essence  of  an  individual, 
they  did  not  mean  the  properties  imphed  in  its  name,  for  the  names 
of  individuals  imply  no  properties.  They  regarded  as  of  the  essence  of 
an  individual  whatever  was  of  the  essence  of  the  species  in  which  they 
were  accustomed  to  place  that  individual ;  ^.  e.,  of  the  class  to  which 
it  was  most  familiarly  referred,  and  to  which,  therefore,  they  conceived 
that  it  by  natm-e  belonged.  Thus,  because  the  proposition,  Man  is  a 
rational  being,  was  an  essential  proposition,  they  affirmed  the  same 
thing  of  the  proposition,  Julius  Ctesar  is  a  rational  being.  This  fol- 
lowed veiy  naturally  if  genera  and  species  wei'e  to  be  considered  as 
entities,  distinct  from,  but  inhering  in,  the  individuals  composing  them. 
If  man  was  a  substance  inhering  in  each  individual  man,  the  essence  of 
man  (whatever  that  might  mean),  was  naturally  supposed  to  accom- 
pany it ;  to  inhere  in  John  Thompson,  and  form  the  common  essence 
of  Thompson  and  Julius  CcBsar.  It  might  then  be  fairly  said,  that  ra- 
tionality, being  of  the  essence  of  Man,  was  of  the  essence  also  of 
Thompson.  But  if  Man  altogether  be  only  the  individual  men  and  a 
name  bestowed  upon  them  in  consequence  of  certain  common  proper- 
ties, what  becomes  of  John  Thompson's  essence  % 

A  fundamental  error  is  seldom  expelled  from  philosophy  by  a  single 

victory.     It  retreats  slowly,  defends  every  inch  of  gi'ound,  and  often 

retains  a  footing  in  some  remote  fastness  after  it  has  been  driven  from 

\      the  open  country.     The  essences  of  individuals  were  an  unmeaning 

■  ';  figment  aiising  from  a  misapprehension  of  the  essences  of  classes,  yet 
even  Locke,  when  he  extirpated  the  parent  error,  could  not  shake 
liimself  free  from  that  which  was  its  fruit.  He  distinguished  two  sorts 
of  essences.  Real  and  Nominal.  His  nominal  essences  were  the  es- 
sences of  classes,  explained  nearly  as  we  have  now  explained  them. 
Nor  is  anything  wanting  to  render  the  third  book  of  Locke's  Essay  a 

•^  .  nearly  perfect  treatise  on  the  connotation  of  names,  except  to  free  its 
language  from  the  assumption  of  what  are  called  Abstract  Ideas,  which 
unfortunately  is  involved  in  the  phraseology,  although  not  necessarily 


78  NAMES     AND    PROPOSITIONS. 

connected  with  the  thoughts,  contained  in  that  immortal  Third  Book.* 
But,  besides  nominal  essences,  he  admitted  real  essences,  or  essences 
of  individual  objects,  which  he  supposed  to  be  the  causes  of  the  sensi- 
ble properties  of  those  objects.  We  know  not  (said  he),  what  these 
are  (and  this  acknowledgment  rendered  the  fiction  comparatively  in- 
nocuous) ;  but  if  we  did,  we  could,  from  them  alone,  demonstrate  the 
sensible  properties  of  the  object,  as  the  properties  of  the  triangle  are 
demonstrated  from  the  definition  of  the  triangle.  I  shall  have  occasion 
to  revert  to  this  theory  in  treating  of  Demonstration,  and  of  the  con- 
ditions under  which  one  property  of  a  thing  admits  of  being  demon- 
strated from  another  property.  It  is  enough  here  to  remark  that 
according  to  this  definition,  the  real  essence  of  an  object  has,  in  the 
progress  of  physics,  come  to  be  conceived  as  nearly  equivalent,  in  the 
case  of  bodies,  to  their  coi-puscular  stiiicture  :  what  it  is  now  supposed 
to  mean  in  the  case  of  any  other  entities,  I  would  not  take  upon  my- 
self to  define. 

§  4.  An  essential  proposition,  .then,  is  one  which  is  purely  verbal ; 
which  asserts  of  a  thing  under  a  particular  name,  only  what  is  asserted 
of  it  in  the  fact  of  calling  it  by  that  name ;  and  which  therefore  either 
gives  no  infonnation,  or  gives  it  respecting  the  name,  not  the  thing. 
Non-essential,  or  accidental  propositions,  on  the  contrary,  may  be  called 
Real  Propositions,  in  opposition  to  Verbal.  They  predicate  of  a  thing, 
some  fact  not  involved  in  the  signification  of  the  name  by  which  the 
proposition  speaks  of  it ;  some  attribute  not  connoted  by  that  name. 
Such  are  all  propositions  concerning  things  individually  designated, 
and  all  general  or  particular  propositions  in  which  the  predicate  con- 
notes any  atti-ibute  not  connoted  by  the  subject.  All  these,  if  true,  add 
to  our  knowledge  :  they  convey  infonnation  not  already  involved  in  the 
names  employed.  Wlien  I  am  told  that  all,  or  even  that  some  objects, 
w^hich  have  certain  qualities,  or  which  stand  in  certain  relations,  have 
also  certain  other  qualities,  or  stand  in  certain  other  relations,  I  learn 
from  this  proposition  a  new  fact ;  a  fact  not  included  in  my  knowledge 
of  the  meaning  of  the  words,  nor  even  of  the  existence  of  Things 
answering  to  the  signification  of  those  words.  It  is  this  class  of  propo- 
sitions only  which  are  in  themselves  instructive,  or  fi-om  which  any 
instructive  propositions  can  be  infeiTed. 

Nothing  has  probably  conti'ibuted  more  to  the  opinion  so  commonly 
prevalent  of  the  futility  of  the  school  logic,  than  the  circumstance  tliat 
almost  all  the  examples  used  in  the  common  school  books  to  illustrate 
the  doctrines  of  predication  and  of  the  syllogism,  consist  of  essential 
propositions.  They  were  usually  taken  either  from  the  branches  or 
from  the  main  trunk  of  the  Predicamental  Tree,  which  included  nothing 
but  what  was  of  the  essence  of  the  species  :  Ovme  corpus  est  suhstantia, 
Omne  animal  est  corpus,  Omnis  homo  est  corpus,  Omnis  homo  est  ani- 
mal, Omnis  homo  est  rationally,  and  so  forth.     It  is  far  from  wonderftil 

*  The  always  acute  and  often  profound  author  of  .4rt  OntUne  of  Sematology  {Mr.  B.  H. 
Smart)  justly  says,  '•  Locke  will  be  much  more  intelligible  if,  in  the  majority  of  places,  we 
substitute  '  the  knowledge  of  for  what  he  calls,  '  the  idea  of  "  (p.  10).  Among  the  many 
criticisms  upon  Locke's  use  of  the  word  Idea,  this  is  the  only  one  which,  as  it  appears  to 
me,  precisely  hits  the  mark ;  and  I  quote  it  for  the  additional  reason  that  it  precisely  ex- 
presses the  point  of  difterence  respecting  the  import  of  Propositions,  between  my  view  and 
what  I  have  called  the  Conceptualist  view  of  them.  \Vhere  a  Conceptualist  says  that  a 
name  or  a  proposition  expresses  our  Idea  of  a  thing,  I  should  generally  say  (instead  of  our 
Idea)  our  Knowledge,  or  Belief,  concerning  the  thing  itself. 


VERBAL    AND    REAL    TROPOSITIONS.  79 

that  the  syllogistic  art  shovikl  have  been  thought  to  be  of  no  use  in 
assisting  coiToct  reasoning,  when  almost  tlie  only  propositions  which, 
in  the  hands  of  its  professed  teachers,  it  was  employed  to  prove,  were 
such  as  every  one  assented  to  without  proof  the  moment  he  compre- 
hended the  meaning  of  the  words :  and  stood  exactly  on  a  level,  in 
point  of  evidence,  with  the  premises  fi-om  which  they  were  drawn.  I 
have,  therefore,  throughout  this  work,  studiously  avoided  the  employ- 
ment of  essential  propositions  as  examples,  except  where  the  nature  of 
the  principle  to  be  illustrated  specifically  required  them. 

§  5.  With  respect  to  propositions  which  do  convey  information, 
which  assert  something  of  a  Thing,  under  a  name  that  does  not  already 
presuppose  what  is  about  to  be  asserted,  there  are  two  different  aspects 
in  which  these,  or  rather  such  of  them  as  are  general  propositions,  may 
be  considered  :  we  may  either  look  at  them  as  portions  of  specula- 
tive ti-uth,  or  as  memoranda  for  practical  use.  According  as  we  con- 
sider propositions  in  one  or  the  other  of  these  lights,  their  import  may 
be  conveniently  expressed  in  one  or  in  the  other  of  two  formulas. 

According  to  the  formula  which  we  have  hitherto  employed,  and 
which  is  best  adapted  to  express  the  import  of  the  proposition  as  a 
portion  of  our  theoretical  knowledge.  All  men  are  mortal,  means  that 
the  attributes  of  man  are  always  accompanied  by  the  attribute  mor-  . 
tality  :  No  men  are  gods,  means  that  the  attributes  of  man  are  never 
accompanied  by  the  attributes,  or  at  least  never  by  all  the  attributes, 
of  a  god.  But  when  the  proposition  is  considered  as  a  memorandum 
for  practical  use,  we  shall  find  a  different  mode  of  expressing  the  same 
meaning  better  adapted  to  indicate  the  oflfice  which  the  proposition 
pei'foiTns.  The  practical  use  of  a  proposition  is  to  apprise  or  remind 
us  what  we  have  to  expect  in  any  individual  case  which  comes  within 
die  assertion  contained  in  the  proposition.  In  reference  to  this  pui'- 
pose,  the  proposition,  All  men  are  mortal,  means  that  the  attributes  of 
man  are  evidence  of,  are  a  marJc  of,  mortality ;  an  indication  by  which 
the  presence  of  that  attribute  is  made  manifest.  No  men  are  gods, 
means  that  the  atti'ibutes  of  man  are  a  mark  or  evidence  that  some  or 
all  of  the  attributes  of  a  god  are  not  there ;  that  where  the  fonner  are, 
we  need  not  ex])ect  to  find  the  latter. 

These  two  forms  of  expression  are  at  bottom  equivalent ;  but  the 
one  points  the  attention  more  directly  to  what  a  jjroposition  means,  the 
latter  to  the  manner  in  which  it  is  to  be  used. 

Now  it  is  to  be  observed  that  Reasoning  (the  subject  to  which  we 
are  next  to  proceed)  is  a  process  into  which  propositions  enter  not  as 
ultimate  results,  but  as  means  to  the  establishment  of  other  proposi- 
tions. We  may  expect,  therefore,  that  the  mode  of  exhibiting  the 
import  of  a  general  proposition  which  shows  it  hi  its  application  to 
practical  use,  will  best  express  the  fimction  which  propositions  per- 
form in  Reasoning.  And  accordingly,  in  the  theory  of  Reasoning,  the 
mode  of  vie\\dng  the  subject  wliich  considers  a  Proposition  as  asserting 
that  one  fact  or  phenomenon  is  a  marh  or  evidence  of  another  fact  or 
phenomenon,  will  bo  found  almost  indispensa])le.  Ff)r  tlie  purposes 
of  tliat  Theory,  the  best  mode  of  defining  the  import  of  a  proposition 
is  not  the  mode  which  shows  the  most  clearly  what  it  is  in  itself,  but 
that  which  most  distinctly  suggests  the  manner  in  which  it  may  be 
made  available  for  advancing  from  it  to  other  propositions. 


80  NAMES    AND    PROPOSITIONS. 

CHAPTER  VII. 

OF  THE  NATURE  OF  CLASSIFICATION,  AND  THE  FIVE  PREDICABLES. 

§  1.  In  examining  into  the  nature  of  general  propositions,  we  have 
adverted  much  less  than  is  usual  vi^ith  Logicians,  to  the  ideas  of  a 
Class,  and  Classification ;  ideas  which,  since  the  Realist  doctrine  of 
General  Substances  went  out  of  vogue,  have  formed  the  basis  of  almost 
every  attempt  at  a  philosophical  theory  of  general  terms  and  general 
projjositions.  We  have  considered  general  names  as  having  a  mean- 
ing, quite  independently  of  their  being  the  names  of  classes.  That 
circumstance  is  in  truth  accidental,  it  being  wholly  immaterial  to  the 
signification  of  the  name  whether  there  are  many  objects  or  only  one 
to  which  it  happens  to  be  applicable,  or  whether  there  be  any  at  all. 
God  is  as  much  a  general  term  to  the  Christian  or  the  Jew  as  to  the 
Polytheist ;  and  dragon,  hipj30gi-iff,  chimera,  mennaid,  ghost,  are  as 
much  so  as  if  real  objects  existed,  corresponding  to  those  names. 
Every  name  the  signification  of  which  is  constituted  by  attributes,  is 
potentially  a  name  of  an  indefinite  number  of  objects  ;  but  it  needs 
not  be  actually  the  name  of  any;  and  if  of  any,  it  may  be  the  name  of 
only  one.  As  soon  as  we  employ  a  name  to  connote  atti'ibutes,  the 
things,  be  they  more  or  fewer,  which  happen  to  possess  those  attri- 
butes, are  constituted,  ipso  facto,  a  class.  But  in  predicating  the  name 
we  predicate  only  the  attributes ;  and  the  fact  of  belonging  to  a  class 
does  not,  in  ordinary  cases,  come  into  view  at  alb 

Although,  however.  Predication  does  not  presuppose  Classification, 
and  although  the  theory  of  Names  and  of  Propositions  is  not  cleared 
up,  but  only  encumbered,  by  intruding  the  idea  of  classification  into 
it,  there  is  nevertheless  a  close  connexion  between  Classification,  and 
the  employment  of  General  Names.  By  every  general  name  which 
we  introduce,  we  create  a  class,  if  there  be  any  existing  things  to 
compose  it ;  that  is,  any  Things  corresponding  to  the  signification  of 
the  name.  Classes,  therefore,  mostly  owe  their  existence  to  general 
language.  But  general  language,  also,  though  that  is  not  the  most 
common  case,  sometimes  owes  its  existence  to  classes.  A  general, 
which  is  as  much  as  to  say  a  significant,  name,  is  indeed  mostly  intro- 
duced because  we  have  a  signification  to  express  by  it ;  because  we 
need  a  word  by  means  of  which  to  predicate  the  attributes  which  it 
connotes.  But  it  is  also  true  that  a  name  is  sometimes  introduced  be- 
cause we  have  found  it  convenient  to  create  a  class ;  because  we  have 
thought  it  useful  for  the  regulation  of  our  mental  operations,  that  a 
certain  gi'oup  of  objects  should  be  thought  of  together.  A  naturalist, 
for  purposes  connected  with  his  particular  science,  sees  reason  to  dis- 
tribute the  animal  or  vegetable  creation  into  certain  groups  rather 
than  into  any  others,  and  he  requires  a  name  to  bind,  as  it  were,  each 
of  his  groups  together.  It  must  not,  however,  be  supposed  that  such 
names,  when  introduced,  differ  in  any  respect,  as  to  their  mode  of  sig- 
nification, from  other  connotative  names.  The  classes  which  they  de- 
note are,  as  much  as  any  other  classes,  constituted  by  certain  common 
atti-ibutes ;  and  their  names  are  significant  of  those  attributes,  and  of 
nothing  else.  The  names  of  Cuvier's  classes  and  orders,  Planti- 
grades, Digitigrades,  &c.,  are  as  much  the  expression  of  attiibutes,  as 


CLASSIFICATION    A\D    THE    PREDICABLES.  81 

if  those  names  had.  preceded,  Instead  of  gi'owing  out  of,  his  Classifica- 
tion of  Animals.  The  only  peculiarity  of  the  case  is,  that  the  conve- 
nfence  of  classification  was  here  the  primary  motive  for  liitioducing  the 
n'aimes ;  while  in  other  cases  the  name  is  introduced  as  a  means  of 
predication,  and  the  formation  ef  a  class  denoted  by  it  is  only  an  indi- 
rect consequence. 

The  principles  which  ought  to  regulate  Classification  as  a  logical 
process  subservient  to  the  investigation  of  truth,  cannot  be  discussed  to 
any  pm-pose  until  a  much  later  stage  of  oui*  inquiry.  But,  of  classifi- 
cation as  resulting  from,  and  im2)lied  in,  the  fact  of  employing  general 
language,  we  cannot  forbear  to  treat  here,  without  leaving  the  theory 
of  general  names,  and  of  their  employment  in  oredication,  mutilated 
and  formless. 

§  2.  This  portion  of  the  theory  of  general  language  is  the  subject  of 
what  is  teiTned  the  doctrine  of  the  Predicables ; — a  set  of  distinctions 
handed  down  from  Aristotle  and  his  follower.  Porphyry,  many  of 
which  have  taken  a  finn  root  in  scientific,  and  some  of  them  even  in 
popular,  phraseology.  The  Predicables  are  a  five-fold  division  of  Gen- 
eral Names,  not  grounded  as  usual  upon  a  difference  in  their  mean- 
ing, that  is,  in  the  attribute  which  they  connote,  but  upon  a  difference 
in  the  kind  of  class  which  they  denote.  We  may  predicate  of  a  thing 
five  different  varieties  of  class-name  :-— 

A  genus  of  the  thing         {yevog). 

A  species  (eldog). 

A  differentia  (dicupopd). 

A  proprium  {I6i6v^. 

An  accidens  (avfi[3E(i7]K6g). 

It  is  to  be  remarked  of  these  distinctions,  that  they  express,  not 
what  the  predicate  is  in  its  own  meaning,  but  what  relation  it  bears  to 
the  subject  of  which  it  happens  on  the  particular  occasion  to  be  predi- 
cated. There  are  not  some  names  which  are  exclusively  genera,  and 
others  which  are  exclusively  species,  or  differentia? :  but  the  same 
name  is  refen-ed  to  one  or  another  Predicable,  according  to  the  sub- 
ject of  which  it  is  predicated  on  the  particular  occasion.  Animal,  for 
instance,  is  a  genus  with  respect  to  Man,  or  John ;  a  species  with  re- 
spect to  Substance  or  Being.  Rectangular  is  one  of  the  Differentia  of 
a  geometrical  square  :  it  is  merely  one  of  the  Accidentia  of  the  table 
on  which  I  am  wiiting.  The  words,  genus,  species,  &c.,  are  therefore 
relative  terms  ;  they  ai'e  names  applied  to  certain  predicates,  to  ex- 
press the  relation  between  them  and  some  given  subject :  a  relation 
grounded,  as  we  shall  see,  not  upon  what  the  predicate  connotes,  but 
upon  the  class  which  it  denotes,  and  upon  the  place  which,  in  some 
given  classification,  that  class  occupies  relatively  to  tlie  particular 
subject. 

§  3.  Of  these  five  names,  two.  Genus  and  Species,  arc  not  only  used 
by  naturalists  in  a  technical  acceptation  not  precisely  agreeing  with 
their  philosophical  meaning,  but  have  also  acquired  a  popular  accep- 
tation, much  more  general  than  either.  In  this  popular  sense  any  two 
classes,  one  of  which  includes  the  whole  of  the  other  and.  more,  may 
l)e  called  a  Genus  and  a  Species.  Such,  for  instance,  are  Animal  and 
Man;  Man  and  Mathematician.  'Animal  is  a  genus;  Man  and  Brule 
L 


82 


NAMES    AND    PROPOSITIONS. 


are' its  two.  species;  or  we  may  divide  it  into  a  greater  number  of 
epecies,  as  man,  horse,  dog,  &c.  Biped,,  ot  two-footed  anmuil,  may 
also  be  considered  a  genus,  of  which  man  and  bird  are  two  species. 
Taste  is  a  genus,  of  which  sweet  taste,  sour  taste,  sak  taste,  &c.,  are 
species.  Virtue  is  a  -genus  ;  justice,  prudence,  courage,  fortitude, 
generosity,  &c.,  are  its  species. 

The  same  class  which  is  a  genus  with  reference  to  the  sub-classes 
or  species  included  in  it,  may  be  itself  a  species  with  reference  to  a 
more  comprehensive,  or,  as  it  is  often  called,  a  superior,  genus.  Man 
is  a  species  with  reference  to  animal,  but  a  genus  with  reference  to 
the  species  mathematician.  Animal  is  a  genus,  divided  into  two 
species,  man  and  brute;  but  animal  is  also  a  species,  which,  with 
another  species,  vegetable,  makes  up  the  genus,  organized  being. 
Biped  is  a  genus  with  reference  to  man  and  bird,  but  a  species  with 
respect  to  the  superior  genus,  animal.  Taste  is  a  genus  divided  into 
species,  but  also  a  species  of  the  genus  sensation.  Virtue,  a  genus 
with  reference  to  justice,  temperance,  &c.,  is  one  of  the  species  of  the 
genus,  mental  quality; 

In  this  jjopular  "sense  the  words  Genus  and  Species  have  passed 
into  common  discourse.  And  it  should  be  observed  that,  in  ordinary 
parlance,  not  the  name  of  the  class,  but  the  class  itself,  is  said  to  be 
the  genus  or  species  ;  not,  of  course,  the  class  in  the  sense  of  each 
individual  of  that  class,  but  the  individuals  collectively,  considered  as 
an  aggi-egate  whole  ;  the  names  by  which  the  class  is  designated  being 
then  called  not  the  genus -or  species,  but  the  generic  or  specific  name. 
And  this  is  an  admissible  fonn  of  expression ;  nor  is  it  of  any  import- 
ance which  of  the  two  modes  of  speaking  we  adopt,  provided  the  rest 
of  our  language  is  consistent  with  it ;  but  if  we  call  the  class  itself  the 
genus,  we  must  not  talk  of  predicating  the  genus.  We  predicate  of 
man  th6  name  niortal ;  and  by  predicating  the  name,  we  may  be  said, 
in  an  intelligible  sense,  to  predicate  what  the  name  expresses,  the 
attribute  mortality ;  but  in  no  allowable  sense  of  the  word  predication 
do  we  predicate  of  man,  the  class  mortal.  We  predicate  of  him  the 
fact  of  belongi'ng  to  the  class. 

By  the  Ai-istotelian  logicians,  the  terms  genus  and  species  were 
used  in  a  more  restricted  sense.  They  did  not  iidmit  every'  class 
which  could  be  divided  into  other  classes  to  be  a  genus,  or  every  class 
which  could  be  included  in  a  larger  class  to  be  a  species.  Animal 
was  by  them  'considered  a  genus  :  and  man  and  brute  co-ordinate 
species  under  that  genus  :  hiped  would  not  have  been  admitted  to  be 
a  genus  with  reference  to  man,  but  a  proprium  or  accidens  ohly.  It 
was  requisite,  according  to  their  theory,  that  geiius  and  speciesxshould 
be  of  the  essence  of  the  subject.  Animal  was  of  the  essence  of  man ; 
hiped  was  not.  And  in  every  classification  they  considered  some  one 
class  as  the  lowest  or  injima  species ;  man,  for  instance,  was  a  lowest 
species.  Any  further  divisions  into  which  the  class  might  be  capable 
of  being  broken  down,  as  man  into  white,  black,  and  red  man,  or  into 
priest  and  layman,  they  did  not  admit  to  be  species. 

It  has  been  seen,  however,  in  the  preceding, chapter,  that  the  dis- 
tinction between  the  essence  of  a  class,  and  the  attributes  or  properties 
which  are  not  of  its  essence^-^a  distinction  which  has  given  occasion 
to  so  much  abstruse  speculation,  and  to  which  so  mysterious  a  charac- 
ter was  formerly,  and  by  many  wi'iters  is  still,  attached, — amounts  to 


CLASSIFICATION    AND    TUB    PREDICABLES.  83 

nothing  more  than  the  JifTerence  between  those  attributes'  of  the  class 
which  are,  and  those  which  are  not,  involved  in  the  signification  of  the 
class-name.  As  applied  to  individuals,  the  word  Essence,  we  found, 
has  no  meaning,  except  in  connexion  with  the  exploded  tenets  of  the 
Realists ;  and  what  the  schoohnen  chose  to  call  the  essence  of  an  indi- 
^■idual,'wa6  simply  the  essence  of  the  class  to  which  that  individual 
was  most  familiarly  referred. 

Is  there  no  difference,  then,  except  this  merely  verbal  one,  between 
the  classes  which  the  schoolmen  admitted  to  be  genera  or  species,  and 
those  to  which  they  refused  the  title  i  Is  it  an  error  to  regai"d  some  of 
the  differences  which  exist  among  objects  as  differences  in  kind  (genere 
or  specie),  and  others  oidy  as  differences  in  the  accidents  1  Were  the 
schoolmen  right  or  wrong  in  giving  to  some  of  tlie  classes  into  which 
things  may  be  divided,  the  name  of  kinds,  and  considering  others  as 
secondary  divisions,  grounded  upon  differences  of  a  comparatively 
supei-ficial  nature  ?  Examination  will  show  that  the  Aristotelians  did 
mean  something  by  this  distinction,  and  something  important;  but 
which,  being  but  indistinctly  conceived,  was  inadequately  expressed 
by  the  phraseology  of  essences,  and  by  the  various  other  modes  of 
speech  to  which  they  had  recourse. 

§  4.  It  is  a  fundamental  principle  in  logic,  that  the  power  of  framing 
classes  is  unlimited,  as  long  as  there  is  any  (even  the  smallest)  differ- 
ence to  found  a  distinction  upon.  Take  any  attribute  whatever,  and 
if  some  things  have  it,  and  others  have  not,  we  may  ground  upon  the 
attribute  a  di^nsion  of  all  things  into  two  classes  ;  and  we  actually  do 
so,  the  moment  we  create  a  name  which  connotes  the  attribute.  The 
number  of  possible  classes,  therefore,  is  boundless ;  and  there  are  as 
many  actual  classes  (either  of  real  or  of  imaginary  things)  as  there  are 
general  names,  positive  and  negative  together. 

But  if  we  contemplate  any  one  of  the  classes  so  fonned,  such  as  the 
class  animal  or  plant,  or  the  class  sulphur  or  phosphorus,  or  the  class 
white  or  red,  and  consider  in  what  particulars  the  individuals  included 
in  the  class  differ  from  those  which  do  not  come  within  it,  we  find  a 
very  remarkable  diversity  in  this  respect  between  some  classes  and 
others.  There  are  some  classes,  the  things  contained  in  which  differ 
from  other  things  only  in  certain  particulars  which  may  be  nmnbered ; 
while  others  differ  in  more  than  can  be  numbered,  more  even  than  we 
need  ever  expect  to  know.  Some  classes  have  little  or  nothing  in 
common  to  characterize  them  by,  except  precisely  what  is  connoted 
by  the  name  :  white  things,  for  example,  are  not  distii\guishcd  by  any 
common  properties  except  whiteness-;  or  if  they  are,  it  is  only  by  such 
as  are  in  some  way  dependent  upon,  or  connected  with,  whiteness. 
But  a  hundred  generations  have  not  exhausted  the  common  properties 
of  animals  or  of  plants,  of  sulphur  or  of  phosphorus  ;  nor  do  we  suppose 
them  to  be  exhaustible,  but  proceed  to  new  obsei-vations  and  experi- 
ments, in  the  full  confidence  of  discovering  new  properties  which  were 
by  no  means  implied  in  those  we  previously  knew.  Wliile,  if  any  one 
were  to  propose  for  investigation  the  common  properties  of  all  things 
which  are  of  the  same  color,  the  same  shape,  or  the  same  specific 
gravity,  the  absurdity  would  be  palpable.  We  have  no  ground  to 
believe  that  any  such  common  propeities  exist,  cXcejJt  such  as  maybe 
shown  to  be  involved  in  the  supjiosition  itself,  or  to  be  derivable  from 


84  NAMES    AND   PROPOSITIONS. 

it  by  some  law  of  causation.  It  appears,  therefore,  that  the  properties, 
on  which  we  ground  our  classes^  sometimes  exhaust  all  that  the  class 
has  in  common,  or  contain  it  all  by  some  mode  of  implication;  but  in 
other  instances  we  make  a  selection  of  a  few  properties  from  among 
not  only  a  greater  number,  but  a  number  inexhaustible  h^  us,  and  to 
which  as  we  know  no  bounds,  they  may,  so  far  as  we  are  concerned, 
be  regarded  as  infinite. 

There  is  no  impropriety  in  saying  that  of  these  two  classifications, 
the  one  answers  to  a  much  more  radical  distinction  in  the  things  them- 
selves, than  the  other  does.  And  if  any  one  even  chooses  to  say  that 
the  one  classification  is  made  by  nature,  the  other  by  us  for  our  conve- 
nience, he  will  be  right ;  pro\"ided  he  means  no  more  than  this — that 
where  a  certain  apparent  difference  between  things  (although  perhaps 
in  itself  of  little  moment)  answers  to  we  know  not  what  number  of 
other  differences,  pei'\'ading  not  only  their  known  properties  but  prop- 
erties yet  undiscovered,  it  is  not  optional  but  imperative  to  recognize 
this  difference  as  the  foundation  of  a  specific  distinction  :  while,  on  the 
contrary,  differences  that  are  merely  finite  and  determinate,  like  those 
designated  by  the  words  white,  black,  or  red,  may  be  disregarded  if 
the  purpose  for  which  the  classification  is  made  does  not  require  atten- 
tion to  those  particular  properties.  The  differences,  however,  are  made 
by  nature,  in  both  cases ;  while  the  recognition  of  those  differences  as 
grounds  of  classification  and  of  naming,  is,  equally  in  both  cases,  the  act 
of  man  :  only  in  the  one  case,  the  ends  of  language  and  of  classification 
would  be  subverted  if  no  notice  were  taken  of  the  difference,  while  in 
the  other  case,  the  necessity  of  taking  notice  of  it  depends  upon  the 
importance  or  unimportance  of  the  particular  qualities  in  which  the 
difference  happens  to  consist. 

Now,  these  classes,  distinguished  by  unknown  multitudes  of  prop- 
erties, and  not  solely  by  a  few  determinate  ones,  are  the  only  classes 
which,  by  the  Aristotelian  logicians,  were  considered  as  genera  or 
species.  Differences  which  extended  to  a  certain  property  or  proper- 
ties, and  there  tenninated,  they  considered  as  differences  only  in  the 
accidents  of  things ;  but  where  any  class  differed  fi-om  other  things  by 
an  infinite  series  of  differences,  known  and  unknown,  they  considered 
the  distinction  as  one  of  kind,  and  spoke  of  it  as  being  an  essential 
difference,  which  is  also  one  of  the  usual  meanings  of  that  vague  ex- 
pression at  the  present  day. 

Conceiving  the  schoolmen  to  have  been  justified  in  drawing  a  broad 
line  of  separation  between  these  two  kinds  of  classes  and  of  class-dis- 
tinctions, I  shall  not  only  retain  the  di\'ision  itself,  but  continue  to 
express  it  in  their  language.  According  to  that  language,  the  proxi- 
mate (or  lowest)  Kind  to  which  any  individual  is  referable,  is  called 
its  species.  Conformably  to  this.  Sir  Isaac  Newton  would  be  said  to 
be  of  the  species  man.  There  are  indeed  numerous  sub-classes  in- 
cluded in  the  class  man,  to  which  Sir  Isaac  Newton  also  belongs ;  as, 
for  example,  Christian,  and  Englishman,  and  Mathematician.  But 
these,  though  distinct  classes,  are  not,  in  our  sense  of  the  term,  distinct 
Kinds  of  men.  A  Christian,  for  example,  differs  fixjra  other  human 
beings  ;  but  he  differs  only  in  the  attribute  which  the  word  expresses, 
namely,  belief  in  Christianity,  and  whatever  else  that  implies,  either  as 
involved  in  the  fact  itself,  or  connected  with  it  through  some  law  of 
cause  and  effect.    We  should  never  think  of  inquiring  what  properties, 


CLASSIFICATION    AND    TUB    TREDICABLES.  85 

uncoTinocteJ  with  Christianity,  are  common  to  all  Christians  and  pe- 
culiar to  them  ;  while  in  regard  to  all  Men,  physiologists  are  perpetu- 
ally caiTying  on  such  an  inquiry  ;  nor  is  the  answer  ever  likely  to  be 
completed.  Man,  therefore,  we  may  be  permitted  to  call  a  species ; 
Christian,  or  Mathematician,  we  cannot. 

Note  here,  that  it  is  by  no  means  intended  to  imply  that  there  may 
not  be  different  Kind^,  or  logical  species,  of  man.  The  various  races 
and  temperaments,  the  two  sexes,  and  even  the  various  ages,  may  be 
differences  of  kind,  within  our  meaning  of  the  term.  I  say,  they  may 
be  ;  I  do  not  say,  they  are.  For  in  the  progress  of  jihysiology  it  may 
be  made  out,  that  the  differences  which  distinguis.i  different  races, 
sexes,  &c.,  fi'om  one  another,  follow  as  consequences,  under  laws  of 
nature,  fi-om  some  one  or  a  few  primai-y  differences  which  can  be  pre- 
cisely determined,  and  which,  as  the  phrase  is,  account  for  all  the  rest. 
If  this  be  so,  these  are  not  distinctions  in  kind ;  no  more  than  Chris- 
tian, Jew,  Mussulman,  and  Pagan,  a  difference  which  also  can-ies 
many  consequences  along  with  it.  And  in  this  way  classes  are  often 
mistaken  for  real  kinds,  which  are  afterwards  proved  not  to  be  so. 
But  if  it  shall  turn  out,  that  the  differences  are  not  capable  of  being 
accounted  for,  then  man  and  woman,  Caucasian,  Mongolian,  and  Ne- 
gro, &c.,  are  really  different  Kinds  of  human  beings,  and  entitled  to 
be  ranked  as  species  by  the  logician ;  though  not  by  the  naturalist. 
For  (as  already  hinted)  the  word  species  is  used  in  a  very  different 
signification  in  logic  and  in  natural  history.  By  the  naturalist,  organ- 
ized beings  are  never  said  to  be  of  different  species,  if  it  is  supposed 
that  they  could  possibly  have  descended  fi-om  the  same  stock.  That, 
however,  is  a  sense  aitificially  given  to  the  word,  for  the  technical  pur- 
poses of  a  particular  science.  To  the  logician,  if  a  negro  and  a  white 
man  differ  in  the  same  manner  (however  less  in  degi'ee),  as  a  horse 
and  a  camel  do,  that  is,  if  their  differences  are  inexhaustible,  and  not 
referrible  to  any  common  cause,  they  are  different  species,  whether 
they  are  both  descended  fi-om  Noah  or  not.  But  if  their  differences 
can  all  be  traced  to  climate  and  habits,  they  are  not,  in  the  logician's 
view,  specifically  distinct. 

^Vlien  the  injima  s^pecics,  or  proximate  Kind,  to  which  an  indi^^dual 
belongs,  ha.s  been  ascertained,  the  properties  common  to  that  Kind 
include  necessarily  the  whole  of  the  common  properties  of  every  other 
real  Kind  to  which  the  individual  can  be  refemble.  Let  the  indi\'id- 
ual,  for  example,  be  Socrates,  and  the  pi-oximate  Kind,  man.  Animal, 
or  living  creature,  is  also  a  real  Kind,  and  includes  Socrates ;  but  since 
it  likewise  includes  man,  or  in  other  words,  since  all  men  are  animals, 
the  properties  common  to  animals  form  a  portion  of  the  common  prop- 
erties of  the  sub-class,  man :  and  if  there  be  any  class  which  includes 
Socrates  without  including  man,  that  class  is  not  a  real  Kind.  Let  the 
class,  for  example,  be  fat-nosed ;  that  being  a  class  which  includes 
Socrates,  without  including  all  men.  To  detei-mine  whether  it  is  a 
real  Kind,  we  must  ask  ourselves  this  question :  Have  all  flat-nosed 
animals,  in  addition  to  whatever  is  implied  in  their  flat  noses,  any 
common  properties,  other  than  those  which  are  common  to  all  animals 
whatever  1  If  they  had  ;  if  a  flat  nose  were  a  mark  or  index  to  an  in- 
definite number  of  other  peculiarities,  not  deducible  fi-om  the  former 
by  any  ascertainable  law ;  then  out  of  the  class  man  we  might  cut  an- 
other class,  flat-nosed  man,  which,  according  to  our  definition,  would 


88  NAMES    AND    PROPOBITIONS. 

be  a  Kind.  But  if  we  coxild  do  this,  man  would  not  be,  as  it  was  as- 
sumed to  be,  the  pi-oxiraate  Kind.  Therefore  the  properties  of  the 
proximate  Kind  do  comj^rehend  those  (whether  known  or  unknown) 
of  all  other  Kinds  to  which  the  individual  belongs ;  which  was  the 
point  we  undertook  to  prove.  And  hence,  every  other  Kind  which  is 
predicable  of  the  individual,  will  be  to  the  proximate  Kind  in  the  re- 
lation of  a  genus,  according  to  even  the  popular  acceptation  of  the 
terms  genus  and  species ;  that  is,  it  wall  be  a  larger  class,  including  it 
and  more. 

We  are  now  able  to  fix  also  the  logical  meaning  of  these  terms. 
Every  class  which  is  a  real  Kind,  that  is,  which  is  distinguished  fiom 
all  other  classes  by  an  indeterminate  multitude  of  properties  not  deriv- 
able from  another,  is  eitlier  a  genus  or  a  species.  A  Kind  which  is  not 
divisible  into  other  Kinds,  cannot  be  a  genus,  because  it  has  no  species 
under  it;  but  it  is  itself  a  species,  both  with  reference  to  the  indi- 
viduals below  and  to  the  genera  above  (Species  Praedicabilis  and  Species 
Subjicibilis).  But  every  Kind  which  admits  of  division  into  real  Kinds 
(as  animal  into  quadruped,  bird,  &c.,  or  quadiTiped  into  various  species 
of  quadrupeds)  is  a  genus  to  all  below  it,  a  species  to  all  genera  in 
which  it  is  itself  included.  And  here  we  may  close  this  part  of  the 
discussion,  and  pass  to  the  three  remaining  predicables.  Differentia, 
Proprium,  and  Accidens. 

§  5.  To  b.egin  with  Differentia.  This  word  is  correlative  with  the 
words  genus  and  species,  and  as  all  agree,  it  signifies  the  attribute 
which  distinguishes  a  given  species  from  every  other  species  of  the 
same  genus.  This  is  so  far  clear:  but  which  of  the  distinguishing 
attributes  does  it  signify  1  For  we  have  seen  that  eveiT^  Kind  (and  a 
species  must  be  a  Kind)  is  distinguished  from  other  Kinds  not  by  any 
one  attribute,  but  by  an  indefinite  number.  Man,  for  instance,  is  a 
species  of  the  genus  animal ;  Rational  (or  rationality,  for  it  is  of  no 
consequence  whether  we  use  the  concrete  or  the  abstract  form)  is  gen- 
erally assigned  by  logicians  as  the  Differentia;  and  doubtless  this 
attribute  serves  the  pxu-pose  of  distinction :  but  it  has  also  been  re- 
marked of  man,  that  he  is  a  cooking  animal;  the  only  animal  that 
dresses  its  food.  This,  therefore,  is  another  of  the  attributes  by  which 
"the  species  man  is  distinguished  from  other  species  of  the  same  genus; 
would  this  attribute  serve  equally  well  for  a  differeutia  ]  The  Aristo- 
telians say  No ;  having  laid  it  down  that  the  differentia  must,  like  the 
genus  and  species,  be  of  the  essence  of  the  subject. 

And  here  we  lose  even  that  vestige  of  a  meaning  gi'ounded  in  the 
nature  of  the  things  themselves,  which  maybe  supposed  to  be  attached 
to  the  word  essence  when  it  is  said  that  genus  and  species  must  be  of 
the  essence  of  the  thing.  There  can  be  no  doubt  that  when  the  school- 
men talked  of  the  essences  of  things  as  opposed  to  their  accidents,  they 
had  confusedly  in  view  the  distinction  between  differences  of  kind,  and 
the  differences  which  are  not  of  kind ;  they  meant  to  intimate  that 
genera  and  species  must  be  Kinds.  Their-  notion  of  the  essence  of  a 
thing  was  a  vague  notion  of  a  something  which  makes  it  what  it  is,  ?'.  e., 
which  makes  it  the  Kind  of  thing  that  it  is — which  causes  it  to  have  all^ 
that  variety  of  properties  which  distinguish  its  Kind.  But  when  the 
matter  cam^  to  be  looked  at  more  closely,  nobody  could  discover  what 
caused  the  thing  to  have  all  those  properties,  nor  even  that  there  was 


CLASSIFICATION    AND    THE    PREDICABLES.  87 

anything  which  caused  it  to  have  them.  Logicians,  liowever,  not  hking 
to  admit  this,  and  being  unable  to  detect  what  made  the  thing  to  be 
what  it  was,  satisfied  themselves  with  what  made  it  to  be  what  it  was 
called.  Of  the  innumerable  properties,  known  and  unknown,  that  are 
connnon  to  the  class  man,  a  j)oition  oidy,  and  of  course,  a  very  small 
portion,  are  connoted  by  its  name:  these  few,  however,  will  naturally 
have  been  thus  distinguished  fioni  the  rest  cither  for  their  gi'eater 
obviousness,  or  for  greater  su^iposed  importance.  These  proiieities, 
then,  which  were  connoted  by  the  name,  logicians  seized  upon,  and 
called  them  the  essence  of  the  species ;  and  not  stopping  there,  they 
affirmed  them,  in  the  case  of  the  infima  species,  to  be  the  essence  of  the 
iuvAisadual  too;  for  it  was  their  maxim,  that  the  species  contained  the 
"_  whole  essence"  of  the  thing.  Metaphysics,  that  fertile  field  of  delu- 
sion propagated  by  language,  does  not  afford  a  more  signal  instance  of 
such  delusion.  On  this  account  it  was  that  rationality,  being  connoted 
by  the  name  man,  was  allowed  to  be  a  differentia  of  the  class ;  but  the 
peculiarity  of  cooking  their  food,  not  being  connoted,  was  relegated  to 
the  class  of  accidental  properties. 

The  distinction,  therefore,  between  Differentia,  Proprium,  and  Acci- 
dens,  is  not  founded  in  the  nature  of  things,  but  in  the  connotation  of 
names;   and  we  must  seek  it  there  if  we  wish  to  find  what  it  is. 

From  the  fact  that  the  genus  includes  the  species,  in  other  words, 
<^fiiotes  more  than  the  species,  or  is  predicable  of  a  greater  number  of 
individuals,  it  follows  that  the  species  must  connote  more  than  the 
genus.  It  must  connote  all  the  attributes  which  the  genus  connotes, 
or  there  would  be  nothing  to  prevent  it  fi-om  denoting  individuals  not 
included  in  the  genus.  And  it  must  connote  something  besides,  other- 
wise it  would  include  the  whole  genus.  Animal  denotes  all  the  indi- 
viduals denoted  by  man,  and  many  more.  Man,  therefore,  must  coji- 
note  all  that  animal  connotes,  otherwise  there  might  be  men  who  were 
not  animals  ;  and  it  must  connote  something  more  than  animal  connotes, 
otherwise  all  animals  would  be  men.  This  surplus  of  connotation — this 
which  the  species  connotes  over  and  above  the  connotation  of  the  genus 
— is  the  Differentia,  or  specific  difference ;  or,  to  state  the  same  prop- 
osition in  other  words,  the  Differentia  is  that,  which  must  be  added 
to  the  connotation  of  the  genus,  to  complete  the  connotation  of  the 
species. 

The  word  man,  for  instance,  exclusively  of  what  it  connotes  in  com- 
mon with  animal,  also  connotes  rationality,  and  at  least  some  approxi- 
mation to  that  external  form,  which  we  all  know,  but  which,  as  we 
have  no  name  for  it  considered  in  itself,  we  are  content  to  call  the 
human.  The  differentia,  or  specific  difference,  therefore,  of  man,  as 
referred  to  the  genus  animal,  is  that  outward  form  and  the  possession 
of  reason.  The  Aristotehans  said,  the  possession  of  reason,  without 
the  outward  form.  But  if  they  adhered  to  this,  they  would  have  been 
obliged  to  call  the  Houyhnhms  men.  The  question  never  arose,  and 
they  were  never  called  upon  to  decide  how  such  a  case  would  have 
affected  their  notion  of  essentiality.  But,  so  far  as  it  is  possible  to 
determine  how  language  would  be  used  in  a  case  which  is  purely 
imaginary,  we  may  say  that  the  Houyhnhms  would  not  be  called  men, 
and  that  the  term  man,  therefore,  rc(juiros  other  conditions  besides 
rationality.  The  schoolmen,  however,  were  satisfied  with  taking  such 
a  portion  of  the  differentia  as  sufficed  to  distinguish  the  species  from 


88  NAiMES    AND    PROPOSITIONS. 

all  other  existing  things,'  although  by  so  doing  they  might  not  exhaiist 
the  connotation  of  the  name. 

§  6.  And  here,  to  prevent  the  notion  of  differentia  from  being 
restricted  within  too  naiTow  limits,  it  is  necessary  to  remark,  that  a 
species,  even  as  referred  to  the  same  genus,  will  not  always  have  the 
same  differentia,  but  a  different  one,  according  to  the  principle  and 
pui-pose  which  presides  over  the  particular  classification.  For  ex- 
ample, a  naturalist  surveys  the  various  kinds  of  animals,  and  looks  out 
for  the  classification  of  them  most  in  accordance  with  the  order  in 
which,  for  zoological  purposes,  it  is  desirable  that  his  ideas  should 
an'ange  themselves.  With  this  view  he  finds  it  ad\asable  that  one  of 
his  fundamental  divisions  should  be  into  warm-blooded  and  cold-blood- 
ed animals  ;  or  into  animals  which  breathe  with  lungs  and  those  which 
breathe  with  gills  ;  or  into  carnivorous,  and  frugivorous  or  graminivor- 
ous ;  or  into  those  which  walk  on  the  flat  part  and  those  which  walk  on 
the  extremity  of  the  foot,  a  distinction  on  which  some  of  Cu\'ier's  fami- 
lies are  founded.  In  doing  this,  the  naturalist  creates  as  many  new 
classes,  which  are  by  no  means  those  to  which  the  individual  animal  is 
familiarly  and  spontaneously  referred ;  nor  should  we  ever  think  of 
assigning  to  them  so  prominent  a  position  in  our  arrangement  of  the 
animal  kingdom,  unless  for  a  preconcerted  purpose  of  scientific  con- 
venience. And  to  the  liberty  of  doing  this  there  is  no  limit.  In  the 
examples  we  have  given,  the  new  classes  are  real  Kinds,  since  each 
of  the  peculiarities  is  an  index  to  a  multitude  of  properties  belonging 
to  the  class  which  it  characterizes  :  but  even  if  the  case  were  other- 
wise— if  the  other  properties  of  those  classes  could  all  be  derived,  by 
any  process  known  to  us,  from  the  one  peculiarity  on  which  the  class 
is  founded — even  then,  if  those  derivative  properties  were  of  primary 
importance  for  the  purposes  of  the  naturalist,  he  would  be  warranted 
in  founding  his  primary  division  upon  them. 

If,  however,  practical  convenience  is  a  sufficient  wai'rant  for  making 
the  main  demarcations  in  our  aiTangement  of  objects  run  in  lines  not 
coinciding  with  any  distinction  of  Kind,  and  so  creating  genera  and 
species  in  the  popular  sense  which  are  not  genera  or  species  in  the 
rigorous  sense  at  all ;  a  fortiori  must  we  be  warranted,  when  our 
genera  and  species  are  real  genera  and  species,  in  marking  the  distinc- 
tion between  them  by  those  of  their  properties  which  considerations 
of  practical  convenience  most  sti'ongly  recommend.  If  we  cut  a 
species  out  of  a  given  genus — the  species  man,  for  instance,  out  of  the 
genus  anim.al — with  an  intention  on  our  part  that  the  peculiarity  by 
which  we  are  to  be  guided  in  the  application  of  the  name  man  should 
be  rationality,  then  rationality  is  the  differentia  of  the  species  man. 
Suppose,  however,  that,  being  naturalists,  we,  for  the  purposes  of  our 
particidar  study,  cut  out  of  the  genus  animal  the  same  species  man, 
but  with  an  intention  that  the  distinction  between  man  and  all  other 
species  of  animal  should  be,  not  rationality,  but  the  possession  of  "  four 
incisors  in  each  jaw,  tusks  solitary,  and  erect  posture."  It  is  evident 
that  the  word  man,  when  used  by  us  as  naturalists,  no  longer  connotes 
rationality,  but  connotes  the  three  other  properties  specified;  for  that 
w^hich  we  have  expressly  in  view  when  we  impose  a  name,  assuredly 
forms  part  of  the  meaning  of  that  name.  We  may,  therefore,  lay  it 
down  as  a  maxim,  that  wherever  there  is  a  Genus,  and  a  Species 


CLASSIFICATION    AND    THE    PREDICABLES,  89 

marked  out  from  that  genus  by  an  assignable  differentia,  the  najne  of 
the  species  must  be  connotative,  and  must  connote  the  differentia; 
but  the  connotation  may  be  special,  not  involved  in  the  signification  of 
the  term  as  ordinarily  used,  but  given  to  it  when  employed  as  a  term  of 
art  or  science.  The  word  Man,  in  common  use,  connotes  rationality 
and  a  certain  form,  but  does  not  connote  the  number  or  character  of 
the  teeth ;  in  the  Linna?an  system  it  connotes  the  number  of  incisor 
and  canine  teeth,  but  does  not  connote  rationality  nor  any  ])articular 
form.  The  word  man  has,  therefore,  two  diftbrent  meanings  ;  al- 
though not  commonly  considered  as  ambiguous,  because  it  happens  in 
both  cases  to  denote  the  same  individual  objects.  But  a  case  is  con- 
ceivable in  which  the  ambiguity  would  become  evident :  we  have  only 
to  imagine  that  some  new  kind  of  animal  were  discovered,  having 
Linna^us's  three  characteristics  of  humanity,  but  not  rational,  or  not 
of  the  human  form.  In  ordinary  parlance  these  animals  would  not  be 
called  men  ;  but  in  natural  history,  they  must  still  be  called  so  by 
those,  if  any  there  be,  who  adhere  to  the  Linngean  classification  ;  and 
the  question  would  arise,  whether  the  word  should  continue  to  be  used 
in  two  senses,  or  the  classification  be  given  up,  and  the  technical 
sense  of  the  term  be  abandoned  along  with  it. 

Words  not  otherwise  connotative  may,  in  the  mode  just  adverted  to, 
acquire  a  special  or  technical  connotation.  Thus  the  word  whiteness, 
as  we  have  so  often  remarked,  connotes  nothing,  it  merely  denotes  the 
attribute  coiTesponding  to  a  certain  sensation ;  but  if  we  are  making 
a  classification  of  colors,  and  desire  to  justify,  or  even  merely  to  point 
out,  the  particular  place  assigned  to  whiteness  in  our  aiTangement,  we 
may  define  it,  "  the  color  produced  by  the  mixture  of  all  the  simple 
rays;"  and  this  fact,  though  by  no  means  implied  in  the  meaning  of 
the  word  whiteness  as  ordinarily  used,  but  only  known  by  subsequent 
scientific  investigation,  is  part  of  its  meaning  in  the  particular  essay  or 
treatise,  and  becomes  the  differentia  of  the  species.* 

The  differentia,  tlierefore,  of  a  species,  may  be  defined  to  be,  that 
part  of  the  connotation  of  the  specific  name,  whether  ordintuy,  or 
special  and  technical,  which  distinguishes  the  species  in  question  fiom 
all  other  species  of  the  genus  to  which  on  the  pai'ticular  occasion  we 
are  referring  it. 

§  7.  Ha\'ing  disposed  of  Genus,  Species,  and  Differentia,  we  shall 
not  find  much  difficulty  in  attaining  a  clear  conception  of  the  distinction 
between  the  other  two  predicables. 

In  the  Aristotelian  phraseology.  Genus  and  Differentia  are  of  the, 
essence  of  the  subject ;  by  which,  as  we  have  seen,  is  really  meant  that 
the  properties  signified  by  the  genus  and  those  signified  by  the  differ- 
entia, form  part  of  the  connotation  of  the  name  denoting  the  species. 
Proprium  and  Accidens,  on  the  other  hand,  form  no  part  of  the  essence, 
but  are  jiredicated  of  the  species  only  accidental  hi.  l^oth  va'e  Acci- 
dents in  the  wider  sense,  in  which  the  accidents  of  a  thing  are  opposed 
to  its  essence  ;  although,  in  the  doctrine  of  the  Predicables,  Accidena 
is  used  for  one  sort  of  accident  only,  Proprium  being  another  sort. 

*  If  we  allow  a  differentia  to  what  is  not  really  a  species.  For  the  distinction  of  Kinds, 
in  the  sense  explained  by  us,  not  being  in  any  way  applicable  to  attributes,  it  of  course  fol- 
lows, that  although  attributes  may  be  put  into  classes,  those  classes  can  be  admitted  to  be 
genera  or  species  only  by  courtesy. 

M 


90  NAMES    AND    mOPOSITIONS. 

Proprium,  continue  the  sclioolmeri,  is  predicated  accidentally,  indeed, 
but  necessarily;  or,  as  tliey  further  explain  it,  signifies  an  attribute 
which  is  not  indeed  part  of  the  essence,  but  which  flows  fi-om,  or  is  a 
consequence  of,  the  essen'ce,  and  is,  therefore,  inseparably  attached  to 
the  species ;  e.  g.,  the  various  properties  of  a  ti'iangle,  which,  though 
no  part  of  its  definition,  must  necessarily  be  possessed  by  whatever 
comes  under  that  definition.  Accidens,  on  the  contrary,  has  no  con- 
nexion whatever  with  the  essence,  but  may  come  and  go,  and  the 
species  still  remain  what  it  was  before.  If  a  species  could  exist 
without  its  Propria,  it  must  be  capable  of  existing  without  that  upon 
which  its  Propria  are  necessarily  consequent,  and  therefore  without  its 
essence,  without  that  which  constitutes  it  a  species.  But  an  Accidens, 
whether  separable  or  inseparable  from  the  species  in  actual  experience, 
may  be  supposed  separated,  without  the  necessity  of  supposing  any 
other  alteration ;  or  at  least,  without  supposing  any  of  the  essential 
properties  of  the  species  altered,  since  with  them  an  Accidens  has  no 
connexion. 

A  Proprium,  therefore,  of  the  species,  may  be  defined,  any  attribute 
which  belongs  to  all  the  individuals  included  in  the  species,  and  which, 
although  not  connoted  by  the  specific  name  (either  ordinarily  if  the 
classification  we  are  considering  be  for  ordinary  purposes,  or  specially 
if  it  be  for  a  special  purpose),  yet  follows  from  some  attribute  which 
the  name  either  ordinarily  or  specially  connotes. 

One  attribute  may  follow  from  another  in  two  ways ;  and  there  are 
consequently  two  kinds  of  Proprium.  It  may  follow  as  a  conclusion 
follows  premisses,  or  it  may  follow  as  an  effect  follows  a  cause.  Thus, 
the  attribute  of  having  the  opposite  sides  equal,  which  is  not  one  of 
those  connoted  by  the  word  Parallelogi'am,  nevertheless  follows  from 
those  connoted  by  it,  namely,  from  having  the  opposite  sides  straight 
lines,  and  parallel,  and  the  number  of  sides  four.  The  attribute, 
therefore,  of  having  the  opposite  sides  equal,  is  a  Proprium  of  the 
class  parallelogram  ;  and  a  Proprium  of  the  first  kind,  which  follows 
from  the  connoted  attributes  by  way  of  demonstration.  The  attribute 
of  being  capable  of  understanding  language  is  a  Proprium  of  the 
species  num,  since,  without  being  connoted  by  the  word,  it  follows 
from  an  atti'ibute  which  the  word  does  connote,  viz.,  from  the  attribute 
of  rationality.  But  this  is  a  Proprium  of  the  second  kind,  which  fol- 
lows by  way  of  causation.  How  it  is  that  one  property  of  a  thing 
follows,  or  can  be  inferred  from  another ;  under  what  conditions  this 
is  possible,  and  what  is  the  exact  meaning  of  the  phrase ;  are  among 
the  questions  which  will  occupy  us  in  the  two  succeeding  Books.  At 
present  it  needs  only  be  said,  that  whether  a  Proprium  follows  by 
demonstration  or  by  causation,  it  follows  necessarily ;  that  is  to  say,  it 
cannot  hut  follow,  consistently  with  some  law  which  we  regard  as  a 
part  of  the  constitution  either  of  our  thinking' faculty  or  of  the  universe. 

§  8.  Under  the  remaining  predicable,  Accidens,  are  included  all 
attributes  of  a  thing  which  are  neither  involved  in  the  signification  of 
the  name  (whether  ordinarily  or  as  a  term  of  art),  nor  have,  so  far  as 
we  know,  any  necessary  connexion  with  attributes  which  are  so  in- 
volved. They  are  commonly  divided  into  Separable  and  Inseparable 
Accidents.  Inseparable  accidents  are  those  which — although  we  know 
of  no  connexion  between  them  and  the  attributes  constitutive  of  the 


DEFINITION.  91 

Bpccies,  and  although,  therefore,  so  far  as  we  are  aware,  they  might 
be  absent  without  making  the  name:  inapplicable  and  the  species  a 
different  species — are  yet  never,  in  fact,  known  to  be  absent.  A  con- 
cise mode  of  expressing  the  same  meaning  is,  that  inseparable  acci- 
dents are  properties  which  are  universal  to  the  species  but  not  neces- 
sary to  it.  Thus,  blackness  is  an  attribute  of  a  crow,  and,  as  far  as  we 
know,  an  universal  one.  But  if  we  were  to  discover  a  race  of  white 
birds,  in  other  respects  resembling  crows,  we  should  not  say,  These 
are  not  crows  ;  we  should  say.  These  are  white  crows.  Crow,  there- 
fore, does  not  connote  blackness  ;  nor,  from  any  of  the  attributes  which 
it  does  connote,  whether  as  a  word  in  popular  use  or  as  a  term  of  art, 
could  blackness  be  inferred.  Not  only,  therefore,  can  wc  conceive  a 
white  crow,  but  we  know  of  no  reason  why  such  an  animal  should  not 
exist.  Since,  however,  none  but  black  crows  are  known  to  exist, 
blackness,  in  the  present  state  of  our  knowledge,  ranks  as  an  accident, 
but  an  inseparable  accident,  of  the  species  crow. 

Separable  Accidents  are  those  which  are  found,  in  point  of  fact,  to 
be  sometimes  absent  fiom  the  species  ;  which  are  not  only  not  neces- 
sary, but  not  even  universal.  They  are  such  as  do  not  belong  to  every 
individual  of  the  species,  but  only  to  some  indi^•iduals  ;  or  if  to  all,  not 
at  all  times.  Thus,  the  color  of  an  European  is  one  of  the  separable 
accidents  of  the  species  man,  because  it  is  not  an  attribute  of  all  human 
creatures.  Being  born,  is  also  a  separable  accident  of  the  species 
man,  because  although  an  attribute  of  all  human  beings,  it  is  so  only 
at  one  particular  time.  A  fortiori  those  attributes  which  are  not 
constant  even  in  the  same  individual,  as,  to  be  in  one  or  in  another 
place,  to  be  hot  or  cold,  sitting  or  walking,  must  be  ranked  as  Sepa- 
rable accidents. 


CHAPTER  VIII. 

OP   DEFINITION. 

§  1.  One  necessary  part  of  the  theory  of  Names  and  of  Proposition^ 
remains  to  be  treated  of  in  this  place ;  the  theory  of  Definitions.  As 
being  the  most  important  of  the  (;lass  of  propositions  which  we  have 
characterized  as  purt^ly  verbal,  they  have  already  received  some  notice 
in  the  chapter  preceding  the  last.  But  their  fuller  treatment  was  at 
that  time  postponed,  because  definition  is  so  closely  connected  with 
classification,  that,  until  the  nature  of  the  latter  process  is  in  some 
measure  understood,  the  former  cannot  be  discussed  to  much  jjurpose. 

§  2.  The  simplest  and  most  correct  notion  of  a  Definition  is,  a  prop- 
osition declaratory  of  the  meaning  of  a  word;  namely,  either  the 
meaning  which  it  bears  in  common  acceptation,  or  that  Avhich  the 
speaker  or  writer,  for  the  particular  purposes  of  his  discourse,  intends 
to  annex  to  it. 

The  definition  of  a  word  being  the  proposition  which  enunciates  its 
meaning,  words  which  have  no  meaning  are  unsusceptible  of  definition. 
Proper  names,  therefore,  cannot  be  defined.  A  proper  name  being  a 
mere  mark  put  upon  an  individual,  and  of  which  it  is  the  characteristic 


92  NAMES    AND    PEOPOSITIOXS. 

property  to  be  destitute  of  meaning,  its  meaning  cannot  of  course  be 
declared ;  though  we  may  indicate  by  language,  as  we  might  indicate 
still  more  conveniently  by  pointing  with  the  finger,  upon  what  individ- 
ual that  particular  mark  has  been,  or  is  intended  to  be,  put.  It  is  no 
definition  of  "  John  Thomson"  to  say  he  is  "  the  son  of  General 
Thomson ;"  for  the  name  John  Thomson  does  not  express  this.  Nei- 
ther is  it  any  definition  of  "  John  Thomson"  to  say  he  is  "  the  man 
now  crossing  the  street."  These  propositions  may  serve  to  make 
known  who  is  the  particular  man  to  whom  the  name  belongs ;  but 
that  may  be  done  still  more  unambiguously  by  pointing  to  him,  which, 
however,  has  not  usually  been  esteemed  one  of  the  modes  of  definition. 

In  the  case  of  connotative  names,  the  meaning,  as  has  been  so  often 
observed,  is  the  connotation ;  and  the  definition  of  a  connotative  name 
is  the  proposition  which  declares  its  connotation.  This  may  be  done 
either  directly  or  indirectly.  The  direct  mode  would  be  by  a  propo- 
sition in  this  &>xm  :  "  Man"  (or  whatsoever  the  word  may  be)  "  is  a 
name  connoting  such  and  such  attributes,"  or  "is  a  name  which,  when 
predicated  of  anything,  signifies  the  possession  of  such  and  such  attri- 
butes by  that  thing."  Or  thus  :  JNIan  is  everything  which  possesses 
such  and  such  attributes :  Man  is  everything  which  possesses  corpo- 
reity, organization,  life,  rationality,  and  a  form  resembling  that  of  the 
descendants  of  Adam. 

This  form  of  definition  is  the  most  precise  and  least  equivocal  of 
any ;  but  it  is  not  brief  enough,  and  is  besides  too  technical  and  pe- 
dantic for  common  discourse.  The  more  usual  mode  of  declaring  the 
connotation  of  a  name,  is  to  predicate  of  it  another  name  or  names  of 
known  signification,  which  connote  the  same  aggi'egation  of  attributes. 
This  may  be  done  either  by  predicating  of  the  name  intended  to  be 
defined,  another  connotative  name  exactly  synonymous,  as,  "  Man  is  a 
human  being,"  which  is  not  commonly  accounted  a  definition  at  all; 
or  by  predicating  two  or  more  connotative  names,  which  make  up 
among  them  the  whole  connotation  of  the  name  to  be  defined.  In  this 
last  case,  again,  we  may  either  compose  our  definition  of  as  many  con- 
notative names  as  there  are  attributes,  each  attribute  being  connoted 
by  one ;  as,  Man  is  a  corporeal,  organized,  animated,  rational  being, 
shaped  so  and  so ;  or  we  may  employ  names  which  connote  several  of 
the  attributes  at  once,  as,  Man  is  a  rational  animal,  shaped  so  and  so. 

The  definition  of  a  name,  according  to  this  view  of  it,  is  the  simi 
total  of  all  the  essential  propositions  which  can  be  framed  with  that 
name  for  their  subject.  All  propositions  the  truth  of  which  is  implied 
in  the  name,  all  those  which  we  are  made  aware  of  by  merely  hearing 
the  name,'  are  included  in  the  definition  if  complete,  and  may  be 
evolved  from  it  without  the  aid  of  any  other  premisses  ;  whether  the 
definition  expresses  them  in  two  or  three  words,  or  in  a  larger  num- 
ber. It  is,  therefore,  not  -without  reason  that  Condillac  and  other  ^\Ti- 
ters  have  affirmed  a  definition  to  be  an  analysis.  To  resolve  any 
complex  whole  ijitQ_the  elements  of  which  it  is  comp^Sfded,  is  the" 
meaning  of  analysis  ;  and  this  we  do  when  we  fepTacl§t>fie"word  which 
connotes  a  set  of  attributes  collectively,  by  two  or  more  which  connote 
the  same  attributes  singly,  or  in  smaller  gl'oups. 

§  3.  From  this,  however,  the  question  naturally  arises,  in  what  man- 
ner are  we  to  define  a  name  which  connotes  only  a  single  attribute  1 


DEFINITION.  93 

for  instance,  "white,"  which  connotes  nothing  but  whiteness;  "ra- 
tional," which  connotes  nothing  but  the  possession  of  reason.  It  might 
seem  that  the  meaning  of  such  names  could  only  be  declared  in  two 
ways ;  by  a  synonymous  tei'm,  if  any  such  can  be  found ;  or  in  the 
direct  way  already  alluded  to  :  "  White  is  a  name  connoting  the  attri- 
bute whiteness."  Let  us  see,  however,  whether  the  analysis  of  the 
meaning  of  the  name,  that  is,  the  breaking  down  of  that  meaning  into 
separate  parts,  admits  of  being  carried  further.  Without  at  present 
deciding  this  question  as  to  the  word  white,  it  is  obvious  that  in  the 
case  oi  rational  some  further  explanation  may  be  given  of  its  meaning 
than  is  contained  in  the  proposition,  "  Rational  is  that  which  possesses 
the  attiibute  of  reason  ;"  since  the  attribute  reason  itself  admits  of  be- 
ing defined.  And  here  we  must  turn  our  attention  to  the  definitions 
of  attributes,  or  rather  of  the  names  of  attributes,  that  is,  of  abstract 
names. 

In  regard  to  such  names  of  attributes  as  are  connotative,  and  ex- 
press attributes  of  those  attributes,  there  is  no  difficulty :  like  other 
connotative  names,  they  are  defined  by  declaring  their  connotation. 
Thus,  the  word  Jiiult  may  be  defined,  "  a  quality  productive  of  evil  or 
inconvenience."  Sometimes,  again,  the  attribute  to  be  defined  is  not 
one  attribute,  but  an  union  of  several :  we  have  only,  therefore,  to  put 
together  the  names  of  all  the  attributes  taken  separately,  and  we  ob' 
tain  the  definition  of  the  names  which  belong  to  them  all  taken  together ; 
a  definition  which  will  correspond  exactly  to  that  of  the  coiTesponding 
concrete  name.  For,  as  we  define  a  concrete  name  by  enumerating 
the  attributes  which  it  connotes,  and  as  the  attributes  connoted  by  a 
concrete  name  form  the  entire  signification  of  the  corresponding  ab- 
stract one,  the  same  enumeration  will  serve  for  the  definition  of  both. 
Thus,  if  the  definition  of  a  Imvian  being  be  this,  "  A  being,  corporeal, 
animated,  rational,  and  shaped  so  and  so,"  the  definition  of  7i«w?a??zVy 
wall  be,  corporeity  and  animal  life,  combined  with  rationality,  and  with 
such  and  such  a  shape. 

When,  on  the  other  hand,  the  abstract  name  does  not  express  a 
complication  of  attributes,  but  a  single  attribute,  we  must  remember 
that  every  attribute  is  grounded  upon  some  fact  or  phenomenon,  from 
which  and  which  alone  it  derives  its  meaning.  To  that  fact  or  phe- 
nomenon, called  in  a  former  chapter  the  foundation  of  the  attribute, 
we  must,  therefore,  have  recourse  for  its  definition.  Now,  the  foun- 
dation of  the  attribute  may  be  a  phenomencoi  of  any  degree  of  com- 
plexity, consisting  of  many  different  parts,  either  coexistent  or  in 
succession.  To  obtain  a  definition  of  the  attribute,  we  must  analyze 
the  phenomenon  into  these  parts.  Eloquence,  for  example,  is  the 
name  of  one  attribute  only  ;  but  this  atti'ibute  is  grounded  upon  exter- 
nal effects  of  a  complicated  nature,  flowing  fi-om  acts  of  the  person  to 
whom  we  ascribe  the  attribute ;  and  by  resolving  this  phenomenon  of 
causation  into  its  two  parts,  the  cause  and  the  effect,  we  obtain  a  defi- 
nition of  elo^iieiice,  viz.,  thjLJjOwer  of  influencing  the  affections  of  hu- 
man  beinggljy  means  of  speech  or  writing. 

A  name,  thefefbre,  wli ether  coiici'^Te'lof  abstract,  admits  of  defini- 
tion, provided  we  are  able  to  analyze,  that  is,  to  distinguish  into  parts, 
the  attribute  or  set  of  attributes  which  constitute  the  meaning  both  of 
the  concrete  name  and  of  the  coiTesponding  abstract :  if  a  set  of  attri- 
butes, by  enumerating  them  ;  if  a  single  attribute,  by  dissecting  the 


94  NAMES    AND    PROPOSITIONS. 

fact  or  phenomenon  ^vhether  of  perception  or  of  internal  consciousness, 
which  is  the  foundation  of  the  attribute.  But,  further,  even  when  the 
fact  is  one  of  our  simple  feelings  or  states  of  consciousness,  and  there- 
fore unsusceptible  of  analysis,  the  names  both  of  the  object  and  of  the 
atti'ibute  still  admit  of  definition ;  or,  rather,  would  do  so  if  all  our 
Bimple  feelings  had  names.  Whiteness  may  be  defined,  the  property 
or  power  of  exciting  the  sensation  of  white.  A  white  object  may  be 
defined  an  object  which  excites  the  sensation  of  white.  The  only 
names  which  are  unsusceptible  of  definition,  because  their  meaning  is 
unsusceptible  of  analysis,  are  the  names  of  the  simple  feelings  them- 
selves. These  are  in  the  same  condition  as  proper  names.  They  are 
not,  indeed,  like  proper  names,  unmeaning;  for  the  words  sensation 
of  white  signify,  that  the  sensation  which  I  so  denominate  resembles 
other  sensations  which  I  remember  to  have  had  before,  and  to  have 
called  by  that  name.  But  as  we  have  no  words  by  whith  to  recall 
tliose  former  sensations,  except  the  very  word  which  we  seek  to  de- 
fine, or  some  other  which,  being  exactly  synonymous  with  it,  requires 
definition  as  much,  words  cannot  unfold  the  signification  of  this  class 
of  names  ;  and  we  are  obliged  to  make  a  direct  appeal  to  tlie  personal 
experience  of  the  individual  whom  we  address. 

§  4.  Having  stated  what  seems  to  be  the  true  idea  of  a  Definition,  we 
proceed  to  examine  some  opinions  of  philosophers,  and  some  popular 
conceptions  on  the  subject,  which  conflict  more  or  less  with  the  above. 

The  only  adequate  definition  of  a  name  is,  as  already  remarked,  one 
which  declares  the  fiicts,  and  the  whole  of  the  facts,  which  the  name 
involves  in  its  signification.  But  with  most  persons  the  object  of  a 
definition  does  not  embrace  so  much;  they  look  for  nothing  more,  in 
a  definition,  than  a  guide  to  the  correct  use  of  the  term — a  protection 
against  applying.it^  in  a  manner  inconsistent  with  custom.  aJad_^cpjiyen- 
tion.  AhytTimg,  thereft)re,'Ts  to  them  a  sufiicientltelTnition  of  a  term, 
which  will  serve  as  a  correct  index  to  wl>at  the  term  (denotes  ;  although 
not  embracing  the  whole,  and  sometimes,  perhaps,  not  even  any  part, 
of  what  it  connotes.  This  gives  rise  to  two  sorts  of  unperfect,  or  un- 
scientific definitions  ;  namely,  Essential  but  incomplete  Definitions,  and 
Accidental  Definitions,  or  Descriptions.  In  the  fofmer,  a  connotative 
name  is  defined  by  a  part  only  of  its  connotation ;  in  the  Jatter,  by 
something  which  forms  no  part  of  the  connotation  at  all. 

An  example  of  the  first  kind  of  imperfect  definitions  is  the  follow- 
ing :  Man  is  a  rational  animal.  It  is  impossible  to  consider  this  as  a 
complete  definition  of  the  word  Man,  since  (as  before  remarked)  if  we 
adhered  to  it  we  should  be  obliged  to  call  the  Houyhnhms  men ;  but 
as  there  happen  to  be  no  Houyhnhms,  this  imperfect  definition  is  suf- 
ficient to  mark  out  and  distinguish  from  all  other  things,  the  objects  at 
present  denoted  by  "  man  ;"  all  the  beings  actually  known  to  exist,  of 
whom  the  name  is  predicable.  Though  the  word  is  defined  -by  some 
only  among  the  attributes  which  it  connotes,'  not  by  all,  it  happens  that 
all  known  objects  which  possess  the  enumerated  attributes,  possess 
also  those  which  are  omitted ;  so  that  the  field  of  predication  which  the 
word  covers,  and  the  employment  of  it  wliicliJs-^wiformableJ.o-as^^^ 
are  as  well  indicated  by  the  inadequate  definition  as  by  an  adeqiiafe" 
one.  Such  definitions,  however,  are  always  liable  to  be  overthrown 
by  the  discovery  of  new  objects  in  natm'e. 


DEFINITION.  95 

Definitions  of  this  kind  are  what  logicians  have  had  in  view  when 
they  laid  down  the  rule,  that  the  definition  of  a  species  should  be  per 
genus  et  different iam.  Pift'erentia  being  seldom  taken  to  mean  the 
whole  of  the  peculiarities  constitutive  of  the  species,  but  some  one  of 
those  peculiarities  only,  a  complete  definition  would  be  j)C)-  genus  et 
dffercnfias,  rather  than  different'uim.  It  would  include,  with  the  name 
of  the  superior  genus,  not  merely  some  attribute  which,  distinguishes 
the  species  intended  to  be  defined  from  all  other  Species  of  the  same 
genus,  but  all  the  attributes  implied  in  the  name  of  the  species,  which 
tlie  name  of  the  superior  genus  has  not  already  implied.  The  asser- 
tion, however,  that  a  definition  must  of  necessity  consist  of  a  genus 
and  difierentice,  is  not  tenable.  It  was  early  remarked  by  logicians, 
that  the  sunnnuiii  genus  in  any  classification,  having  no  genus  superior 
to  itself,  could  not  be  defined  in  this  manner.  Yet  we  have  seen  that 
all  names,  except  those  of  our  elementary  feelings,  are  susceptible  of 
definition  in  the  strictest  sense;  by  setting  fortli  in  words  the  constit- 
uent parts  of  the  fact  or  phenomenon,  of  which  the  connotation  of  every 
word  is  ultimately  composed. 

§  5.  Although  the  first  kind  of  imperfect  definition  (which  defines  a 
cohnotative  term  by  a  part  only  of  what  it  connotes,  but  a  part  sufficient 
to  mark  out  con-ectly  the  boundaries  of  its  denotation),  has  been  con- 
sidered by  the  ancients,  and  by  logicians  in  general,  as  a  complete 
definition ;  it  has  always  been  deemed  necessary  that  the  attributes 
employed  should  really  form  part  of  the  connotation;  for  the  rule  was 
that  the  definition  must  be  drawn  from  the  essence  of  the  class  ;  and  this 
would  not  have  been  the  case  if  it  had  been  in  any  degree  made  up  of 
attributes  not  connoted  by  the  name.  The  second  kind  of  imperfect 
definition,  therefore,  in- which  the  name  of  a  class  is  defined  by  any  of 
its  accidents — that  is,  by  attributes  which  are  not  included  in  its  conno- 
tation— has  been  rejected  from  the  rank  of  genuine  Definition  by  all 
philosophers,  and  has  been  termed  Description. 

This  kind  of  imperfect  definition,  however,  takes  its,  rise  frortl  the 
same  cause  as  the  other,  namely,  the  willingness  to  accept  as  a  defini- 
tion anything  which,  whether  it  expounds  the  meaning  of  the  name  or 
not,  enables  us  to  discriminate  the  things  denoted  by  the  name  from  all 
other  things,  and  consequently  to  employ  the  term  in  predication  with- 
out deviating  from  established  usage.  This  purpose  is  .duly  answered 
by  stating  any  (no  matter  what)  of  the  attributes  which  are  common  to 
the  whole  of  the  class,  and  peculiar  to  it ;  or  any  combination  of  attri- 
butes which  may  happen  to  be  peculiar  to  it,  although  separately  each 
of  those  attributes  may  be  common  to  it  with  some  other  things.  It  ia 
only  necessary  that  the  definition  (or  description)  thus  formed,  shcmld 
be  convertible  with  the  name  which  it  professes  to  define  ;  that  is,  should 
1x3  exactly  co-extensive  with  it,  being  predicable  of  everything  of  ^vhich 
it  is  predicable,  and  of  nothing  of  which  it  is  not  predicable  :  although 
the  attributes  specified  may  have  nc^  connexion  with  those  which  men 
had  in  view  Avhen  they  foi-pied  or  recognized  the  class,  and  gave  it  a 
name.  The  following  are  coiTect  definitions  of  Man,  according  to  this 
test :  Man  is  a  mammiferous  animal,  baring  (by  nature)  two  hands 
(for  the  human  species  answers  to  this  description,  and  no  other  animal 
does) :  Man  is  an  animal  who  cooks  his  food ;  Man  is  a  featherless 
biped. 


96  NAMES    AND    PROPOSITIONS. 

"What  would  otherwise  be  a  mere  description,  may  be  raised  to  the 
rank  of  a  real  definition  by  the  peculiar  purpose  which  the  speaker  or 
"Writer  has  in  view.  As  was  seen  in  the  preceding  chapter,  it  may,  for 
the  ends  of  a  particular  art  or  science,  or  for  the  more  convenient 
statement  of  an  author's  particular  views,  be  advisable  to  give  to  some 
general  name,  without  altering  its  denotation,  a  special  connotation, 
different  from  its  ordinary  one.  When  this  is  done,  a  definition  of  the 
name  by  means  of  the  attributes  which  make  up  the  special  connota- 
tion, though  in  genqral  a  mere  accidental  definition,  or  description, 
becomes  on  the  particular  occasion  and  for  the  particular  purpose,  a 
complete  and  genuine  definition.  This  actually  occurs  with  respect 
to  one  of  the  preceding  examples,  "  Man  is  a  maramiferous  animal 
having  two  hands,"  which  is  the  scientific  definition  of  man  con- 
sidered as  one  of  the  species  in  Cuvier's  distribution  of  the  animal 
kingdom! 

In  cases  of  this  sort,  although  the  definition  is  still  a  declaration  of 
the  meaning  which  in  the  particular  instance  the  name  is  appointed  to 
convey,  it  cannot  be  said  that  to  state  the  meaning  of  the  word  is  the 
purpose  of  the  definition.  The  purpose  is  not  to  expound  a  name,  but 
to  help  to  expound  a  classification.  The  special  meaning  which  Cuvier 
assigned  to  the  word  Man  (quite  foreign  to  its  ordinary  meaning,, 
though  involving  no  change  in  the  denotation  of  the  word),  was  inci- 
dental to  a  plan  of  arranging  animals  into  classes  on  a  certain  principle, 
that  is,  according  to  a  certain  set  of  distinctions.  And  since  the  defi- 
nition of  Man  according  to  the  ordinary  connotation  of  the  word,  though 
it  would  have  answered  every  other  purpose  of  a  definition,  would  not 
have  pointed  out  the  place  Avhich  the  species  ought  to  occupy  in  that 
particular  classification ;  he  gave  the  word  a  special  connotation,  that 
he  might  be  able  to  define  it  by  the  kind  of  attributes  upon  which,  for 
reasons  of  scientific  convenience,  he  had  resolved  to  found  his  division 
of  animated  nature. 

Scientific  definitions,  whether  they  are  definitions  of  scientific  terms  ' 
or  of  common  terms, used  in  a  scientific  sense,  are  almost  always  of  the 
kind  last  spoken  of:  .their  main  purpose  is  to  serve  as  the  landmarks 
of  scientific  classification.  And  since  the  classifications  in  any  science 
are  continua,lly  rnodified  as'  scientific  knowledge  iadvances,  the  defi- 
nitions in  the  sciences  are  also  constantly  varying.  A  striking  mstance 
is  afforded  by  the  words  Acid  and  Alkali,  especially  the  foniier.  As 
experimental  discovery  advanced,  the  substances  classed  with  acids 
have  been  constantly  multiplying,  and  by  a  natural  consequence  the 
attributes  connoted  by  the  word  have  receded  and  become  fewer.  At 
first  it  connoted  the  attributes,  of  combining  with  an  alkali  to  form  a 
neutral  substance  (called  a  Salt) ;  being  compounded  of  a  base  and 
oxygen;  causticity  to  the  taste  and  touch;  fluidity,  &c.  The  true 
analysis  of  muriatic  acid,  into  chlorine  and  hydrogen,  caused  the  second 
property,  composition  from  a  base  and  oxygen,  to  be  excluded  from 
the  connotation.  The  same ,  discovery  fixed  the  attention  of  chemists 
upon  hydrogen  as  an  important  element  in  acids ;  and  more  recent 
discoveries  having  led  to  the  recognition  of  its  presence  in  sulphuric, 
nitric,  and  many  other  acids,  where  its  existence  was  not  previously 
suspected,  there  is  now  a  tendency  to  include  the  presence  of  this  ele- 
ment in  the  connotation  of  the  word.  But  carbonic  acid,  silica,  sulphu- 
rous acid,  have  no  hydrogen  in  their  composition ;  that  property  can- 


DKFIMTION.  97 

not  therefore  be  connoted  by  the  term,  unless  those  substances  are  no 
longer  to  be  considered  acids.  Causticity  and  fluidity  have  long  since 
been  excluded  from  the  characteristics  of  the  class,  by  the  inclusion  of 
silica  and  many  other  substances  in  it ;  and  the  fonnation  of  neutral 
bodies  by  combination  with  alkalis,  together  with  such  electro-chemi- 
cal peculiarities  as  this  is  supposed  to  imply,  are  now  the  only  differ- 
entia; which  form  the  fixed  connotation  of  the  word  Acid,  as  a  term  of 
chemical  science. 

Scientific  men  are  still  seeking,  and  may  be  long  ere  they  find,  a 
suitable  definition  of  one  of  the  earliest  word^  in  the  vocabulary  of  the 
human  race,  and  one  of  those  of  which  the  popular  sense  is  plainest 
and  best  understood.  The  word  I  mean  is  Heat ;  and  the  source  of 
the  difficulty  is  the  imperfect  state  of  our  scientific  knowledge,  which 
has  shown  to  us  multitudes  of  phenomena  certainly  coimected  with  the 
same  power  which  is  the  cause  of  what  our  senses  recognize  as  heat, 
but  has  not  yet  taught  us  the  laws  of  those  phenomena  with  sufficient 
accuracy  to  admit  of  our  determinhig  under  what  characteristics  the 
whole  of  those  phenomena  shall  ultimately  be  embodied  as  a  class : 
which  characteristics  would  of  course  be  so  many  diffisrentice  for  the 
definition  of  the  power  itself  AVe  have  advanced  far  enough  to  know- 
that  one  of  thee  attributes  connoted  must  be  that  of  operating  as  a 
repulsive  force  :  but  this  is  certainly  not  all  which  must  ultimately  be 
included  in  the  scientific  d.efinition  of  heat. 

What  is  true  of  the  definition  of  any  term  of  science,  is  of  course 
true  of  the  definition  of  a  science  itself:  and  accordingly,  we  showed 
in  the  Introductory  Chapter  of  this  work,  that  the  definition  of  a  science 
must  necessarily  be  progi'essive  and  provisional.  Any  extension  of  ' 
knowledge,  or  alteration  in  the  current  opinions  respecting  the  subject 
matter,  may  lead  to  a  change  more  or  less  extensive  in  the  paiticulars 
included  in  the  science  ;  and  its  composition  being  thus  altered,  it  may  / 
easily  happen  that  a  different  set  of  characteristics  will  be  found  better 
adapted  as  differentiae  for  defining  its  name. 

In  the  same  manner  in  which,  as  we  have  now  shown,  a  special  or 
technical  definition  has  for  its  object  to  expound  the  artificial  classi- 
fication out  of  which  it  grows ;  the  Aristotelian  logicians  seem  to  have 
imagined  that  it  was  also  the  business  of  ordinary  definition  to  expound 
the  ordinary,  and  what  they  deemed  the  natural,  classification  of  things, 
namely,  the  division  of  them  into  Kinds ;  and  to  show  the  place  which 
each  Kind  occupies,  as  superior,  collateral,  or  subordinate,  among 
other  Kinds.  This  notion  would  account  for  the  rule  that  all  defi- 
nition must  necessarily  be  per  genus  et  differentiam,  and  would  also 
explain  why  any  one  differentia  was  deemed  sufficient.  But  to 
expound,  or  exjiress  in  words,  a  distinction  of  Kind,  has  already  been 
shown  to  be  an  impossibility  :  the  very  meaning  of  a  Kind  is,  that  tin; 
properties  which  distinguish  it  do  not  grow  out  of  one  another,  and 
cannot  therefore  be  set  forth  in  words,  even  by  implication,  othei"wise 
than  by  enumerating  them  all :  and  all  are  not  known,  nor  ever  will  be 
60.  It  is  idle,  therefore,  to  look  to  this  as  one  of  the  pui-poses  of  a 
definition :  while,  if  it  be  only  required  that  the  definition  of  a  Kind 
should  indicate  what  Kinds  hiclude  it  or  are  included  by  it,  any  defi- 
nitions which  expound  the  connotation  of  the  names  will  do  this  :  for 
the  name  of  each  class  must  necessarily  connote  enough  of  its  proper- 
ties to  fix  the  boundaries  of  the  class.  If  the  definition,  therefore,  is 
N 


98  NAMES    AND    PROPOSITIONS. 

a  full  Statement  of  the  connotation  it  is  all  that  a  definition  can  be 
required  to  be. 

§  6.  Of  the  two  incomplete  or  unscientific  modes  of  definition,  and 
in  what  they  differ  from  the  complete  or  scientific  mode,  enough  has 
now  been  said.  We  shall  next  examine  an  ancient  doctrine,  once 
generally  prevalent  and  still  by  no  means  exploded,  which  I  regard  as 
the  source  of  a  great  part  of  the  obscurity  hanging  over  some  of  the 
most  important  processes  of  the  understanding  in  the  pursuit  ofjxutlu- 
According  to  this,  the  definitions  of  which  we  have  now  treated  are 
only  one  of  two  sorts  into  which  definitions  may  be  divided,  viz., 
definitions  of  names,  and  definitions  of  things.  The  fonner  are  intended 
to  explain  the  meaning  of  a  term  ;  the  latter,  the  nature  of  a  thing ;  the 
last  being  incomparably  the  most  important. 

This  opinion  was  held  by  the  ancient  philosophers,  and  by  their  fol- 
lowers, with  the  exception  of  the  Nominalists ;  but  as  the  spirit  of 
modern  metaphysics,  until  a  recent  period,  has  been  on  the  whole  a 
Nominalist  spirit,  the  notion  of  definitions  of  things  has  been  to  a  cer- 
tain extent  in  abeyance,  still  continuing,  however,  to  breed  confusion 
in  logic,  by  its  consequences  indeed  rather  than  by  itself  Yet  the 
docti'ine  in  its  own  proper  form  now  and  then  breaks  out,  and  has  ap- 
peared (among  other  places)  where  it  was  scarcely  to  be  expected,  in 
a  deservedly  popular  work,  Archbishop  Whately's  Logic.  In  a  re- 
view of  that  work  published  by  me  in  the  Westminster  Review  for 
January  1828,  and  containing  some  opinions  wliich  I  no  longer  enter- 
tain, I  find  the  following  observations  on  the  question  now  before  us  ; 
obsex'vations  with  which  my  present  views  on  that  question  are  still 
sufficiently  in  accordance. 

"  The  distinction  between  nominal  and  real  definitions,  between 
definitions  of  words  and  what  are  called  definitions  of  things,  though 
conformable  to  the  ideas  of  most  of  the  Aristotelian  logicians,  cannot, 
as  it  appears  to  us,  be  maintained.  We  apprehend  that  no  definition 
is  ever  intended  to  '  explain  and  unfold  the  nature  of  the  thing.'  It  is 
some  confirmation  of  our  opinion,  that  none  of  those  writers  who  have 
thought  that  there  were  definitions  of  things',  have  ever  succeeded  in 
discovering  any  criterion  by  which  the  definition  of  a  thing  can  be  dis- 
tinguished from  any  other  proposition  relating  to  the  thing.  The 
definition,  they  say,  unfolds  the  nature  of  the  thing :  but  no  definition 
can  unfold  its  whole  nature  ;  and  every  proposition  in  which  any  qual- 
ity whatever  is  predicated  of  the  thing,  unfolds  some  part  of  its  nature. 
The  true  state  of  the  case  we  take  to  be  this.  All  definitions  are  of 
names,  and  of  names  only :  but,  in  some  definitions,  it  is  clearly  ap- 
parent, that  nothing  is  intended  except  to  explain  the  meaning  of  the 
word ;  while  in  others,  besides  explaining  the  meaning  of  the  word,  it 
is  intended  to  be  implied  that  there  exists  a  thing,  corresponding  to 
the  word.  Whether  this  be  or  be  not  implied  in  any  given  case, 
cannot  be  collected  from  the  mere  form  of  the  expression.  '  A  cen- 
taur is  an  animal  with  the  upper  parts  of  a  man  and  the  lower  parts  of 
a  horse,'  and  '  A  triangle  is  a  rectilineal  figure  with  three  sides,'  are, 
in  form,  expressions  precisely  similar ;  although  in  the  former  it  is  not 
implied  that  any  thing,  conformable  to  the  term,  really  exists,  while  in 
the  latter  it  is  ;  as  may  be  seen  by  substituting,  in  both  definitions,  the 
Vford  means  fori*.     In  the  first  expression,  '  A  centaur  means  an  an- 


DEFINITION.  99 

imal,'  &:c.,  the  sense  would  remain  unchanged  :  in  the  second,  '  A  tri- 
angle means,'  &c.,  the  meaning  would  bo  altered,  since  it  would  be 
obviously  impossible  to  deduce  any  of  the  truths  of  geometry  from  a 
proposition  expressive  only  of  the  maimer  in  which  we  intend  to  em- 
ploy a  particular  sign. 

"  There  are,  therefore,  expressions,  commonly  passing  for  definitions, 
which  include  in  themselves  more  than  the  mere  explanation  of  the 
meaning  of  a  temi.  But  it  is  not  correct  to  call  an  expression  of  this 
sort  a  peculiar  kind  of  definition.  Its  difference  fi-om  the  other  kind 
consists  in  this,  that  it  is  not  a  definition,  but  a  definition  and  sometliing 
more.  The  definition  above  given  of  a  triangle,  obviously  comprises 
not  one,  but  two  propositions,  perfectly  distinguishable.  The  one  is, 
*  There  may  exist  a  figure,  bounded  by  three  straight  lines  :'  the  other, 
'  And  this  figui'e  may  be  termed  a  triangle.'  The  former  of  these  pro- 
positions is  not  a  definition  at  all :  the  latter  is  a  mere  nominal  defini- 
tion, or  explanation  of  the  use  and  application  of  a  term.  The  first  is 
susceptible  of  truth  or  falsehood,  and  may  therefore  be  made  the  foun- 
dation of  a  train  of  reasoning.  The  latter  can  neither  be  true  nor  false ; 
the  only  character  it  is  susceptible  of  is  that  of  conformity  or  discon- 
formity  to  the  ordinary  usage  of  language." 

There  is  a  i-eal  distinction,  then,  between  definitions  of  names,  and 
what  are  erroneously  called  definitions  of  things  ;  but  it  is,  that  the 
latter,  along  with  the  meaning  of  a  name,  covertly  asserts  a  matter  of 
fact.  This  covert  assertion  is  not  a  definition,  but  a  postulate.  The 
definition  is  a  mere  identical  proposition,  which  gives  information  only 
about  the  use  of  language,  and  from  which  no  conclusions  affecting 
matters  of  fact  can  possibly  be  drawn.  The  accompanying  postulate, 
on  the  other  hand,  affirms  a  fact,  which  may  lead  to  consequences  of 
every  degi-ee  of  importance.  It  affii-ms  the  real  existence  of  Things 
possessing  the  combination  of  attributes  set  forth  in  the  definition  ;  and 
this,  if  true,  may  be  foundation  sufficient  on  which  to  build  a  whole 
fabric  of  scientific  ti'uth. 

We  have  already  made,  and  shall  often  have  to  repeat,  the  remark, 
that  the  philosophers  who  overthrew  Realism  by  no  means  got  rid  of 
the  consequences  of  Realism,  but  retained  long  afterwards,  in  their 
own  philosophy,  numerous  propositions  which  could  only  have  a  ra- 
tional meaning  as  part  of  a  Realistic  system.  It  had  been  handed  down 
from  Aristotle,  and  probably  from  earlier  times,  as  an  obvious  truth, 
that  the  science  of  Geometry  is  deduced  fi-om  definitions.  This,  so 
long  as  a  definition  was  considered  to  be  a  proposition  "  unfoldino-  the 
nature  of  the  thing,"  did  well  enough.  But  Hobbes  came,  and  re- 
jected utterly  the  notion  that  a  definition  declares  the  natm-e  of  the 
thing,  or  does  anything  but  state  the  meaning  of  a  name ;  yet  he  con- 
tinued to  affirm  as  broadly  as  any  of  his  predecessors,  that  the  dpxac, 
principia,  or  original  premisses  of  mathematics,  and  even  of  all  science, 
are  definitions  ;  producing  the  singular  paradox,  that  systems  of  scien- 
tific truth,  nay,  all  truths  whatever  at  which  we  airive  by  reasoning, 
are  deduced  fiom  the  arbitrary  conventions  of  mankind  concerning  the 
signification  of  words. 

To  save  the  credit  of  the  doctrine  that  definitions  are  the  premisses 
of  scientific  knowledge,  the  proviso  is  sometimes  added,  that  they  are 
so  only  under  a  certain  condition,  namely,  that  they  be  firamed  con- 
formably to  the  phenomena  of  nature ;  that  is,  that  they  ascribe  such 


100  NAMES   AND  PROPOSITIONS, 

meanings  to  terms  as  shall  suit  objects  actually  existing.     But  this  is  \ 
only  an  instance  of  the  attempt,  too  often  made,  to  escape  from  the  ,' 
necessity  of  abandoning  old  language  after  the  ideas  which  it  expresses/ 
have  been  exchanged  for  contrary  ones.    From  the  meaning  of  a  name 
(we  are  told)  it  is  possible  to  infer  physical  facts,  provided  the  name 
has,  corresponding  to  it,  an  existing  thing.     But  if  this  proviso  be  ne- 
cessary, from  which  of  the  two  is  the  inference  really  drawn  1  from  the 
existence  of  a  thing  having  the  properties  1  or  from  the  existence  of  a 
name  meaning  them  1 

Take,  for  instance,  any  of  the  definitions  laid  down  as  premisses  in 
Euclid's  Elements  ;  the  definition,  let  us  say,  of  a  circle.  This,  being 
analyzed,  consists  of  two  propositions ;  the  one  an  assumption  with 
respect  to  a  matter  of  fact,  the  other  a  genuine  definition.  "A  figure 
may  exist,  having  all  the  points  in  the  line  which  bounds  it  equally 
distant  from  a  single  point  within  it:"  "Any  figure  possessing  this 
property  is  called  a  circle."  Let  us  look  at  one  of  the  demonstrations 
which  are  said  to  depend  on  this  definition,  and  observe  to  which  of 
the  two  propositions  contained  in  it  the  demonstration  really  appeals. 
"  About  the  centre  A,  describe  the  circle  B  C  D."  Here  is  an  assump- 
tion, that  a  figure,  such  as  the  definition  expresses,  ma^/  be  described : 
which  is  no  other  than  the  postulate,  or  covert  assumption,  involved  in 
the  so-called  definition.  But  whether  that  figure  be  called  a  circle  or 
not  is  quite  immaterial.  The  purpose  would  be  as  well  answered,  in 
all  respects  except  brevity,  were  we  to  say,  "  Through  the  point  B, 
draw  a  line  returning  into  itself,  of  which  every  point  shall  be  at  an 
equal  distance  from  the  point  A."  By  this  the  definition  of  a  circle 
would  be  got  rid  of,  and  rendered  needless,  but  not  the  postulate  im- 
plied in  it ;  Avithout  that  the  demonstration  could  not  stand.  The  circle 
being  now  described,  let  us  proceed  to  the  consequence.  "  Since 
B  C  D  is  a  circle,  the  radius  B  A  is  equal  to  the  radius  C  A."  B  A  is 
equal. to  C  A,  not  because  B  C  D  is  a  circle,  but  because  B  C  D  is  a 
figure  with  the  radii  equal.  Our  warrant  for  assuming  that  such  a 
figure  about  the  centre  A,  with  the  radius  B  A,  may  be  made  to  exist, 
is  the  postulate. — The  admissibility  of  these  assumptions  may  be 
intuitive,  or  may  admit  of  proof;  but  in  either  case  they  are  the 
premisses  on  which  the  theorems  depend ;  and  while  these  are  retained 
it  would  make  no  difference  in  the  certainty  of  geometi-ical  truths, 
though  every  definition  in  Euclid,  and  every  technical  terai  therein 
defined,  were  laid  aside. 

It  is,  perhaps,  superfluous  to  dwell  at  so  much  length  upon  what  is 
so  nearly  self-evident ;  but  when  a  distinction,  obvious  as  it  may 
appear,  has  been  confounded,  and  by  men  of  the  most  powerfid  intel- 
lect, it  is  better  to  say  too  much  than  too  little  for  the  purpose  of 
rendering  such  mistakes  impossible  in  fiiture.  AVe  will,  therefore, 
detain  the  reader  while  we  point  out  one  of  the  absurd  consequences 
flowing  from  the  supposition  that  definitions,  as  such,  are  the  premisses 
in  any  of  our  reasonings,  except  such  as  relate  to  words  only.  If  this 
supposition  were  true,  we  might  argue  coiTectly  from  true  premisses, 
and  amve  at  a  false  conclusion.  We  should  only  have  to  assume  as  a 
premiss  the  definition  of  a  non-entity :  or  rather  of  a  name  which  has 
no  entity  con-esponding  to  it.  Let  this,  for  instance,  be  our  definition  : 
A  dragon  is  a  serpent  breathing  flame. 

This  proposition,   considered  only  as  a  definition,  is  indisputably 


DEFINITION.  101 

coiTcct.  A  dragon  is  a  serpent  breathing  flame :  the  word  means  tliat. 
The,  tacit  assumption,  indeed  (if  there  were  any  such  understood 
assertion),  of  the  existence  of  an  object  with  properties  conesponding 
to  the  definition,  would,  in  the  present  instance,  be  false.  Out  of  this 
definition  we  may  carve  the  premisses  of  the  following  syllogism  : 

A  dragon  is  a  thing  which  breathes  flame  : 

But  a  dragon  is  a  sei-jjent : 
From  which  the  conclusion  is, 

Therefoie  some  serpent  or  serpents  breathe  flame  : — 
an  unexceptionable  syllogism,  in  the  first  mode  of  the  third  figure,  in 
which  both  premisses  are  true  and  yet  the  conclusion  false ;  which 
every  logician  knows  to  be  an  absurdity.  The  conclusion  being  false 
and  the  syllogism  con-ect,  the  j^rcmisses  cannot  be  true.  But  the 
premisses,  considered  as  parts  of  a  definition,  are  true  :  there  is  no 
possibility  of  controverting  them.  Therefore,  the  premisses  considered 
as  parts  of  a  definition  cannot  be  the  real  ones.  The  real  premisses 
must  be : 

A  dragon  is  a  really  existing  thing  which  breathes  flame  : 

A  dragon  is  a  really  existing  serpent : 
which  implied  premisses  being  false,  the  falsity  of  the  conclusion  pre- 
sents no  absurdity.  If  we  would  determine  what  conclusion  follows 
from  the  same  ostensible  premisses  when  the  tacit  assumption  of  real 
existence  is  left  out,  let  us,  according  to  the  recommendation  in  the 
Westminster  Review,  substitute  means  for  is.     We  then  have : 

A  dragon  is  a  word  meaning  a  thing  which  breathes  flame  : 

A  dragon  is  a  word  meaning  a  serpent : 
From  which  the  conclusion  is. 

Some  word  or  words  whieh  mean  a  serpent,  also  mean  a  thing 
which  breathes  flame : 
where  the  conclusion  (as  well  as  the  premisses)  is  true,  and  is  the  only 
kind  of  conclusion  which  can  ever  follow  from  a  definition,  namely,  a 
proposition  relating  to  the  meaning  of  words.  If  it  relate  to  anything 
else,  we  may  know  that  it  does  not  follow  from  the  definition,  but  from 
the  tacit  assumption  of  a  matter  of  fact. 

It  is  only  necessary  further  to  inquire,  in  what  cases  that  tacit  as- 
sumption is  really  made,  and  in  what  cases  not.  Unless  we  declare 
the  contrary,  we  always  convey  the  impression  that  we  intend  to  make 
the  assumption,  when  we  profess  to  define  any  name  which  is  already 
known  to  be  a  name  of  really  existing  objects.  On  this  account  it  is, 
that  the  assumption  was  not  necessarily  implied  in  the  definition  of  a 
dragon,  while  there  was  no  doubt  of  its  being  included  in  the  defini- 
tion of  a  circle. 

§  7.  One  of  the  circumstances  which  have  contributed  to  keep  up 
the  notion,  that  demonstrative  truths  follow  from  definitions  rather 
than  from  the  postulates  implied  in  those  definitions,  is,  that  the  pos- 
tulates, even  in  those  sciences  which  are  considered  to  surpass  all 
others  in  demonstrative  certainty,  are  not  always  exactly  true.  It  is 
not  true  that  a  circle  exists,  or  can  be  described,  which  has  all  its  radii 
exactly  equal.  Such  accuracy  is  ideal  only ;  it  is  not  found  in  nature, 
still  less  can  it  be  realized  by  art.  People  had  a  difficulty,  therefore, 
in  conceiving  that  the  most  certain  of  all  conclusions  could  rest  upon 
premisses  which,  instead  of  being  certainly  true,  are  certainly  not  true 


102  NAMES    AND    PROPOSITIONS. 

to  the  whole  extent  asserted.  This  apparent  paradox  will  be  examined 
when  we  come  to  treat  of  Demonstration ;  where  we  shall  be  able  to 
show  that  as  much  of  the  postulate  is  true,  as  is  required  to  support  as 
much  as  is  true  of  the  conclusion.  Philosophers,  however,  to  whom 
this  view  had  not  occuiTed,  or  whom  it  did  not  satisfy,  have  thought  it 
indispensable  that  there  should  be  found  in  definitions  something  morn 
certain,  or  at  least  more  accurately  true,  than  the  implied  postulate  of 
the  real  existence  of  a  corresponding  object.  And  this  something 
they  flattered  themselves  they  had  found,  when  they  laid  it  down  that 
a  definition  is  a  statement  and  analysis  not  of  the  mere  meaning  of  a 
word,  nor  yet  of  the  nature  of  a  thing,  but  of  an  idea.  Thus,  the 
proposition,  "  A  circle  is  a  plane  figure  bounded  by  a  line  all  the  points 
of  which  are  at  an  equal  distance  fi'om  a  given  point  within  it,"  was 
considered  by  them,  not  as  an  assertion  that  any  real  circle  has  that 
property  (which  would  not  be  exactly  true),  but  that  we  conceive  a 
circle  as  having  it :  that  our  abstract  idea  of  a  circle  is  an  idea  of  a 
figurfe  with  its  radii  exactly  equal. 

Conformably  to  this  it  is  said,  that  the  subject  matter  of  mathemat- 
ics, and  of  every  other  demonstrative  science,  is  not  things  as  they 
really  exist,  but  abstractions  of  the  mind.  A  geometrical  line  is  a  line 
without  breadth ;  but  no  such  line  exists  in  nature  ;  it  is  a  mere  notion 
made  up  by  the  mind,  out  of  the  materials  in  nature.  The  definition 
(it  is  said)  is  a  definition  of  this  mental  line,  not  of  any  actual  line  : 
and  it  is  only  of  the  mental  line,  not  of  any  line  existing  in  nature,  that 
the  theorems  of  geometry  are  accurately  true. 

Allowing  this  docti'ine  respecting  the  nature  of  demonstrative  truth 
to  be  correct  (which,  in  a  subsequent  place,  I  shall  endeavor  to  prove 
that  it  is  not)  ;  even  on  that  supposition,  the  conclusions  which  seem 
to  follow  from  a  definition,  do  not  follow  from  the  definition  as  such, 
but  from  an  implied  postulate.  Even  if  it  be  true  that  there  is  no 
object  in  nature  answering  to  the  definition  of  a  line,  and  that  the 
geometrical  properties  of  lines  are  not  true  of  any  lines  in  nature,  but 
only  of  the  idea  of  a  line ;  the  definition,  at  all  events,  postulates  the 
real  existence  of  such  an  idea :  it  assumes  that  the  mind  can  frame,  or 
rather  has  framed,  the  notion  of  length  without  breadth,  and  without 
any  other  sensible  property  whatever.  According  to  what  appears  to 
me  the  sounder  opinion,  the  mind  cannot  form  any  such  notion;  it 
cannot  conceive  length  without  breadth  :  it  can  only,  in  contemplating 
objects,  attend  to  their  length  exclusively  of  their  other  sensible  quali- 
ties, and  so  determine  what  properties  may  be  predicated  of  them  in 
virtue  of  their  length  alone.  If  this  be  true,  the  postulate  involved  in 
the  geometrical  definition  of  a  line,  is  the  real  existence,  not  of  length 
without  breadth,  but  merely  of  length,  that  is,  of  long  objects.  This 
is  quite  enough  to  support  all  the  truths  of  geometry,  since  every 
property  of  a  geometrical  line  is  really  a  property  of  all  physical 
objects  possessing  length.  But  even  what  I  hold  to  be  the  false  doc- 
trine on  the  subject,  leaves  the  conclusion  that  pur  reasonings  are 
grounded  upon  the  matters  of  fact  postulated  in  definitions,  and  not 
upon  the  definitions  themselves,  entirely  unaffected ;  and  accordingly 
I  am  able  to  appeal  in  confirmation  of  this  conclusion,  to  the  authoi-ity 
of  Mr.  Whewcll,  in  his  recent  treatise  on  The  Philosophy  of  the  In- 
ductive Sciences.  On  the  nature  of  demonstrative  truth,  Mr.  Whewell's 
opinions  are  gi-eatly  at  variance  with  mine,  but  on  the  particular  point 


DEFINITIONS.  103 

in  question  it  gives  me  great  pleasure  to  observe,  that  there  is  a  com- 
plete agieement  between  us.  And  here,  as  in  many  other  instances, 
I  gladly  acknowledge  that  his  writings  are  eminently  serviceable  in 
clearing  from  confusion  the  initial  stej)s  in  the  analysis  of  the  mental 
processes,  even  where  his  views  respecting  the  ultimate  analysis  (a 
matter  generally  of  far  less  importance)  are  such  as  (though  with  un- 
feigned respect)  I  cannot  but  regard  as  fundamentally  eiToneous. 

§  8.  Although,  according  to  the  views  here  presented,  Definitions 
are  properly  of  names  only,  and  not  of  things,  it  does  not  follow  that 
definition  is  an  easy  matter.  How  to  define  a  name,  may  not  only  be 
an  inquiry  of  considerable  difficulty  and  intricacy,  but  may  turn  upon 
considerations  going  deep  into  the  nature  of  the  things  which  are 
denoted  by  the  name.  Such,  for  instance,  are  the  incjuiries  which 
form  the  subjects  of  the  most  important  of  Plato's  Dialogues;  as, 
*'  What  is  ihetoric  ]"  the  topic  of  the  Gorgias,  or  "  What  is  justice  ]" 
that  of  the  Republic.  Such,  also,  is  the  question  scornfully  asked  by 
Pilate,  "  AVliat  is  truth  1"  and  the  fundamental  question  with  specula- 
tive moralists  in  all  ages,  "  What  is  virtue  V 

It  would  be  a  mistake  to  represent  these  difficult  and  noble  in- 
quiries as  having  nothing  in  view  beyond  ascertaining  the  conven- 
tional meaning  of  a  name.  They  are  inquiries  not  so  much  to 
determine  what  is,  as  what  should  be,  the  meaning  of  a  name ;  which, 
like  other  practical  questions  of  terminology,  requires  for  its  solution 
that  we  should  enter,  and  sometimes  enter  very  deejily,  into  the  prop- 
erties not  merely  of  names  but  of  the  things  named. 

Although  the  meaning  of  every  concrete  general  name  resides  in 
the  attributes  which  it  connotes,  the  objects  were  named  before  the 
attributes  ;  as  appears  from  the  fact  that  in  all  languages,  abstract 
names  are  mostly  compounds  or  derivatives  of  the  concrete  names 
which  coiTespond  to  them.  Connotative  names,  therefore,  were,  after 
proper  names,  the  first  which  were  used  :  and  in  the  sim])ler  cases, 
no  doubt,  a  distinct  connotation  was  present  to  the  minds  of  those  who 
first  used  the  name,  and  was  distinctly  intended  by  them  to  be  conveyed 
by  it.  The  first  person  who  used  the  word  wkife,  as  applied  to  snow 
or  to  any  other  object,  knew,  no  doubt,  very  well  what  quality  he  in- 
tended to  predicate,  and  had  a  perfectly  distinct  conception  in  his  mind 
of  the  attribute  signified  by  the  name. 

But  where  the  resemblances  and  diffijrences  on  which  our  classifi- 
cations are  founded  are  not  of  this  palpable  and  easily  determinable 
kind ;  especially  where  they  consist  not  in  any  one  quality  but  in  a 
number  of  qualities,  the  effects  of  which  being  blended  together  are  not 
very  easily  discriminated  and  referred  each  to  its  true  source  ;  it  often 
happens  that  names  are  applied  to  nameable  objects,  with  no  distinct 
connotation  present  to  the  minds  of  those  who  apply  them.  They  are 
only  influenced  by  a  general  resemblance  between  the  new  object  and 
all  or  some  of  the  old  familiar  objects  which  they  have  been  accustom- 
ed to  call  by  that  name.  This,  as  we  have  seen,  is  the  law  which  even 
the  mind  of  the  philosopher  must  follow,  in  giving  names  to  the  simple 
elementary  feelings  of  our  nature  :  but,  whei-e  the  things  to  be  named 
are  complex  wholes,  a  philosopher  is  not  content  with  noticing  a  gen- 
eral resemblance  ;  he  examines  what  the  resemblance  consists  in  ;  and 
he  only  gives  the  same  name  to  things  which  resemble  one  another  in 


104  NAMES   AND   PROPOSITIONS. 

the  same  definite  particulars.  The  philosopher,  therefore,  habitually 
employs  his  general  names  with  a  definite  connotation.  But  language 
was  not  made,  and  can  only  in  some  small  degree  be  mended,  by 
philosophers.  In  the  minds  of  the  real  arbiters  of  language,  general 
names,  especially  where  the  classes  they  denote  cannot  be  brought 
before  the  tribunal  of  the  outward  senses  to  be  identified  and  discrim- 
inated, connote  little  more  than  a  vague  gross  resemblance  to  the 
things  which  they  were  earliest,  or  have  been  most,  accustomed  to  call 
by  those  names.  When,  for  instance,  ordinary  persons  predicate  the 
words  just  or  unjust  of  any  action,  nohle  or  mean  of  any  sentiment, 
expressipn,  or  demeanor,  statesman  or  charlatan  of  any  personage 
figuring  in  politics,  do  they  mean  to  affirm  of  those  various  subjects, 
any  determinate  attributes,  of  whatever  kind  %  No ;  they  merely 
recognize,  as  they  think,  some  likeness,  more  or  less  vague  and  loose, 
between  them  and  some  other  things  which  they  have  been  accustomed 
to  denominate  or  to  hear  denominated  by  those  appellations. 

Language,  as  Sir  James  Mackintosh  used  to  say  of  governments, 
"  is  not  made,  but  gi'ows."  A  name  is  not  imposed  at  once  and  by 
previous  purpose  upon  a  class  of  objects,  but  is  first  applied  to  one 
thing,  and  then  extended  by  a  series  of  transitions  to  another  and 
another.  By  this  process  (as  has  been  remarked  by  several  writers, 
and  illustrated  with  gi-eat  force  and  clearness  by  Dugald  Stewart,  in 
his  Philosophical  Essays),  a  name  not  unfrequently  passes  by  suc- 
cessive links  of  resemblance  from  one  object  to  another,  until  it 
becomes  applied  to  things  having  nothing  in  common  with  the  first 
things  to  which  the  name  was  given ;  which,  however,  do  not,  for  that 
reason,  drop  the  name ;  so  that  it  at  last  denotes  a  confused  huddle  of 
ebjects,  having  nothing  whatever  in  common ;  and  connotes  nothing, 
not  even  a  vague  and  general  resemblance.  When  a  name  has  fallen 
into  this  state,  in  which  by  predicating  it  of  any  object  we  assert 
literally  nothing  about  the  object,  it  has  become  unfit  for  the  pui-jioses 
either  of  thought  or  of  the  communication  of  thought ;  and  can  only 
be  made  serviceable  by  stripping  it  of  some  part  of  its  multifarious 
denotation,  and  confining  it  to  objects  possessed  of  some  attributes  in 
common,  which  it  may  be  made  to  connote.  Such  are  the  inconve- 
niences of  a  language  which  "  is  not  made,  but  gi'ows."  Like  a  road 
which  is  not  made  but  has  made  itself,  it  requires  continual  mending 
in  order  to  be  passable. 

From  this  it  is  already  evident,  why  the  question  respecting  the 
definition  of  an  abstract  name  is  often  one  of  so  much  difficulty.  The 
(question.  What  is  justice]  is,  in  other  words.  What  is  the  attribute 
which  mankind  mean  to  predicate  when  they  call  an  action  just  ?  To 
which  the  first  answer  is,  that  having  come  to  no  precise  agreement  on 
the  point,  they  do  not  mean  to  predicate  distinctly  any  attribute  at  all. 
Nevertheless,  all  believe  that  there  is  some  common  attribute  belonging 
to  all  the  actions  which  they  are  in  the  habit  of  calling  just.  The 
question  then  must  be,  whether  there  is  any  such  common  attribute  1 
and,  in  the  first  place,  whether  mankind  agree  sufficiently  with  one 
another  as  to  the  particvilar  actions  which  they  do  or  do  not  call  just, 
to  render  the  inquiry,  what  quality  those  actions  have  in  common,  a 
possible  one :  if  so,  whether  the  actions  really  have  any  quality  in 
common  ;  and  if  they  have,  what  it  is.  Of  these  three,  the  first  alono 
is  an  inquiry  into  usage  and  convention ;  the  other  two  ai-e  inquiries 


DEFINITION.  105 

into  matters  of  fact.  Ami  if  the  second  question  (vvhethex*  the  actions 
form  a  class  at  all),  has  been  answered  negatively,  there  retnains  a 
fourth,  often  more  arduous  than  all  the  rest,  hamely,  how  best  to  form 
a  class  arliticially,  which  the  name  may  denote. 

And  here  it  is  fitting  to  remark,  that  the  study  of  tlie  spontaneous 
growth  of  languages  is  of  the  utmost  importance  to  the  philosopher 
who  would  logically  remodel  them.  The  classifications  rudely  made 
by  established  language,  when  retouched,  as  they  almost  always  require 
to  be,  by  the  hands  of  the  logician,  are  often  in  themselves  excellently 
suited  to  many  of  his  purposes.  When  compared  with  the  classifica- 
tions of  a  philosopher,  they  are  like  the  customary  law  of  a  country, 
which  has  gi'own  up  as  it  were  spontaneously,  compared  with  laws 
methodized  and  digested  into  a  code  :  the  former  are  a  far  less  perfect 
instrument  than  the  latter;  but  being  the  result  of  a  long,  though 
unscientific,  course  of  experience,  they  contain  the  greater  part  of  the 
materials  out  of  which  the  systematic  body  of  written  law  may  and 
ought  to  be  fomied.  In  like  manner,  the  established  grouping  of 
objects  under  a  common  name,  though  it  may  be  founded  only  upon  a 
gross  and  general  resemblance,  is  evidence,  in  the  first  place,  that  the 
resemblance  is  obvious,  and  therefore  considerable ;  and,  in  the  next 
place,  that  it  is  a  resemblance  which  has  struck  great  numbers  of 
persons  during  a  sei'ies  of  years  and  ages.  Even  when  a  name,  by 
successive  extensions,  has  come  to  be  applied  to  things  among  which 
there  does  not  exist  even  a  gross  resemblance  common  to  them  all, 
still  at  every  step  in  its  progress  we  shall  find  such  a  resemblance. 
And  these  transitions  of  the  meaning  of  words  are  often  an  index  to 
real  connexions  between  the  things  denoted  by  them,  which  might 
otherwise  escape  the  notice  even  of  philosophers ;  of  those  at  least 
who,  from  using  a  different  language,  or  from  any  difference  in  their 
habitual  associations,  have  fixed  their  attention  in  preference  upon 
some  other  aspect  of  the  things.  The  history  of  philosophy  abounds 
in  examples  of  such  oversights,  which  would  not  have  been  committed 
if  a  philosopher  had  seen  the  hidden  link  that  connected  together  the 
seemingly  disparate  meanings  of  some  ambiguous  word.* 

Whenever  the  inquiry  into  the  definition  of  the  name  of  any  real  ob- 
ject consists  of  anything  else  than  a  mere  comparison  of  authorities, 
we  tacitly  assume  that  a  meaning  must  be  found  for  the  name,  com- 
patible with  its  continuing  to  denote,  if  possible  all,  but  at  any  rate  the 
greater  or  the  more  important  part,  of  the  things  of  which  it  is  com- 
monly predicated.  The  inquiry,  therefore,  into  the  definition,  is  an 
inquiry  into  the  resemblances  and  differences  among  those  things  : 
whether  there  be  any  resemblance  running  though  them  all;  if  not, 
through  what  portion  of  them  such  a  general  resemblance  can  be  traced  : 

*  "Few  people"  (I  have  said  in  another  place)  "have  reflected  how  great  a  knowledge 
of  Things  is  required  to  enable  a  man  to  aflirin  that  any  given  argument  turns  wholly  upon 
words.  There  is,  perhaps,  not  one  of  the  leading  terms  of  philosophy  which  is  not  used 
in  almost  innumerable  shades  of  meaning,  to  express  ideas  more  or  less  widely  ditlerent 
from  one  another.  IJetween  two  of  these  ideas  a  sagacious  and  penetrating  mind  will 
discern,  as  it  were  intuitively,  an  unobvious  link  of  connexion,  upon  which,  though  per- 
haps unable  to  give  a  logical  account  of  it,  he  will  found  a  perfectly  valid  argument,  which 
his  critic,  not  having  so  keen  an  insight  into  the  Things,  will  mistake  for  a  fallacy  turning 
on  the  double  meaning  of  a  term.  And  the  greater  the  genius  of  him  who  thus  safely  leaps 
over  the  chasm,  the  greater  will  probably  be  the  crowing  and  vain-glory  of  the  mere 
logician,  who,  hobbling  after  him,  evinces  his  own  superior  wisdom  by  pausing  on  its  brink, 
and  giving  up  as  desperate  his  proper  business  of  bridging  it  over." 


106  NAMES    AND    PROPOSITIONS. 

and  finally,  what  are  the  common  attributes,  the  possession  of  which 
gives  to  them  all,  or  to  that  portion  of  them,  the  character  of  resem- 
blance which  has  led  to  their  being  classed  together.  Wlien  these 
common  attributes  have  been  ascertained  and  specified,  the  name 
which  belongs  in  common  to  the  resembling  objects,  acquires  a  dis- 
tinct instead  of  a  vague  connotation ;  and  by  possessing  this  distinct 
connotation,  becomes  susceptible  of  definition. 

In  giving  a  distinct  connotation  to  the  general  name,  the  philosopher 
will  endeavor  to  fix  upon  such  atti-ibutes  as,  while  they  are  common  to 
all  the  things  usually  denoted  by  the  name,  are  also  of  greatest  impor- 
tance in  themselves,  either  directly,  or  from  the  number,  the  conspic- 
uousness,  or  the  interesting  character,  of  the  consequences  to  which 
they  lead.  He  will  select,  as  far  as  possible,  such  differentice  as  lead 
to  the  greatest  number  of  intei-esting  2>ropria.  For  these,  rather  than 
the  more  obscure  and  recondite  qualities  on  which  they  often  depend, 
give  that  general  character  and  aspect  to  a  set  of  objects,  which  deter- 
mine the  groups  into  which  they  naturally  fall.  But  to  mount  up  to 
the  more  hidden  agreement  upon  which  these  obvious  and  superficial 
agreements  depend,  is  often  one  of  the  most  difficult  of  scientific  prob- 
lems. As  it  is  among  the  most  difficult,  so  it  seldom  fails  to  be  among 
the  most  important.  And  since  upon  the  result  of  this  inquiry  respect- 
ing the  causes  of  the  properties  of  a  class  of  things,  there  incidentally 
depends  the  question  what  shall  be  the  meaning  of  a  word ;  some  of 
the  most  profound  and  most  valuable  investigations  which  philosophy 
presents  to  us,  have  been  introduced  by,  and  have  offered  themselves 
under  the  guise  of,  inquiries  into  the  definition  of  a  name. 


BOOK  II. 

OF  REASONING. 


Aiupianivuv  6e  tovtuv,  Tih/ufiEv  f/671,  diu  rivuv,  Kai  nore,  Kat  nuc  yivtrai  rruf  troAAo- 
yicT/idc'  varepov  6^  XeKriov  nKpl  utto Jtjff wf.  JlpoTepov  yap  Tvepl  (TV%?.oyiaiiWV  TiEKriov,  fj 
TTfpl  uTToihiieuc,  ^lu  to  KaOo'Aov  fiuA?iOV  eival  rov  avX'koyLaiiov.  'H  fiiv  yap  uK6dei^i(, 
<rv?^Aoyi(jfi6g  rig-  6  ayXXoyLCjiog  6i  ov  Traf ,  uttu6ei^ic. 

Arist.  Analyt.  Prior.,  1.  i.  cap.  4. 


CHAPTER  1. 

OF  INFERENCE,  OR  REASONING,  IN  GENERAL. 

§  1,  In  the  preceding  Book,  we  have  been  occupied  not  with  the 
nature  of  Proof,  but  with  the  nature  of  Assertion :  the  import  conveyed 
by  a  Proposition,  whether  that  Proposition  be  true  or  false ;  not  the 
means  by  which  to  discriminate  true  from  false  Propositions.  The 
proper  subject,  however,  of  Logic  is  Proof,  Before  we  could  under- 
stand what  Proof  is,  it  was  necessary  to  understand  what  that  is  to 
which  proof  is  applicable ;  what  that  is  which  can  be  a  subject  of  be- 
lief or  disbelief,  of  afiirmation  or  denial ;  what,  in  short,  the  different 
kinds  of  Propositions  assert. 

This  preliminary  inquiry  we  have  prosecuted  to  a  definite  result. 
Assertion,  in  the  first  place,  relates  either  to  the  meaning  of  words,  or 
to  some  property  of  the  things  which  words  signify.  Assertions  re- 
specting the  meaning  of  words,  among  which  definitions  are  the  most 
important,  hold  a  place,  and  an  indispensable  one,  in  philosophy  ;  but 
as  the  meaning  of  words  is  essentially  arbitrary,  this  class  of  assertions 
is  not  susceptible  of  truth  or  falsity,  nor  therefore  of  proof  or  dis- 
proof. Assertions  resjiecting  Things,  or  what  may  be  called  Real 
Propositions  in  contradistinction  to  verbal  ones,  ore  of  various  sorts. 
We  have  analyzed  the  im]>ort  of  each  sort,  and  have  ascertained  the 
nature  of  the  things  they  relate  to,  and  the  nature  of  what  they  sever- 
ally assert  respecting  those  things.  We  found  that  whatever  be  the 
form  of  the  proposition,  and  whatever  its  nominal  subject  or  predicate, 
the  real  subject  of  every  proposition  is  some  one  or  more  facts  or  phe- 
nomena of  consciousness,  or  some  one  or  more  of  the  hidden  causes  or 
powers  to  which  we  ascribe  those  facts  ;  and  that  what  is  predicated 
or  asserted,  either  in  the  affirmative  or  negative,  of  those  phenomena 
or  those  powers,  is  always  either  Existence,  Order  in  Place,  Order  in 
Time,  Causation,  or  Resemblance.  This,  then,  is  the  theory  of  the 
Import  of  Propositions,  reduced  to  its  ultimate  elements  :  but  there  is 
another  and  a  less  abstnise  expression  for  it,  which  though  stopping 
short  in  an  earlier  stage  of  the;  analysis,  is  sufficiently  scientific  for 
many  of  the  puqioses  for  which  such  a  general  expression  is  required. 


108  REASONING. 

This  expression  recognizes  the  commonly  received  distinction  between 
Subject  and  Attribute,  and  gives  the  follow^ing  as  the  analysis  of  the 
meaning  of  propositions  : — Every  Proposition  asserts,  that  some  given 
subject  does  or  does  not  possess  some  attribute  ;  or  that  some  attribute 
is  or  is  not  (either  in  all  or  in  some  portion  of  the  subjects  in  which  it 
is  met  with)  conjoined  with  some  other  attribute. 

We  shall  now  for  the  present  take  our  leave  of  this  portion  of  our 
inquir}',  and  proceed  to  the  peculiar  problem  of  the  Science  of  Logic, 
namely,  how  the  assertions,  of  which  we  have  analyzed  the  import, 
are  proved,  or  disproved :  such  of  them,  at  least,  as,  not  being  amena- 
ble to  direct  consciousness  or  intuition,  are  appropriate  subjects  of 
proof 

We  say  of  a  fact  or  statement,  that  it  is  proved,  when  we  be- 
lieve its  ti-uth  by  reason  of  some  other  fact  or  statement  fi-om  which 
it  is  said  to  folloic.  Most  of  the  propositions,  whether  affirmative  or 
negative,  universal,  particular,  or  singular,  which  we  believe,  are  not 
believed  on  their  own  evidence,  but  on  the  ground  of  something  pre- 
viously assented  to,  and  from  which  they  are  said  to  be  inferred.  To 
infer  a  proposition  from  a  previous  proposition  or  propositions  ;  to 
give  credence  to  it,  or  claim  credence  for  it,  as  a  conclusion  from 
something  else ;  is  to  reason,  in  the  most  extensive  sense  of  the  term. 
There  is  a  nan'ower  sense,  in  which  the  name  reasoning  is  confined  to 
the  form  of  inference  which  is  termed  ratiocination,  and  of  which  the 
syllogism  is  the  general  type.  The  reasons  for  not  conforming  to  this 
restricted  use  of  the  teim  were  stated  in  an  early  stage  of  our  inquiry, 
and  additional  motives  will  be  suggested  by  the  considerations  on 
which  we  are  now  about  to  enter. 

§  2.  In  proceeding  to  take  into  consideration  the  cases  in  which 
inferences  can  legitimately  be  drawn,  we  shall  first  mention  some  cases 
in  which  the  inference  is  apparent,  not  real ;  and  which  require  notice 
chiefly  that  they  may  not  be  confounded  with  cases  of  inference  prop- 
erly so  called.  This  occurs  when  the  proposition  ostensibly  inferred 
from  another,  appears  on  analysis  to  be  merely  a  repetition  of  the  same, 
or  part  of  the  same,  assertion,  which  ■A'as  contained  in  the  first.  All 
the  cases  mentioned  in  books  of  Logic,  as  examples  of  yEquipollency 
or  equivalence  of  propositions,  are  of  this  nature.  Thus,  if  we  were 
to  argue,  No  man  is  incapable  of  reason,  for  every  man  is  rational ; 
or.  All  men  ai'c  mortal,  for  no  man  is  exempt  from  death ;  it  would 
be  plain  that  we  were  not  proving  the  proposition,  but  only  appealing 
to  another  mode  of  wording  it,  which  may  or  may  not  be  more  readily 
comprehensible  by  the  hearer,  or  better  adapted  to  suggest  the  real 
proof,  but  which  contains  in  itself  no  shadow  of  proof 

Another  case  is  where,  from  an  universal  proposition,  we  affect  to 
infer  another  which  differs  from  it  only  in  being  particular :  as.  All  A 
is  B,  therefore  Some  A  is  B  :  No  A  is  B,  therefore  Some  A  is  not  B. 
This,  too,  is  not  to  conclude  one  proposition  fi-om  another,  but  to 
repeat  a  second  time  something  which  had  been  asserted  at  fii'st ;  with 
the  difference,  that  we  do  not  here  repeat  the  whole  of  the  previous 
assertion,  but  only  an  indefinite  part  of  it. 

A  third  case  is  where,  the  antecedent  having  affirmed  a  predicate 
of  a  given  subject,  the  consequent  affirms  of  the  same  subject  some- 
thing already  connoted  by  the  fonner  -predicate :    eus,  Socrates  is  a 


INFERENCE    IN    GENERAL.  109 

man,  therefore  Socrates  is  a  living  creature  ;  where  all  tliat  is  connoted 
by  living  creature  was  aflirmcd  of  Socrates  when  he  was  asserted  to 
be  a  man.  If  the  propositions  are  negative,  we  must  invcit  their 
order,  thus :  Socrates  is  not  a  living  creature,  therefore  he  is  not  a 
man ;  for  if  we  deny  tlie  less,  the  greater,  which  includes  it,  is  already 
denied  by  implication.  These,  therefore,  are  not  really  cases  of  infer- 
ence ;  and  yet  the  trivial  examples  by  which,  in  manuals  of  Logic,  the 
rules  of  the  syllogism  are  illustrated,  arc  often  of  this  ill-choscu  kind ; 
demonstrations  in  form,  of  conclusions  to  which  whoever  understands 
the  terms  used  in  the  statement  of  the  data,  has  already,  and  con- 
sciously, assented. 

The  most  complex  case  of  this  sort  of  apparent  inference  is  what  is 
called  the  Conversion  of  Propositions ;  which  consists  in  making  the 
predicate  become  a  subject,  and  the  subject  become  a  predicate,  and 
framing  out  of  the  same  terms,  thus  reversed,  another  j^roposition, 
which  must  be  true  if  the  former  is  true.  Thus,  fi-om  the  particular 
affirmative  proposition,  Some  A  is  B,  we  may  infer  that  Some  B  is  A.' 
From  the  universal  negative.  No  A  is  B,  we  may  conclude  that  No 
B  is  A.  From  the  universal  affirmative  proposition,  All  A  is  B,  it 
cannot  be  inferred  that  All  B  is  A ;  though  all  water  is  liquid,  it  is  not 
implied  that  all  liquid  is  water  ;  but  it  is  implied  that  some  liquid  is 
so  ;  and  hence  the  proposition.  All  A  is  B,  is  legitimately  conveitible 
into  Some  B  is  A.  This  process,  which  converts  an  universal  propo- 
sition into  a  particular,  is  termed  conversion  per  accidens.  From  the 
proposition.  Some  A  is  not  B,  \ye  cannot  even  infer  that  Some  B  is 
not  A :  though  some  men  are  not  Englishmen,  it  does  not  follow  that 
some  Englishmen  are  not  men.  The  only  legitimate  conversion,  if 
such  it  can  be  called,  of  a  particular  negative  proposition,  is  in  the 
form.  Some  A  is  not  B,  therefore,  something  which  is  not  B  is  A ;  and 
this  is  termed  conversion  by  contraposition.  In  this  case,  however, 
the  predicate  and  subject  are  not  merely  reversed,  but  one  of  them  is 
altered.  Instead  of  [A]  and  [B],  the  terms  of  the  new  proposition 
are  [a  thing  which  is  not  B],  and  [A].  The  original  proposition, 
Some  A  is  not  B,  is  first  changed  into  a  proposition  asquipollent  with 
it.  Some  A  is  "  a  thing  which  is  not  B ;"  and  the  proposition,  being 
now  no  longer  a  paiticular  negative,  but  a  particular  affirmative,  admits 
of  conversion  in  the  first  mode,  or,  as  it  is  called,  simple  conversion. 

In  all  these  cases  there  is  not  really  any  infei'ence ;  there  is  m  the 
conclusion  no  new  truth,  nothing  but  what  was  already  asserted  in  the 
premisses,  and  obvious  to  whoever  apprehends  them.  The  fact  as- 
serted in  the  conclusion  is  either  the  very  same  fact,  or  part  of  the  fact, 
asserted  in  the  original  proposition.  This  follows  fi'om  our  previous 
analysis  of  the  Import  of  Propositions.  When  we  say,  for  example, 
that  some  la\vful  sovereigns  arc  tyrants,  what  is  the  meaning  of  the 
assertion  ?  That  the  attributes  connoted  by  the  temi  "  lawful  sover- 
eign," and  the  attributes  connoted  by  the  term  "  tyrant,"  sometimes 
coexist  in  the  same  individual.  Now  this  is  also  precisely  what  we 
mean,  when  we  say  that  some  tyrants  are  lawful  sovereigns;  which, 
therefore,  is  not  a  second  proposition  inferred  from  the  first,  any  more 
than  the  English  translation  of  Euclid's  Elements  is  a  collection  of 
theorems  different  from,  and  consequences  of,  those  contained  in  the 
Greek  original.  Again,  if  we  assert  that  no  great  general  is  a  fool,  we 
mean  that  the  attributes  connoted  by  "  great  general,"  and  those  con- 


110  REASONING. 

noted  by  "fool,"  never  coexist  in  the  same  subject;  which  is  also  the 
exact  meaning  which  we  express  when  we  say,  that  no  fool  is  a  great 
general.  Wlien  we  say  that  all  quadrupeds  are  wann-blooded,  we  as- 
sert, not  only  that  the  atti'ibutes  connoted  by  "quadruped"  and  those 
connoted  by  "  warm-blooded"  sometimes  coexist,  but  that  the  former 
never  exist  without  the  latter :  now  the  proposition.  Some  wann- 
blooded  creatures  are  quadrupeds,  expresses  the  first  half  of  this  mean- 
ing, dropping  the  latter  half;  and,  therefore,  has  been  already  affirmed 
in  the  antecedent  proposition,  All  quadrupeds  are  wann-blooded.  But 
that  all  wann-blooded  creatures  are  quadrupeds,  or,  in  other  words, 
that  the  attributes  connoted  by  "warm-blooded"  never  exist  without 
those  connoted  by  "  quadruped,"  has  not  been  asserted,  and  cannot  be 
infened.  In  order  to  reassert,  in  an  inverted  form,  the  whole  of  what 
was  affii-med  in  the  proposition,  All  quadrupeds  are  warm-blooded,  we 
must  convert  it  by  contraposition,  thus.  Nothing  which  is  not  wann- 
blooded  is  a  quadruped.  This  proposition,  and  the  one  from  which  it 
is  derived,  are  exactly  equivalent,  and  either  of  them  may  be  substitu- 
ted for  the  other ;  for,  to  say  that  when  the  attributes  of  a  quadruped 
are  present,  those  of  a  warm-blooded  creature  are  present,  is  to  say, 
that  when  the  latter  are  absent  the  former  are  absent. 

In  a  manual  for  young  students,  it  would  be  proper  to  dwell  at 
gi-eater  length  upon  the  conversion  and  Eequipollency  of  propositions. 
For,  although  that  cannot  be  called  reasoning  or  inference  which  is  a 
mere  reassertion  in  different  words  of  what  had  been  asserted  before, 
there  is  no  more  important  intellectual  habit,  nor  any  the  cultivation 
of  which  falls  more  strictly  within  the  pi'ovince  of  the  ait  of  logic,  than 
that  of  discerning  rapidly  and  surely  the  identity  of  an  assertion  when 
disguised  under  diversity  of  language.  That  important  chapter  in 
logical  treatises  which  relates  to  the  Opposition  of  Propositions,  and 
the  excellent  technical  language  which  logic  provides  for  distinguisliing 
the  different  kinds  or  modes  of  opposition,  are  of  use  chiefly  for  this 
purpose.  Such  considerations  as  these,  that  conti-ary  propositions  may 
both  be  false,  but  cannot  both  be  tnie ;  that  sub-contrary  propositions 
may  both  be  true,  but  cannot  both  be  false;  that  of  two  contradictory 
propositions  one  must  be  true  and  the  other  false ;  that  of  two  subal- 
ternate  propositions  the  truth  of  the  universal  proves  the  truth  of  the 
particular,  and  the  falsity  of  the  particular  proves  the  falsity  of  the 
universal,  but  not  vice  versci;*  are  apt  to  appear,  at  first  sight,  very 
technical  and  mysterious,  but  when  explained,  seem  almost  too  obvious 
to  require  so  formal  a  statement,  since  the  same  amount  of  explanation 
which  is  necessary  to  make  the  principles  intelligible,  would  enable 
the  truths  which  they  convey  to  be  apprehended  in  any  pai'ticulai-  case 
which  can  occur.  In  this  respect,  however,  these  axioms  of  logic  are 
on  a  level  with  those  of  mathematics.  That  things  which  are  equal  to 
the  same  thing  are  equal  to  one  another,  is  as  obvious  in  any  pai'ticular 

'fo      iSlho-traries. 

«JL^  ^  ^-^  Lf  -a  \  contradictories, 
some  A  is  not  B  J 

Some  A  is  B  5  ^^^°  contradictories. 

tielis  ^  S  -'^ilelSnot  b  | -spectxvely subaltemate. 


INFERENCE    IN    GENERAL.  Ill 

case  as  it  is  in  the  general  statement ;  and  if  no  such  general  maxim 
had  ever  been  laid  down,  the  demonstrations  in  .Euclid  would  never 
have  halted  for  any  difficulty  in  stepping  across  the  gap  which  this 
axiom  at  present  sei-ves  to  bridge  over.  Yet  no  one  has  ever  censured 
writers  on  geometiy,  for  placing  a  list  of  these  elementaiy  genci-aliza- 
tions  at  the  head  of  their  treatises,  as  a  first  exercise  to  the  leanier  of 
the  faculty  which  -will  be  required  in  him  at  every  step,  that  of  appre- 
hending a  general  truth.  And  tlie  student  of  logic,  in  tiie  discussion 
even  of  such  truths  as  we  have  cited  above,  acquires  habits  of  circum- 
spect intei-}5retation  of  words,  and  of  exactly  measuring  the  length  and 
breadth  of  his  assertions,  which  are  among  the  most  indispensable  con- 
ditions of  any  considerable  attainment  in  science,  and  which  it  is  one 
of  the  primary  objects  of  logical  discipline  to  cultivate. 

§  3.  Having  noticed,  in  order  to  exclude  from  the  province  of  Rea- 
soning or  Inference  properly  so  called,  the  cases  in  which  the  progress 
from  one  truth  to  another  is  only  apparent,  the  logical  consequent  being 
a  mere  repetition  of  the  logical  antecedent ;  we  now  pass  to  those 
which  ai'e  cases  of  inference  in  the  proper  acceptation  of  the  term, 
those  in  which  we  set  out  from  known  tniths,  to  anive  at  others  really 
distinct  from  them. 

Reasoning,  in  the  extended  sense  in  which  I  use  the  terra,  and  in 
which  it  is  synonymous  with  Inference,  is  popularly  said  to  be  of  two 
kinds  :  reasoning  from  particulars  to  generals,  and  reasoning  from  gen- 
erals to  particulars ;  the  fonner  being  called  Induction,  the  latter 
Ratiocination  or  Syllogism,  It  will  presently  be  shown  that  there  is 
a  third  species  of  reasoning,  which  falls  imder  neither  of  these  descrip- 
tions, and  which,-  nevertheless,  is  not  only  valid,  but  the  foundation  of 
both  the  others. 

It  is  necessary  to  observe,  that  the  expressions,  reasoning  from  par- 
ticulars to  generals,  and  reasoning  from  generals  to  particulars,  are 
recommended  by  brevity  rather  than  by  precision,  and  do  not  ade- 
quately mark,  without  the  aid  of  a  commentary,  the  distinction  between 
Induction  and  Ratiocination.  The  meaning  intended  by  these  expres- 
sions is,  that  Induction  is  infemng  a  proposition  from  propositions  less 
general  than  itself,  and  Ratiocination  is  infeiTing  a  proposition  from 
propositions  equally  or  more  general.  When,  from  the  observation  of 
a  number  of  individual  instances,  we  ascend  to  a  general  proposition, 
or  when,  by  combining  a  number  of  general  propositions,  we  conclude 
from  them  another  proposition  still  more  general,  the  process,  which  is 
substantially  the  same  in  both  instances,  is  called  Induction.  When 
fi-om  a  general  proposition,  not  alone  (for  from  a  single  proposition 
nothing  can  be  concluded  which  is  not  involved  in  the  terms),  but  by 
combining  it  with  other  propositions,  we  infer  a  proposition  of  the 
same  degree  of  geuerahty  wiih  itself,  or  a  less  general  proposition,  or 
a  proposition  merely  individual,  the  process  is  Ratiocination.  Wlien, 
in  short,  the  conclusion  is  more  general  than  the  largest  of  the  prem- 
isses, the  argument  is  commonly  called  Induction ;  when  less  general, 
or  equally  general,  it  is  Ratiocination. 

As  all  experience  begins  with  individual  cases,  and  proceeds  from 
them  to  generals,  it  might  seem  most  conformable  to  the  natural  order 
of  thought  that  Induction  should  be  treated  of  before  we  touch  upon 
Ratiocination.     It  wiU,  however,  be  advantageous,  iii  a  science  which 


112  EEASONING. 

aims  at  tracing  our  acquired  knowledge  to  its  sources,  that  the  inquirer 
should  commence  with  the  later  rather  than  with  the  earlier  stages  of 
the  process  of  constructing  our  knowledge ;  and  should  trace  deriva- 
tive ti-uths  backward  to  the  ti'uths  from  which  they  are  deduced,  and 
upon  which  they  depend  for  their  evidence,  before  attempting  to  point 
out  the  original  spring  from  which  both  ultimately  take  their  rise. 
The  advantages  of  this  order  of  proceeding  in  the  present  instance  will 
manifest  themselves  as  we  advance,  in  a  manner  superseding  the  ne- 
cessity of  any  further  justification  or  explanation. 

Of  Induction,  therefore,  we  shall  say  no  more  at  present,  than  that 
it  at  least  is,  without  doubt,  a  process  of  real  inference.  The  conclu- 
sion in  an  induction  embraces  more  than  is  contained  in  the  premisses. 
The  principle  or  law  collected  from  particular  instances,  the  general 
proposition  in  which  we  embody  the  result  of  our  experience,  covers 
a  much  larger  extent  of  ground  than  the  individual  experiments  which 
are  said  to  form  its  basis.  A  principle  ascertained  by  experience,  is 
more  than  a  mere  summing  up  of  what  we  have  specifically  observed 
in  the  individual  cases  that  we  have  examined  ;  it  is  a  generalization 
grounded  on  those  cases,  and  expressive  of  our  belief,  that  what  we 
there  found  ti'ue  is  true  in  an  indefinite  number  of  cases  which  we  have 
not  examined,  and  are  never  likely  to  examine.  The  nature  and 
gi'ounds  of  this  inference,  and  the  conditions  necessary  to  make  it 
legitimate,  will  be  the  subject  of  discussion  in  the  Third  Book :  but 
that  such  inference  really  takes  place  is  not  susceptible  of  question. 
In  every  induction  we  proceed  from  truths  which  we  knew,  to  truths 
which  we  did  not  know :  from  facts  certified  by  observation,  to  facts 
which  we  have  not  observed,  and  even  to  facts  not  capable  of  being 
now  obsen^ed ;  future  facts,  for  example  :  but  which  we  do  not  hesitate 
to  believe  upon  the  sole  evidence  of  the  induction  itself 

Induction,  then,  is  a  real  process  of  Reasoning  or  Inference. 
Whether,  and  in  what  sense,  so  much  can  be  said  of  the  Syllogism, 
remains  to  be  determined  by  the  examination  into  which  we  are  about 
to  enter. 


CHAPTER  II. 

OF  RATIOCINATION,  OR  SYLLOGISM. 


§  1.  The  analysis  of  the  Syllogism  has  been  so  accurately  and  fully 
performed  in  the  common  manuals  of  Logic,  that  in  the  present  work, 
which  is  not  designed  as  a  manual,  it  is  sufficient  to  recapitulate,  me- 
mories causd,  the  leading  results  of  that  analysis,  as  a  foundation  for 
the  remarks  to  be  afi:erwards  made  upon  the  functions  of  the  syllogism, 
and  the  place  which  it  holds  in  philosophy. 

To  a  legitimate  syllogism  it  is  essential  that  there  should  be  three, 
and  no  more  than  three,  propositions,  namely,  the  conclusion,  or  propo- 
sition to  be  proved,  and  two  other  propositions  which  together  prove 
it,  and  which  are  called  the  premisses.  It  is  essential  that  there  should 
be  three,  and  no  more  than  three  terms,  namely,  the  subject  and  pred- 
icate of  the  conclusion,  and  another  called  the  middleterm,  which  must 


RATIOCINATION,    OR    SYLLOGISM.  113 

be  found  in  both  premisses,  since  it  is  by  means  of  it  that  the  (tthcr 
two  terms  are  to  be  connected  together.  The  predicate  of  the  conchi- 
sion  is  called  the  major  tenn  of  the  syllogism;  the  subject  of  the  con- 
clusion is  called  tlie  minor  term.  As  theie  can  be  but  three  terms, 
the  major  and  minor  terms  must  each  be  found  in  one,  and  only  one, 
of  the  premisses,  together  with  the  middleterm  which  is  in  them  both. 
The  premiss  which  contains  the  middleterm  and  the  mnjt)r  term  is 
called  the  major  premiss ;  that  w^hich  contains  the  middleterm  and  the 
niinor  term  is  called  the  mmor  premiss  of  the  syllogism. 

Syllogisms  are  divided  by  some  logicians  into  throe  Jigures,  by  oth- 
ers into  four,  according  to  the  position  of  the  middleterm,  which  may 
either  be  the  subject  in  both  premisses,  the  predicate  in  both,  or  the 
subject  in  one  and  the  predicate  in  the  other.  Tlie  most  common 
case  is  that  in  which  the  middleterm  is  the  subject  of  the  major  prem- 
iss and  the  predicate  of  the  minor.  This  is  reckoned  as  the  first  figure. 
When  the  middleterm  is  the  predicate  in  both  premisse.s,  the  syllogism 
belongs  to  the  second  figure ;  when  it  is  the  subject  in  both,  to  the 
third.  In  the  fourth  figure  the  middleterm  is  the  subject  of  the  minor 
premiss  and  the  predicate  of  the  major.  Those  WTiters  who  reckon 
no  more  than  tluree  figures,  include  this  case  in  the  first. 

Each  figure  is  subdivided  into  modes,  according  to  what  are  called 
the  quantity  and  qimlitij  of  the  propositions,  that  is,  according  as  they 
are  universal  or  particular,  aflirmative  or  negative.  The  following  are 
examples  of  all  the  legitimate  modes,  that  is,  all  those  in  which  the. 
conclusion  coiTectly  follows  from  the  premisses;  A  is  the  minor  term, 
C  the  major,  B  the  middleterm. 

'  FiKST  Figure. 

All  B  is  C  No  B  is  C  All  B  is  C  No  B  is  C 

All  A  is  B  All  A  is  B  Some  A  is  B  Some  A  is  B 

therefore  therefore              therefore  therefore 

All  A  is  C  No  A  is  C  Some  A  is  C  Some  A  is  not  C 

Second  Figure. 

Xo  C  is  B  All  C  is  B  No  C  is  B  All  C  is  B 

All  A  is  B  No  A  is  B  Some  A  is  B  Some  A  is  not  B 

therefore  therefore  therefore  therefore 

No  A  is  C  No  A  IS  C  Some  A  is  not  C  Some  A  is  not  C 

Third  Figure. 

All  B  is  C  NoBisC  Some B is C  All  Bis  C  iSomeBisnotC  No  B  is  C 

All  B  is  A  All  Bis  A  All  Bis  A  Some  B  is  A  All  B  is  A  Some  B -is  A 

therefore  therefore  therefore         therefore  therefore  therefore 

Some  A  is  C  Some  A  is  not  C  Some  A  is  C  Some  A  is  C  Some  A  is  not  C  Some  A  is  not  C 

Fourth  Figure. 

,  All  C  is  B  All  C  is  B  Some  C  is  B  No  C  is  B  No  C  is  B 

All  B,  is  A      -  No  Bis  A  All  Bis  A  All  B  is  A  Some  Bis  A 

therefore  therefore  therefore  therefore  therefore 

Some  A  i^C  Some  A  i.s  C  Some  A  is  C  Some  A  is  not  C  Some  A  is  not  C 

In  these  exemplars,  or  blank  fonns  for  making  syllogisms,  no  place 
is  assigned  to  singular  propositions ;  not,  of  course,  because  such  pro- 
positions are  not  used  in  ratiocination,  but  because,  their  predicate 
being  affirmed  or  denied  of  the  whole  of  the  subject,  they  are  ranked, 
for  the  purposes  of  the  syllogism,  with  universal  propositions.  Thus, 
these  two  syllogisms — 


114  REASONING. 

All  men  are  mortal  All  men  are  mortal, 

All  kings  are  men,  _     Socrates  is  a  man, 

therefore  ,  therefore 

All  kings  are  mortal,  Socrates  is  mortal, 

are  arguments  precisely  similar,  and  are  both  ranked  in  the  first  mode 
of  the  first  figure. 

■"  The  reasons'  why  syllogisms  in  any  of  the  above  forms  are  legitimate, 
that  is,  why,  if  the  premisses  be  true,  the  conclusion  must  necessarily  be 
so,  and  why  this  is  not  the  case  in  any  other  ipossihle  7?iode,  that  is,  in 
any  other  combination  of  universal  and  particular,  affirmative  and 
negative  propositions,  any  person  taking  interest  in  these  inquiries  may 
be  presumed  to  have  either  learnt  from  the  common  school  books  of 
the  syllogistic  logic,  or  to  be  capable  of  di%Tiiing  for  himself.  The 
reader  may,  however,  be  referred,  for  every  needful  explanation,  to 
Archbishop  Whately's  Elements  of  Logic,  where  he  will  find  stated  with 
philosophical  precision,  and .  explained  with  peculiar  perspicuity,  the 
whole  of  the  common  docti'ine  of  the  syllogism. 

'  AH  valid  ratiocination  ;  all  reasoning  by  which,  from  general  propo- 
sitions previously  admitted,  other  propositions  equally  or  less  general 
are  infeiTed  ;  may  be  exhibited  in  some' of  the  above  forms.  The  whole 
of  Euclid,  for  example,  might  be  thrown  without  difficulty  into  a  series 
of  syllogisms,  regidar  in  mode  and  figure. 

•  Although  a  syllogism  framed  according  to  any  of  these  formulffi  is  a 
valid  argument,  all  correct  ratiocination  admits  of  being, stated  in  syllo- 
gisms of  the  first  figure  alone.  The  rules  for  throwing  an  argument  in 
any  of  the  other  figures  into  the  first  figiire,  are  called  rules  for  the  re- 
duction  of  syllogisms.  It  is  done  by  the  conversion  of  one  or  other,  or 
both,  of  the  premisses.  Thus,  an  argument  in  the  first  mode  of  the 
second  figure,  as — 

No  C  is  B    ' 
All  A  is  B 

therefore 

No  A  is  C, 
may  be  reduced  as  follows.  The  proposition.  No  O  is  B,  being  an  uni- 
versal negative,  admits  of  siniple  conversion,  and  may  be  changed  into 
No  B  is  C,  which,  as  we  showed,  is  the  veiy  same  assertion  in  other 
words — the  same  fact  differently  expressed.  This  ti-ansformation  hav- 
ing been  effected,  the  argument  assumes  the  followdng  fonn  : — 

No  B  is  C 

AH  A  is  B 
therefore 

No  A  is  C, 
which  is  a  good  syllogism  in  the  second     ode  of  the  first  figure.     Again, 
an  argument  in  the  first  mode  of  the  third  figure  must  resemble  the 
following : — 

All  B  is  C 

All  B  is  A 
therefore 

Some  A  is  C, 
where  the  minor  premiss.  All  B  is  A,  conformably  to  what  was  laid 
dawn  in  the  last  chapter  respecting  universal  afflnnatives,  does  not  ad- 
mit of  simple  conversion,  but  may  be  converted ^er  accidens,  thus;  Some 


EATIOCINATION,  OR    SYLLOGISM.  115 

A  is  B  ;  wliich,  though  it  does  not  express. the  whole  of  what  is  assert- 
ed in  the  proposition,  All  B  is  A,  expresses,  as  was  formerly  sliown,  part 
of  it,  and  must  therefore  lie  true  if  the  whole  is  true.  We  have,  then, 
as  the  result  of  the  reduction,  the  following  syllogism  in  the  third  mode 
of  the  lirst  figiu'e  : — 

All  B  is  C 
Some  A  is  B, 
from  which  it  obviously  follows,  that 

Some  A  is  C. 
In  the  same  manner,  or  in  a  manner  on  which,  after  these  examples, 
it  is  not  necessary  to  enlarge,  every  rrtode  of  the  second,  third,  and 
fourth  figures  may  be  reduced  to  some  one  of  the  four  modes  of  the 
first.  In  other  words,  every  conclusion  which  can  be  proved  in  any  of 
the  last  three  figures,  may  be  proved  in  the  first  figure  from  the  same 
premisses,  with  a  slight  alteration  in  the  mere  manner  of  expnissiug 
them.  Eveiy  valid  ratiocination,. therefore,  may  be  stated  in  the  first 
figure,  that  is,  in  one  of  the  following  forms  : — 
Every  B  is  C  No  B  is  C 

All  A  )       •    -p  All  A  )       •    T5 

Some  A      }      ''^'  Some  A      J      ^^  ^ 

therefore  therefore 

All  A.  I      is  c  No  A  is  I      C 

Some  A      )  ■  Some  A-is  not    ) 

•Or,  if  more  significant  symtjols  are  preferred,—^ 

To  prove  an  affii:;rnative,  the  argument  must  %dmit  of  being  stated 
in  this  form  : —  y 

All  animals  are  mortal ; 

All  men  ^ 

Some  men       >      arc  animals ; 

Socrates.        .  )        ' 

therefore 
All  men  ") 

Some  men      >      are  mortal. 
Socrates  ) 

To  prove    a   negative,  the   argument  must   be   capable   of  being 
expressed  in  this  form  : — 

No  one  who  is  capable  of  self-control  is  necessarily  vicious ; 
All  negi-oes  ) 

Some  negroes         >    are  capable  of  self-control ; 
Mr.  A's  negro        ) 

therefore 
No  negroes  are  i 

Some  negroes  are  not  >  necessarily  vicious. 
Mr.  A's  negro  ,is  not  ) 
Although  all  ratiocination  admits  of  being  thrown  into  one  or  the 
other  of  these  fontis,  and  sometimes  gains  considerably  by  the  trans- 
formation, both  in  clearness  and  in  the  obviousness  of  its  consequence  ; 
there  axe,  no  doubt,  cases  in  which  the  argument  falls  more  naturally 
into  one  of  the  other  three  figures,  and  in  which  its  conclusiveness  is 
more  apparent  at  the  first  glance  in  those  figures,  than  when  reduced 
into  the  first.     Thus,  if  the  proposition  were  that  pagans  may  be  vir- 


116  REASOXING. 

tuous,  and  the  evidence  to  prove  it  were  the  example  of  Aristides ;  a 
syllogism  in  the  third  figure, 

Aristides  was  virtuous, 

Aristides  was  a  pagan, 
therefore 

Some  pagan  was  \artuous, 
would  be  a  more  natural  mode  of  stating  the  argument,  and  would 
carry  conviction  more   instantly  home,  than   the    same  ratiocination 
sti-ained  into  the  first  figure,  thus — 

Aristides  was  virtuous, 

Some  pagan  was  Aristides, 
therefore 

Some  pagan  was  virtuous. 

A  German  philofsopher,  Lambert,  whose  Neues  Organon  (published 
in  the  year  1TC4)  contains  among  other  things  the  most  elaborate  and 
complete  exposition  of  the  syllogistic  doctrine  which  I  have  happened 
to  meet  with,  has  expressly  examined  what  sorts  of  arguments  fall 
most  naturally  and  suitably  into  each  of  the  four  figures  ;  and  his  solu- 
tion is  characterized  by  great  higenuity  and  clearness  of  thought  * 
The  argument,  however,  is  one  and  the  same,  in  whichever  figure  it  is 
expressed ;  since,  as  Ave  have  already  seen,  the  premisses  of  a  syllo- 
gism in  the  second,  thuxl,  or  fourth  figm-e,  and  those  of  the  syllogism 
in  the  first  fip-ure  to  which  it  may  be  reduced,  are  the  same  premisses, 
in  everything  except  language,  or,  at  least,  as  much  of  them  as  con- 
tributes to  the  proof  of  the  conclusion  is  the  same.  We  are  therefore 
at  liberty,  in  conformity  with  the  general  opinion  of  logicians,  to  con- 
sider the  two  elementary  fonns  of  the  first  figure  as  the  universal 
types  of  all  coiTect  ratiocination ;  the  one,  when  the  conclusion  to  be 
proved  is  affinnative,  the  other,  when  it  is  negative  ;  even  though  cer- 
tain aro-uments  may  have  a  tendency  to  clothe  themselves  in  the  forms 
of  the  second,  third,  and  fourth  figures  ;  which,  however,  cannot  possi- 
bly happen  with  the  only  class  of  arguments  which  are  of  fii'st-rate 
scientific  importance,  those  in  which  the  conclusion  is  an  universal 
affinnative,  such  conclusions  being  susceptible  of  proof  in  the  first 
figui'e  alone. 

§  2.  On  examining,  then,  these  two  genei-al  formulae,  we  find  that  in 
both  of  them  one  premiss,  the  major,  is  an  universal  proposition ;  and 

*  His  conclusions  are,  "  The  first  figure  is  suited  to  the  discovery  or  proof  of  the  proper- 
ties of  a  thing ;  the-second  to  the  discovery  or  proof  of  the  distinctions  between  things ; 
the  third  to  the  discovery  or  proof  of  instances  and  exceptions  ;  the  fourth  to  the  discovery, 
or  exclusion,  of  the  ditferent  species  of  a  genus."  The  reference  of  syllogisms  m  the  last 
three  figures  to  the  dictum  de  omni  et  nulla  is,  in  Lambert's  view,  strained  and  unnatural : 
to  each  of  the  three  belongs,  according  to  him,  a  separate  axiom,  coordinate  and  of  equal 
authority  with  that  dictum,  and  to  which  he  gives  the  names  of  dictum  de  diverso  for  the 
second  figure,  dictum  de  exemplo  for  the  third,  and  dictuin  de  reciproco  for  the  fourth.  See 
part  i.  or  Dianoiologie,  chap.  iv.  %  229  et  seqq.  . 

Were  it  not  that  the  views  I  am  about  to  propound  on  the  functions  and  ultimate  foun- 
dation of  the  syllogism  render  such  distinctions  as  these  of  very  subordinate  importance,  I 
should  have  availed" myself  largely  of  this  and  other  speculations  of  Lambert ;  who  has 
displayed,  within  the  limits  of  the  received  theory  of  the  syllogism,  an  ongmahty  for  which 
it  was  scarcely  to  be  supposed  that  there  could  still  have  been  room  on  so  exhansted  a 
subject,  and  whose  book  may  be  strongly  recommended  to  those  who  may  attempt  still 
further  to  improve  the  excellent  manuals  we  already  possess  of  this  elementary  portion 
the  Art  of  Reasoning. 


RATIOCINATION,    OR    SYLLOGISiM.  117 

according  as  tins  is  affirmative  or  negative,  the  conclusion  is  so  too. 
AH  ratiocination,  therefore,  starts  from  a  general  proposition,  principle, 
or  assumption  :  a  proposition  in  which  a  predicate  is  affirmed  or  denied 
of  an  entire  class;  that  is,  in  which  some  attribute,  or  the  negation  of 
some  attribute,  is  asserted  of  an  hidehnite  number  of  objects,  distin- 
guished by  a  common  characteristic,  and  designated,  in  consequence, 
by  a  common  name.  • 

Tlie  other  premiss  is  alv/ays  affirmative,  and  asserts  that  something 
(which  may  be  either  an  individual,  a  class,  or  part  of  a  class),  belongs 
to,  or  is  included  in,  the  class,  respecting  vs^hich  something  was  affirmed' 
or  denied  in  the  major  premiss.  It  follows  that  the  attribute  affirmed! 
or  denied  of  the  entire  class  may  (if  there  was  truth  in  that  affirmation 
or  denial)  be  affirmed  or  denied  of  the  object  or  objects  alleged  to  be 
included  in  the  class :  and  this  ia  precisely  the  assertion  made  in  the 
conclusion. 

Whether  or  not  the  foregoing  is  an  adequate  account  of  the  coii- 
stituent  parts  of  the  syllogism,  will  be  presently  considered;  but  as 
far  as  it  goes  it  is  a  true  account.  It  has  accordingly  been  generaUzed 
and  erected  into  a  logical  maxim,  on  which  all  ratiocination  is  said  to 
be  founded,  insomuch  that  to  reason  and  to  apply  the  maxim  are 
su|)posed  to  be  one  and  the  same  thing.  The  maxim  is.  That  what- 
ever can  be  affinned  (or  denied)  of  a  class,  may  be  affirmed  (or  denied) 
of  everything  included  in  the  class.  This  axiom,  supposed  to  be  the 
basis  of  the  syllogistic  theory,  is  termed  by  logicians  the  dictum  de 
omni  et  nullo. ' 

This  maxim,  however,  when  considered  as  a  principle  of  reasoning, 
appears  suited  to  a  system  of  metaphysics  once  indeed  generally 
received,  but  which  for  the  last  two  centuries  has  been  considered  as 
finally  abandoned,  thovigh  thei-e  have  not  been  wanting,  in  our  o^^^r 
day,  attempts  at  its  revival.  So  long  as  what  were  termed  Universals 
were  regarded  as  a  peculiar  kind  of  substances,  having  an  objective 
existence  distinct  from  the  individual  objects  classed  under  them,  the 
dictum  de  omni  conveyed  an  important  meaning ;  because  it  expressed 
the  intercommunity  of  nature,  which  it  was  necessary  upon  that  theory 
that  we  should  suppose  to  exist  between  those  general  substances  and 
the  particular  substances  which  were  subordinated  to  them.  That 
everything  predicable  of  the  universal  was  predicable  of  the  various 
individuals  contained  inider  it,  was  then  no  identical  proposition,  but 
a  statement  of  what  was  conceived  as  a  fimdamental  law  of  the  uni- 
verse. The  assertion  that  the  entire  nature  and  properties  of  the 
substantia  secunda  fonnod  part  of  the  properties  of  each  of  the 
bidividual  substances  called  by  the  same  name  ;  that  the  properties  of 
Man,  for  example,  were  properties  of  all  men ;  was  a  proposition  of 
real  significance  when  Man  did  not  viean  all  men,  but  something 
inherent  in  men,  and  vastly  superior  to  them  in  dignity.  Now,  how- 
ever, when  it  is  known  that  a  class,  an  universal,  a  genus  or  species,  is 
not  an  entity  per  se,  but  neither  more  nor  less  than  the  individual 
substances  themselves  which  are  placed  in  the  class,  and  that  there  is 
nothing  real  in  the  matter  except  those  objects,  a  common  name  given 
to  them,  and  common  attributes  indicated  by  the  name  ;  what,  I  should 
be  glad  to  know,  do  \vq  leani  by  being  told,  that  whatever  can  bo 
affirmed  of  a  class,  may  be  affinned  of  every  object  contained  in  the 
class?     The  class  is  nothing  but  the  objects  contained  in  it:  and  the 


118.  REASONING. 

dictum  de  omrii  merely  amouiits  to  the  identical  proposition,  that  what- 
ever is  true  of  certain  objects,  is^true  of  each  of  those  objects:  If  all 
ratiocination  were  no  more  than  the  application  of  this  maxim  to 
particular  cases,  the  syllogism  would  indeed  be,  what  it  has  so  often 
been  declared  to  be,  solemn  trifling.  The  diction  de  omni  is  on  a  par 
with  another  truth,  which  in  its  time  was  also  reckoned  of  great 
importance,  "Whatever  is,  is;"  and  not  to  be  compared  in  point  of 
sionilicance  to  the  cognate  aphorism,  "It  is  impossible  for  the  same 
thino-  to  be  and  not  to  be ;"  since  this  is,  at  the  lowest,  equivalent  to 
the  logical  axiom  that  contradictory  propositions  cannot  both  be  ti'ue. 
To  o-ive  any  real  meaning  to  the  dictum  de  omni,  we  must  consider  it 
not  as  an  axiom  but  as  a  definition ;  we  must  look  upon  it  as  intended 
to  explain,  in  a  circuitous  and  paraphrastic  manner,  the  meaning  of 
the  word  class. 

An  error  which  seemed  finally  refuted  and  dislodged  from  science, 
often  needs  only  put  on  a  new  suit  of  phrases,  to  be  welcomed  back  to 
its  old  quarters,  and  allowed  to  repose  unquestioned  for  another  cycle 
of  ages.  Modern  philosophers  have  not  been  sparing  in  their  contempt 
for  the  scholastic  dogma  that  genera  and  species  are  a  peculiar  kind  of 
substances,  which  general  substances  being  the  only  pennanent  things, 
while  the  individual  substances  comprehended  under  them  are  in  a 
perpetual  flux,  knowledge,  which  necessarily  imports  stability,  can  only 
have  relation  to  those  general  substances  or  universals,  and  not  to  the 
facts  or  particulars  included  under  them.  Yet,  though  nominally  re- 
jected, this  very  doctrine,  whether  disguised  under  the  Abstract  Ideas  of 
Locke  (whose  speculations,  however,  it  has  less  vitiated  than  those  of 
perhaps  any  other  writer  who  has  been  infected  with  it),  under  the 
ultra-nominalism  of  Hobbes  and  Condillac,  or  the  ontology  of  the  later 
Kantians,  has  never  ceased  to  poison  philosophy.  Once  accustomed 
to  consider  scientific  investigation  as  essentially  consisting  in  the  study 
of  universals,  men  did  not  drop  this  habit  of  thought  when  they  ceased 
to  regard  universals  as  possessing  an  independent  existence  :  and  even 
those  who  went  the  length  of  considering  them  as  mere  names,  could 
not  free  themselves  from  the  notion  that  the  investigation  of  truth  con- 
sisted entirely  or  partly  in  some  kind  of  conjuration  or  juggle  with 
those  names.  Wlien  a  philosopher  adopted  fully  the  Nominalist  view 
of  the  signification  of  general  language,  retaining  along  with  if  the 
dictum  de  omni  as  the  foundation  of  all  reasoning,  two  such  premisses 
fairly  put  together  were  likely,  if  he  was  a  consistent  thinker,  to  land 
him  in  rather  startling  conclusions.  Accordingly  it  has  been  seriously 
held  by  Avi'iters  of  deserved  celebrity,  that  the  process  of  ari'iving  at 
new  truths  by  reasoning  consists  in  the  mere  substitution  of  one  set  of 
arbiti-ary  signs  for  another ;  a  doctrine  which  they  supposed  to  derive 
irresistible  confirmation  fi'om  the  example  of  algebra.  If  there  were 
any  process  in  sorcery  or  necromancy  more  preternatural  than  this,  I 
should  be  much  surprised.  Tlie  culminating  point  of  this  philosophy 
is  the  noted  aphorism  of  Condillac,  that  a  science  is  nothing,  or  scarcely 
anything,  but  une  langue  hien  faite :  in  other  words,  that  the  one  suflJi- 
cient  rule  for  discovering  the  nature  and  properties'  of  objects  is  to 
name  them  properly :  as  if  the  reverse  were  not  the  truth,  that  it  is  im- 
possible to  name  them  properly  except  in  proportion  as  we  are  already 
acquainted  with  their  nature  and  properties.  Can  it  be  necessary  to 
say,  that  none,  not  even  the  most  tnvial  knowledge  with  respect  to 


RATIOCINATION,    OR    SYLLOGISM.  119 

Things,  ever  was  or  could  be  originally  got  at  by  any  conceivable 
manipulation  of  mere  names  :  and  that  wlit^t  can  be  learnt  from  names, 
is  only  what  somebody  who  used  the  names,  knew  before  ?  Philoso- 
phical analysis  confirms  the  indication  of  common  sense,  that  the  func- 
tion of  names  is  but  that  of  enabling  us  to  remcmher  and  to  communi- 
cate our  tlioughts.  That  they  also  strengthen,  even  to  an  incalculable 
extent,  the  power  of  thought  itself,  is  most  true :  but  they  do  this  by 
no  intrinsic  and  peculiar  virtue  :  they  do  it  by  the  power  inherent  in 
an  artificial  memory,  an  instrument  of  which  few  have  adequately  con- 
sidered the  immense  potency.  As  an-  artificial  memory,  language  truly 
is,  what  it  has  so  often  been  called,  an  instrument  of  thought :  but  it  is 
one  thing  to  be  the  instrument,  and  another  to  be  the  exclusive  subject 
upon  which  the  instrument  is  ejxercised.  We  think,  indeed,  to  a  con- 
siderable extent,  by  means  of  names,  but  what  Ave  think  of,  are  the 
things  called  by  those  names  ;  and  there  cannot  be  a  greater  eiTor  than 
to  imagine  that  thought  can  be  canied  on  with  nothing  in  our  mind 
but  names,  or  that  we  can  make  the  names  think  for  us. 

§  3.  Those  who  considered  the  dictum  de  omni  as  the  foundation  of 
the  syllogism,  looked  upon  arguments  in  a  manner  coiTesponding  to 
the  erroneous  Anew  which  Hobbes  took  of  propositions.  Because  there 
are  some  propositions  which  are  merely  verbal,  Hobbes,  in  order  (ap- 
parently) that  his  definition  might  be  rigorously  universal,  defined  a 
proposition  as  if  no  propositions  declare'd  anything  except  the  meaning 
of  words.  If  Hobbes  was  right;  if  no  further  account  than  this  could 
be  given  of  the  import  of  propositions  ;  no  theory  could  be  given  but 
the  commonly  received  one,  of  the  combination  of  propositions  in  a 
syllogism.  If  the  minor  premiss  asserted  nothing  more  than  that  some- 
thing belongs  to  a  class,  and  if,  as  consistency  would  require  us  to 
suppose,  the,  major  premiss  asserted  nothing  of  that  class  except  that 
it  is  included  in  another  class,  the  conclusion  would  only  be,  that  what 
was  included  in  the  lower  class  is  included  in  the  higher,  and  the  result, 
therefore,  nothing  except  that  the  classification  is  consistent  Avith  itself. 
But  Ave  have  seen  that  it  is  no  sufficient  account  of  the  meaning  of  a 
proposhion,  to  say  that  it  refers  something  to,  or  excludes  something 
from,  a  class.  EAory  proposition  Avhich  conveys  real  infoi-mation 
asserts  a  matter  of  fact,  dependent  upon  the  laAvs  of  nature  and  not 
upon  artificial  classification.  It  asstits  that  a  given  object  does  or 
does  not  possess  a  given  attribute  ;  or  it  asserts  that  tAvo  attributes,  or 
sets  of  attributes,  do  or  do  not  (constantly  or  occasionally)  coex- 
ist. Since  such  is  the  purport  of  all  propositions  AA'hich  convey 
any  real  knowledge,  and  since  ratiocination  is  a  mode  of  acquir- 
ing real  knowledge,  any  theory  of  ratiocination  Avhich  does  not  re- 
cognize this  import  of  propositions,.cannot,  we  may  be  sure,  be  the 
true  one. 

Applying  this  vieAV  of  propositions  to  the  two  premisses  of  a  syllo- 
gism, Ave  obtain  the  foUoAving  results.  The  major  premiss,  which,  as 
already  remarked,  is  ahvays  universal,  asserts,  that  all  things  Avhich  have 
a  certain  attribute  (or  attributes)  have  or  have  not  along- Avith  it,  a  cer- 
tain other  attribute  (or  attributes).  The  minor  premiss  asserts  that  the 
thing  or  set  of  things  Avhich  are  the  subject  of  that  premiss,  have  the 
first-mentioned  attribute  ;  and  the  conclusion  is,  that  they  have  (or  that 
they  have  not)  the  second.     Thus  in  our  former  example, 


120  REASONING. 

All  men  are  mortal, 

Socrates  is  a  man, 
therefore 

Socrates  is  mortal, 
the  subject  and  predicate  of  the  major  premiss  are  connotative  terms, 
denoting  objects  and  connoting  attributes.  The  assertion  in  the  major 
premiss  is,  that  along  with  one  of  the  two  sets  of  attributes,  we  always 
find  the  other  :  that  the  attributes  connoted  by  "  man"  never  exist  un- 
less conjoined  with  the  attribute  called  mortality.  The  assertion  in  the 
minor  premiss  is  that  the  individual  named  Socrates  possesses  the 
former  attributes ;  and  it  is  concluded  that  he  possesses  also  the  atti-i- 
bute  mortality.     Or,  if  both  the  premisses  are  general  propositions,  as 

All  men  are  m6rtal, 

All  kings  are  men, 
therefore 

All  kings  are  mortal, 

the  minor  premiss  asserts  that  the  attributes  denoted  by  kingship  only 
exist  in  conjunction  with  those  signified  by  the  word  man.  The  major 
asserts  as  before,  that  the  last-mentioned  attiibutes  are  never  found 
without  the  attribute  of  mortality.  The  conclusion  is,  that  wherever 
the  atti-ibutes  of  kingship  are  found,  that  of  mortality  is  found  also. 

If  the  major  premiss  were  negative,  as.  No  men  are  gods,  it  would 
assert,  not  that  the  attributes  connoted  by  "  Man"  never  exist  without, 
but  that  they  never  exist  with,  those  connoted  by  "  God  :"  fi-om  which, 
together  with  the  minor  premiss,  it  is  concluded,  that  the  same  incom- 
patibility exists  between  the  atti-ibutes  constituting  a  god  and  those  con- 
stituting a  king.  In  a  similar  manner  we  might  analyze  any  other  ex- 
ample of  the  syllogism. 

If  we  generalize  this  process,  and  look  out  for  the  principle  or  law 
involved  in  every  such  inference,  and  presupposed  in  every  syllogism 
the  propositions  of  which  are  anything  more  than  merely  verbal ;  we 
find,  not  the  umneaning  dictum  de  omni  et  nullo,  but  a  fundamental 
principle,  or  rather  two  principles,  strikingly  resembling  the  axioms  of 
mathematics.  The  first,  which  is  the  principle  of  afiinnative  syllo- 
gisms, is,  that  things  which  coexist  with  the  same  thing,  coexist  with 
one  another.  The  second  is  the  principle  of  negative  syllogisms,  and 
is  to  this  effect ;  that  a  thing  which  coexists  with  another  thing,  with 
which  other  a  third  thing  does  not  coexist,  is  not  coexistent  with  that 
third  thing.  These  axioms  manifestly  relate  to  facts,  and  not  to  con- 
ventions :  and  one  or  other  of  them  is  the  gi-ound  of  the  legitimacy  of 
every  argument  in  which  facts  and  not  conventions  are  the  matter  treat- 
ed of. 

§  4.  It  only  remains  to  translate  this  exposition  of  the  syllogism 
from  the  one  into  the  other  of  the  two  languages  in  which  we  foiTnerly 
remarked*  that  all  propositions,  and  of  course  therefore  all  combina- 
tions of  propositions,  might  be  expressed.  We  observed  that  a  propo- 
sition might  be  considered  in  two  difterent  lights ;  as  a  portion  of  our 
knowledge  of  nature,  or  as  a  memorandum  for  our  guidance.  Under 
the  former,  or  speculative  aspect,  an  affirmative  general  proposition  is 
an  assertion  of  a  speculative  truth,  viz.,  that  whatever  has  a  certain  at- 
*  Supra,  p.  157. 


RATIOCINATION,    OK    SYLLOGISM.  121 

tribute  lias  a  certain  other  attribute.  Under  the  other  aspect,  it  is  to 
be  regarded  not  as  a  part  of  our  knowledge,  but  as  an  aid  tor  our  prac- 
tical exigencies,  by  enabling  us  when  we  see  or  learn  that  an  object 
possesses  one  of  the  two  attributes,  to  infer  that  it  possesses  the  other; 
thus  employing  the  first  attribute  as  a  mcUfk  or  evidence  of  the  second. 
Thus  regarded,  every  syllogism  comes  within  the  following  general 
formula  : — 

Attribute  A  is  a  mark  of  attribute  B, 

A  given  object  Ims  the  mark  A, 
therefore 

The  given  object  has  the  attribute  B. 
RefeiTed  to  this  type,  the  ai'guments  which  we  have  lately  cited  as 
specimens  of  the  syllogism,  will  express  themselves  in  the  following 
manner : — 

The  attributes  of  man  are  a  mark  of  the  attribute  mortality, 

Socrates  has  the  attributes  of  man, 
therefore 

Socrates  has  the  attribute  mortahty. 
And  again, 

The  attributes  of  man  are  a  mark  of  the  attribute  mortality. 

The  attributes  of  a  king  are  a  mark  of  the  attributes  of  man, 
therefore 

The  attributes  of  a  king  are  a  mark  of  the  attribute  mortality. 
And  lastly. 

The  attributes  of  man  are  a  mark  of  the  absence  of  the  attributes 
of  a  god. 

The  attributes  of  a  king  are  a  mark  of  the  attributes  of  man, 
therefore 

The  attributes  of  a  king  are  a  mark  of  the  absence  of  the  attributes 
signified  by  the  word  god  : 

(or,  are  evidence  of  the  absence  of  those  attributes). 
To  correspond  with  this  alteration  in  the  form  of  the  syllogisms,  the 
axioms  on  which  the  syllogistic  process  is  founded  must  undergo  a 
corresponding  transformation.  In  this  altered  phraseology,  both  those 
axioms  may  be  brought  under  one  general  expression  ;  namely,  that 
whatever  possesses  any  mark,  possesses  that  which  it  is  a  mark  of. 
Or,  when  the  minor  premiss  as  well  as  the  major  is  universal,  we  may 
state  it  thus  :  whatever  is  a  mark  of  any  mark,  is  a  mark  of  that  which 
this  last  is  a  mark  of.  To  trace  the  identity  of  these  axioms  with  those 
previously  laid  down,  may  be  safely  left  to  the  intelligent  reader.  We 
shall  find,  as  we  proceed,  the  great  convenience  of  the  phraseology 
into  which  we  have  last  thrown  them,  and  which  is  better  adapted  than 
any  I  am  acquainted  with,  to  express  with  precision  and  force  what  is 
aimed  at,  and  actually  accomplished,  in  every  case  of  the  ascertain- 
ment of  a  truth  by  ratiocination. 


128  REASONING. 


CHAPTER  III. 

OF  THE  FUNCTIONS,  AND  LOGICAL  VALUE,  OF  THE  SYLLOGISM. 

§  1.  We  hav«  shown  what  is  the  real  nature  of  the  truths  \%'itli 
which  the  Syllogism  is  conversant,  in  contradistinction  to  the  rriore- 
supei-ficial  manner  in  which  their  import  is  conceived  in  the  common 
theory ;  and  what  are  the  fundamental  axioms  on  which  its  probative 
force  or  conclusiveness  depends.  We  have  now  to  inquire,  whether 
the  syllogistic  process,  that  of  reasoning  from  generals  to  particulars, 
is,  or  is  not,  a  process  of  inference  ;  a  progi-ess  from  the  known  to  the 
unknown ;  a  means  of  coming  to  a  knowledge  of  something  which  we 
did  not  know  before. 

Logicians  have  been  remarkably  unanimous  in  their  mode  of  an- 
swering this  question.  It  is  universally  allowed  that  a  syllogism  is 
vicious  if  there  be  anything  more  in  the  conclusion  than  was  assumed 
in  the  premisses.  But  this  is,  in  fact,  to  say,  that  nothing  ever  was,'  or 
can  be,  proved  by  syllogism,  which  was  not  kno^vn,  or  assumed  to  be 
known,  before.  Is  ratiocination,  then,  not  a  process  of  inference "? 
And  is  the  syllogism,  to  which  the  word  reasoning  has  so  often  been 
represented  to  be  exclusively  appropriate,  not  really  entitled  to  be 
called  reasoning  at  all  I  This  seems  an  inevitable  consequence  of  the 
doctrine,  admitted  by  all  writers  on  the  subject,  that  a  syllogism  can 
prove  no  more  than  is  involved  in  the  premisses.  Yet  the  acknowl- 
edgment so  explicitly  made,  has  not  prevented  one  set  of  writers  from 
continuing  to  represent  the  syllogism  as  the  coiTect  analysis  of  what 
the  mind  actually  performs  in  discovering  and  proving  the  larger  half 
of  the  truths,  whether  of  science  or  of  daily  life,  which  we  believe  ; 
while  those  who  have  avoided  this  inconsistency,  and  followed  out  the 
general  theorem  respecting  the  logical  value  of  the  syllogism  to  its 
legitimate  corollary,  have  been  led  to  impute  uselessness  and  frivolity 
to  the  syllogistic  theory  itself,  on  the  gi'ound  of  the  petitio  principii 
which  they  allege  to  be  inherent  in  every  syllogism.  As  I  believe 
both  these  opinions  to  be  fundamentally  erroneous,  I  must  request  the 
attention  of  the  reader  to  certain  considerations,  without  which  any 
just  appreciation  of  the  true  character  of  the  syllogism,  and  the  func- 
tions it  performs  in  philosophy,  appears  to  me  impossible ;  but  which 
seem  to  have  been  either  overlooked,  or  insufficiently  adverted  to, 
both  by  the  defenders  of  the  syllogistic  theory  and  by  its  assailants. 

§  2.  It  must  be  granted  that  in  every  syllogism,  considered  as  an 
argument  to  prove  the  conclusion,  there  is  a  petitio  principii.  Wlien 
we  say, 

All  men  are  mortal, 
Socrates  is  a  man, 

therefore 
Socrates  is  mortal ; 

it  is  unanswerably  urged  by  the  adversaries  of  the  syllogistic  theory, 
that  the  proposition,  Socrates  is  mortal,  is  presupposed  in  the  more 
general  assumption,  All  men  are  mortal :  that  we  cannot  be  assured 
of  the  mortality  of  all  men,  unless  we  were  previously  certain  of  the 


FUNCTIONS  AND  VALUE  OF  THE  SYLLOGISM.       123 

mortality  of  every  individual  man  :  tliat  if  it  be  still  doubtful  whether 
Socrates,  or  any  other  indi-v-idunl  you  choose  to  name,  be  morta:l  or 
not,  the  same  degree  of  uncertainty  must  hang  over  the  assertion,  All 
men  are  mortal :  that  the  general  principle,  instead  of  being  given  as 
evidence  of  the  particular  case,  cannot  itself  be  taken  for  true  without 
exception,  until  every  shadow  of  doubt  which  could  affect  any  caso 
comprised  with  it,  is  dispelled  by  evidence  aliunde.;  and  then  what 
remains  for  the  syllogism  to  prove  ]  that,  in  short,  no  reasoning  fi-om 
generals  to  particulars  can,  as  such,  prove  anything  :  since  from  a 
general  principle  you  cannot  infer  any  particulars,  but  those  which  the 
principle  itself  assumes  as  foreknown. 

This  doctrine  is  irrefragable ;  and  if  logicians,  though  unable  to 
dispute  it,  have  usually  exhibited  a  strong  disposition  to  explain  it 
away,  this  was  not  because  they  could  discover  any  flaw  in  the  argu- 
ment itself,  but  because  the  contrary  opinion  seemed  to  rest  upon 
arguments  equally  indisputable.  In  the  syllogism  last  referred  to,  for 
example,  or  in  any  of  those  which  we  previously  constructed,  is  it  not 
evident  that  the  conclusion  may,  to  the  person  to  whom  the  syllogism 
is  presented,  be  actually  and  boiid  fide  a  new  truth  1  Is  it  not  matter 
of  daily  exjjerience  that  truths  previously  undreamt  of,  facts  which 
have  not  been,  and  cannot  be,  directly  observed,  are  amved  at  by  way 
of  general  reasoning  ?  We  believe  that  the  Duke  of  Wellington  is 
mortal.  We  do  not  know  this  by  direct  observation,  since  he  is  not 
yet  dead.  If  we  were  asked  how,  this  being  the  case,  we  know  the 
duke  to  be  mortal,  we  should  probably  ajiswer.  Because  all  men  are 
so.  Here,  therefore,  we  ari'ive  at  the  knowledge  of  a  truth  not  (as 
yet)  susceptible  of  obsei-vation,  by  a  reasoning  which  admits  of  being 
exhibited  in  the  following  syllogism  : — 

All  men  are  mortal, 

The  Duke  of  Wellington  is  a  man, 

therefore 
The  Duke  of  Wellington  is  mortal. 

And  since  a  large  portion  of  our  knowledge  is  thus  acquired,  logicians 
have  persisted  in  representing  the  syllogism  as  a  process  of  inference 
or  proof;  although  none  of  them  have  cleared  up  the  difficulty  which 
arises  fi-om  the  inconsistency  between  that  assertion  and  the  principle, 
that  if  there  be  anything  in  the  conclusion  which  was  not  already  as- 
serted in  the  premisses,  the  argument  is  ricious.  For  it  is  impossible 
to  attach  any  serious  scientific  value  to  such  a  mere  salvo,  as  the  dis- 
tinction drawn  between  being  involved  by  impUcation  in  the  premisses, 
and  being  directly  asserted  in  them.  When  Archbishop  Whately,  for 
example,  says,*  that  the  object  of  reasoning  is  "merely  to  expand  and 
unfold  the  assertions  wrapt  up,  as  it  were,  and  impHed  in  those  with 
which  we  set  out,  and  to  bring  a  person  to  perceive  and  acknowledge 
the  full  force  of  tliat  which  he  lias  admitted,"  he  docs  not,  I  think, 
meet  the  real  difficulty  requiring  to  be  explained,  namely,  how  it  hap- 
pens that  a  science,  like  geometry,  can  be  all  "  wTSpt  up"  in  a  few 
definitions  and  axioms.  Nor  does  this  defence  of  the  syllogism  differ 
much  from  what  its  assailants  urge  against  it  as  an  accusation,  whert 
they  charge  it  with  being  of  no  use  except  to  those  who  seek  to  press 

*  Logic,  p.  216. 


124  REASONING. 

the  consequences  of  an  admission  into  which  a  man  has  been  entrapped 
without  having  considered  and  understood  its  full  force.  When  yoti 
admitted  the  major  premiss,  you  asserted  the  conclusion;  but,  says 
Archbishop  Whately,  you  asserted  it  by  implication  merely  :  this, 
however,  can  here  only  mean  that  you  asserted  it  unconsciously ;  that 
you  did  not  kuow  you  were  asserting  it ;  but,  if  so,  the  difficulty  re- 
vives in  this  shape — Ought  you  not  to  have  known  ]  Were  you  war- 
ranted in  asserting  the  general  proposition  without  having  satisfied 
yourself  of  the  truth  of  eveiything  which  it  fairly  includes  1  And  if 
not,  what  then  is  the  syllogistic  art  but  a  contiivance  for  catching  you 
in  a  trap,  and  holding  you  fast  in  it  1 

§  3.  From  this  difficulty  there  appears  to  be  but  one  issue.  The 
proposition,  that  the  Duke  of  Wellington  is  mortal,  is  e\idently  an  in- 
ference ;  it  is  got  at  as  a  conclusion  fi'om  something  else  ;  but  do  we,  in 
reality,  conclude  it  from  the  proposition,  All  men  are  mortal  ?  I  an- 
swer, no. 

The  eiTor  committed  is,  I  conceive,  that  of  overlooking  the  distinc- 
tion between  the  two  parts  of  the  process  of  philosophizing,  the  infer- 
ring part,  and  the  registering  part ;  and  ascribing  to  the  latter  the 
functions  of  the  former.  The  mistake  is  that  of  refen'ing  a  man  to  his 
own  notes  for  the  origin  of  his  knowledge.  If  a  man  is  asked  a  ques- 
tion, and  is  at  the  moment  unable  to  answer  it,  he  may  refi-esh  his 
memory  by  turning  to  a  memorandum  which  he  cames  about  A\dth 
him.  But  if  he  were  asked,  how  the  fact  came  to  his  knowledge,  he 
would  scarcely  answer,  because  it  was  set  down  in  his  note-book : 
unless  the  book  was  A\Titten,  like  the  Koran,  with  a  quill  from  the 
wing  of  the  angel  Gabriel. 

Assuming  that  the  proposition.  The  Duke  of  Wellington  is  mortal, 
is  immediately  an  inference  from  the  proposition,  All  men  are  mortal ; 
whence  do  we  derive  our  knowledge  of  that  general  truth  ]  No  super- 
natiu'al  aid  being  supposed,  the  answer  must  be,  by  observation.  Now, 
all  which  man  can  obsei-A'e  are  individual  cases.  From  these  all  gen- 
eral truths  must  be  drawn,  and  into  these  they  may  be  again  resolved : 
for  a  general  truth  is  but  an  aggregate  of  particular  truths ;  a  compre- 
hensive expression,  by  which  an  indefinite  number  of  individual  facts 
are  affirmed  or  denied  at  once.  But  a  general  proposition  is  not 
merely  a  compendious  form  for  recording  and  preserving  in  the  mem- 
ory a  number  of  pai'ticular  facts,  all  of  which  have  been  observed. 
Generalization  is  not  a  process  of  mere  naming,  it  is  also  a  process  of 
inference.  From  instances  which  we  have  observed,  we  feel  warranted 
in  concluding,  that  what  we  found  true  in  those  instances,  holds  in  all 
similar  ones,  past,  present,  and  future,  however  numerous  they  may  be. 
We  then,  by  that  valuable  contrivance  of  language  which  enables  us  to 
speak  of  many  as  if  they  were  one,  record  all  that  we  have  observed, 
together  with  all  that  we  infer  fi-om  our  observations,  in  one  concise 
expression;  and  have  thus  only  one  proposition,  instead  of  an  endless 
number,  to  remember  or  to  communicate.  The  results  of  many  obser- 
vations and  inferences,  and  instructions  for  making  innumerable  infer- 
ences in  unforeseen  cases,  are  compressed  into  one  short  sentence. 

^V^aen,  therefore,  we  conclude  from  the  death  of  John  and  Thomas, 
and  every  other  person  we  ever  heard  of  in  whose  case  the  experi- 
ment had  been  fairly  tried,  that  the  Duke  of  WeUington  is  mortal  like 


FUNCTIONS  AND  VALUE  OF  THE  SYLLOGISM.        125 

the  rest  -y.  wo  may,  indeed,  pass  through  the  generalization.  All  men 
are  mortal,  as  an  intermediate  stage  ;  but  it  is  not  in  the  latter  half  of 
the  process,  the  descent  from  all  men  to  the  Duke  of  Wellington,  that 
the  ittfercncc  resides.  The  inference  is  finished  when  we  have  asserted 
that  all  men  are  mortal.  What  remains  to  be  performed  afterwards 
is  merely  deciphering  our  own  notes. 

Archbishop  Whately  has  contended  that  syllogizing,  or  reasoning 
from  generals  to  particulars,  is  not,  agreeably  to  the  vulgar  idea,  a  pe- 
culiar mode  of  reasoning,  but  the  philosophical  analysis  of  the  mode  in 
which  all  men  reason,  and  must  do  so  if  they  reason  at  alL  With  tbe 
deference  due  to  so  high  an  authority,  I  cannot  helji  thinking  that  the 
vulgar  notion  is,  in  this  case,  the  more  con-ect.  If,  from  our  experi- 
ence of  John,  Thomas,  &c.,  who  once  were  li\'ing,  but  are  now  dead, 
we  are  entitled  to  conclude  that  all  human  beings  are  mortal,  we  might 
surely  without  any  logical  inconsequence  have  concluded  at  once  fi-om 
those  instances,  that  the  Duke  of  Wellington  is  mortal.  The  mortality 
of  John,  Thomas,  and  company  is,  after  all,  the  whole  evidence  we 
have  for  the  mortality  of  the  Duke  of  Wellington.  Not  one  iota  is 
added  to  the  proof  by  intei-polating  a  general  proposition.  Since  the 
individual  cases  are  all  the  evidence  we  can  possess,  evidence  which 
no  logical  form  into  which  we  choose  to  throw  it  can  make  gi'eater 
than  it  is ;  and  since  that  evidence  is  either  sufficient  in  itself,  or,  if  in- 
sufficient for  one  purpose,  cannot  be  sufficient  for  the  other;  I  am 
unable  to  see  why  we  should  be  forbidden  to  take  the  shortest  cut 
from  these  sufficient  premisses  to  the  conclusion,  and  constrained  to 
travel  the  "high  priori  road"  by  the  arbitrary  fiat  of  logicians.  I  can- 
not perceive  why  it  should  be  impossible  to  journey  from  one  place  to 
another  unless  we  "  march  up  a  hill,  and  then- march  down  again."  It 
may  be  the  safest  road,  and  there  may  be  a  resting  place  at  the  top 
of  the  hill,  affi)rding  a  commanding  view  of  the  suiTounding  country ; 
but  for  the  inere  purpose  of  arriving  at  our  journey's  end,  our  taking 
that  road  is  perfectly  optional ;  it  is  a  question  of  time,  trouble,  and 
danger. 

Not  only  may  we  reason  from  particulars  to  particulars,  without 
passing  through  generals,  but"  we  perpetually  do  so  reason.  All  our 
earliest  inferences  are  of  this  nature.  From  the  first  dawn  of  intelli- 
gence we  draw  inferences,  but  years  elapse  before  we  learn  the  use 
of  general  language.  The  child,  who,  having  burnt  his  fingers,  avoids 
to  thrust  them  again  into  the  fire,  has  reasoned  or  inferred,  though  he 
has  never  thought  of  the  general  maxim.  Fire  bums.  He  knows  from 
memory  that  he  has  been  burnt,  and  on  this  evidence  believes,  when 
he  sOes  a  candle,  that  if  he  puts  his  finger  into  the  flame  of  it,  he  will 
be  burnt  again.  He  believes  this  in  every  case  which  happens  to 
arise  ;  but  without  looking,  in  each  instance,  beyond  the  present  case. 
He  is  not  generalizing ;  he  is  infemng  a  particular  from  particulars. 
In  the  same  way,  also,  brutes  reason.  There  is  little  or  no  ground  for 
attributing  to  any  of  the  lower  animals  the  use  of  conventional  signs, 
without  which  general  propositions  are  impossible.  But  those  anima;ls 
profit  by  experience,  and  avoid  what  they  have  found  to  cause  them  pain, 
in  the  same  manner,  though  not  always  with  the  same  skill,  as  a  human 
creature.     Not  only  the  bui'nt  child,  but  the  burnt  dog,  dreads  the  fire. 

I  believe  that,  in  point  of  fact,  when  drawing  inferences  from  our 
personal  experience    and  not  from  maxims  handed  down  to  us  by 


126  REASONING. 

books  or  tradition,  We'much  oftener  conclude  from  particulars  to  par- 
ticulars directly,  than  tJirough  the  intermediate  agency  of  any  general 
proposition.  We  are  constantly  reasoning  from  ourselves  to  other 
people,  or  from  one  person  to  another,  without  giving  ourselves  the 
trouble  to  erect  our  obsei-vations  into  general  maxims  of  human  or 
external  nature.  When  we  conclude  that  some  person  will,  on  some 
given  occasion,  feel  or  act  so  and  so,  we  sometimes  judge  from  an 
enlarged  consideration  of  the  manner  in  which  men  in  general,  or  men 
of  some  paiticular  character,  are  accustomed  to  feel  and  act ;  but 
much  oftener  from  having  known  the  feelings  and  conduct  of  the  same 
man  in  some  previous  instance,  or  from  considering  how  we  should 
feel  or  act  oui'selves.  It  is  not  only  the  village  matron  who,  when 
called  to  a  consultation  upon  the  case  of  a  neighbor's  child,  pronoun- 
ces on  the  evil  and  its  I'emedy  simply  on  the  recollection  and  authority 
of  what  she  accounts  the  similar  case  of  her  Lucy.  We  all,  where 
we  have  no  definite  maxims  to  steer  by,  guide  ourselves  in  the  same 
way;  and  if  we  have  an  extensive  experience,  and  retain  its  impres- 
sions strongly,  we  may  acquire  in  this ,  manner,  a  very  considerable 
power  of  accurate  judgment,  which  we  may  be  utterly  incapable  of 
justifying  or  of  communicating  to  others.  Among  the  higher  order  of 
practical  intellects,  there  have  been  many  of  whom  it  was  remarked 
how  admirably  they  suited  their  means  to  their  ends,  without  being 
able  to  give  any  sufficient  reasons  for  what  they  did ;  and  applied,  or 
seemed  to  apply,  recondite  principles  which  they  were  wholly  unable 
to  state.  Tliis  is  a  natural  consequence  of  having  a  mind  stored 
with '  appropriate  particulars,  and  having  been  long  accustomed  to 
reason  at  once  from  these  to  fresh  particulars,  without  practising  the 
habit  of  stating  to  oneself  or  to  others  the  coiTesponding  general  prop- 
ositions. An  old  waiTior,  on  a  rapid  glance  at  the  .outlines  of  the 
ground,  is  able  at  once  to  give  the  necessary  orders  for  a  skillful  ar- 
rangement of  his  troops ;  though  if  he  has  received  little  theoretical 
instruction,  and  has  seldom  been  called  upon  to  answer  toother  people 
for  his  conduct,  he  may  never  have  had  in  his  mind  a  single  general 
theorem  i-especting  the  relation  between  ground  and  array.  But  his 
experience  of  encampments,  under  circumstances  more  or  less  similar, 
has  left  a  numbesr  of  vivid,  unexpressed,  ungeneralized  analogies  in 
his  mind,  the  most  appropriate  of  which,  instantly  suggesting  itself, 
determines  him  to  a  judicious  arrangement. 

The  skill  of  an  uneducated  person  in  the  use  of  weapons,  or  of  tools, 
is  of  a  precisely  similar  nature.  The  savage  who  executes  unerringly 
the  exact  throw  which  brings  down  his  game,  or  his  enemy,  in  the  man- 
ner most  suited  to  his  purpose,  under  the  operation  of  all  tlie  conditions 
necessarily  involved,  the  weight  and  form  of  the  weapon,  the  direction 
and  distance  of  the  object,  the  action  of  the  wind,  &c.,  owes  this  power 
to  a  long  series  of  previous  experiments,  the  results  of  which  he  cer- 
tainly never  framed  into  any  verbal  theorems  or  rules.  It  is  the  same 
in  all  extraordinary  manual  dexterity.  Not  long  ago  a  Scotch  manufac- 
turer procured  from  England,  at  a  high  rate  of  wages,  a  working  dyer, 
famous  for  producing  very  fine  colors,  with  the  view  of  teaching  to  his 
other  workmen  the  same  skill.  The  workman  came  ;  but  his  mode  of 
proportioning  the  ingredients,  in  which  lay  the  secret  of  the  effects  he 
produced,  was  by  talcing  them  up  in  handflils,  while  the  common  method 
was  to  weigh  them.     The  manufacturer  sought  to  make  him  turn  liis 


FUNCTIONS  AND  VALUE  OF  THE  SYLLOGISM.        127 

handling  system  into  an  equivalent  weighing  system,  that  the  general 
principle  of  his  peculiar  mode  of  proceeding  might  be  ascertained. 
This,  liowever,  the  man  found  himself  quite  unable  to  do,  and  therefore 
could  impart  his  skill  to  nobody.  He  had,  from  the  individual  cases  of 
his  o^vn  experience,  established  a  connexion  in  his  mind  between  fine 
effects  of  color,  and  tactual  perceptions  in  handling  his  dyeing  materi- 
als ;  and  from  these  perceptions  he  could,  in  any  particular  cases,  infer 
the  means  to  be  employed,  and  the  effects  which  would  be  produced, 
but  could  not  put  others  in  possession  of  the  gi'onnds  on  which  he  pro- 
ceeded, from  having  never  generalized  them  in  his  own.  mind,  or  ex- 
pressed them  in  language. 

Almost  every  one  knows  Lord  Mansfield's  advice  to  a  man  of  prac- 
tical good  sense,  who,  being  appointed  governor  of  a  colony,  had  to 
preside  in  its  court  of  justice,  without  previous  judicial  practice  or  legal 
education.  The  ad\-ice  was,  to  give  his  decision  boldly,  for  it  would 
probably  be  right ;  but  never  to  venture  on  assigning  reasons,  for  they 
would  almost  infallibly  be  wi-ong.  In  cases  like  this,  which  are  of  no 
uncommon  occurrence,  it  would  be, absurd  to  suppose  that  the  bad 
reason  was  the  source  of  the  good  decision.  Lord  Mansfield  knew  that 
if  any  reason  were  assigned  it  would  be  necessarily  an  afterthought, 
the  judge  being  in  fact  guided  by  impressions  from  past  experience, 
without  the  circuitous  process  of  framing  general  principles  fi-om  them, 
and  that  if  he  attempted  to  frame  any  such  he  would  assuredly  fail. 
Lord  Mansfield,  however,  would  not  have  doubted  that  a  man  of  equal 
experience,  who  had  also  a  mind  stored  with  general  propositions  de- 
rived by  legitimate  induction  from  tliat  experience,  would  have  been 
greatly  preferable  as  a  judge,  to  one,  howpver  sagacious,  who  could 
not  be  trusted  with  the  explanation  and  justification  of  his  own  judg- 
ments. The  cases  of  able  men  performing  wonderful  things  they  know 
not  how,  are  examples  of  the  less  civilized  and  most  spontaneous  form 
of  the  operations  of  superior  minds.  It  is  a  defect  in  them,  and  often 
a  somxe  of  eiTors,  not  to  have  generalized  as  they  went  on ;  but  gen- 
eralization is  a  help,  the  most  impoitant  indeed  of  all  helps,  yet  not  an 
essential. 

Even  philosophers,  who  possess,  in  the  form  of  general  propositions, 
a  systematic  record  of  the  results  of  the  experience  of  mankind,  need 
not  always  revert  to  those  general  propositions  in  order  to  apply  that 
experience  to  a  new  case.  It  is  justly  remarked  by  Dugald  Stewart, 
that  though  our  reasonings  in  mathematics  depend  entirely  upon  the 
axioms,  it  is  by  no  means  necessary  to  our  seeing  the  conclusiveness  of 
the  proof,  that  the  axioms  should  be  expressly  adverted  to.  Wlien  it 
is  inferred  that  A  B  is  equal  to  C  D  because  each  of  them  is  equal  to 
E  F,  the  most  uncultivated  understanding,  as  soon  as  the  propositions 
were  imderstood,  would  assent  to  the  inference,  without  having  ever 
heard  of  the  general  truth  that  "  things  which  are  equal  to  the  same 
thing  ai-e  equal  to  one  another."  This  remark  of  Stewart,  consistently 
followed  out,  goes  to  the  root,  as  I  conceive,  of  the  philosophy  of 
ratiocination  ;  and  it  is  to  be  regretted  that  he  himself  stopped  short  at 
a  much  more  limited  application  of  it.  He  saw  that  the  general  propo- 
sitions on  which  a  reasoning  is  said  to  depend,  may,  in  certain  cases, 
be  altogedier  omitted,  without  impaii'ing  its  probative  force.  But  he 
imagined  this  to  bo  a  peculiarity  belonging  to  axioms  ;  and  argued  from 
it,  that  axioms  are  not  the  foundations  or  first  principles  of  geometry, 


128  REASONING. 

from  which  all  the  othei*  truths  of  the  science  are  synthetically  deduced 
(as  the  laws  of  motion  and  of  the  composition  of  forces  in  mechanics, 
the  equal  mobility  of  fluids  in  hydrostatics,  the  laws  of  refle.ction  and 
refraction  in  optics,  are  the  first  princijiles  of  those  sciences) ;  but  are 
merely  necessary  assumptions,  self-evident  indeed,  and  the  denial  of 
which  would  annihilate  all  demonstration,  but  firom  which,  as  premisses, 
nothing  can  be  demonstrated.  In  the  present,  as  in  many  other  in- 
stances, this  thoughtful  and  elegant  writer  has  perceived  an  important 
truth,  but  only  by  halves.  Finding,  in  the  case  of  geometrical  axioms, 
that  general  names  have  not  any  talismanic  virtue  for  conjuring  new 
truths  out  of  the  pit  of  darkness,  and  not  seeing  that  this  is  equally  ti'ue 
in  every  other  case  of  generalization,  he  contended  that  axioms  are  in 
their  nature  barren  of  consequences,  and  that  the  really  fruitful  truths, 
the  real  first  principles  of  geometry,  are  the  definitions ;  that  the  defi- 
nition, for  example,  of  the  circle  is  to  the  properties  of  the  circle,  what 
the  laws  of  equilibrium  and  of  the  pressure  of  the  atmosphere  are  to  the 
rise  of  the  mercury  in  the  Torricellian  tube.  Yet  all  that  he  had 
asserted  respecting  the  function  to  which  the  axioms  ai"e  confined  in 
the- demonstrations  of  geometry,  holds  equally  true  of  the  definitions. 
Every  demonstration  in  Euclid  might  be  carried  on  without  them. 
This  is  apparent  from  the  ordinary  process  of  proving  a  proposition  of 
geometry  by  means  of  a  diagi'am.  What  assumption,  in  fact,  do  we 
set  out  fi'om,  to  demonsti'ate  by  a  diagi'am  any  of  the  properties  of  the 
circle  ]  Not  that  in  all  circles  the  radii  are  equal,  but  only  that  they 
are  so  in  the  circle  ABC.  As  our  warrant  for  assuming  this,  we 
appeal,  it  is  true,  to  the  definition  of  a  circle  in  general;  but  it  is  only 
necessary  that  you  should  grant  the  assumption  in  the  case  of  the  par- 
ticular circle  supposed.  From  this,  which  is  not  a  general  but  a  sin- 
gular proposition,  combined  with  other  propositions  of  a  similar  kind, 
some  of  which  when  generalized  are  called  definitions,  and  others 
axiqms,  we  prove  that  a  certain  conclusion  is  true,  not  of  all  circles, 
but  of  the  particular  circle  ABC;  or  at  least  would  be  so,  if  the  facts 
precisely  accorded  with  our  assumptions.  The  enunciation,  as  it  is 
called,  that  is,  the  general  theorem  which  stands  at  the  head  of  the 
demonstration,  is  not  the  proposition  actually  demonstrated.  One 
instance  only  is  demonstrated  :  but  the  process  by  which  this  is  done, 
is  a  process  which,  when  we  consider  its  nature,  we  perceive  might  be 
exactly  copied  in  an  indefinite  number  of  other  instances ;  in  every 
instance  which  conforms  to  certain  conditions.  The  contrivance  of 
general  language  furnishing  us  with  terms  which  connote  these  con- 
ditions, we  are  able  to  assert  this  indefinite  multitude  of  truths  in  a 
single  expression,  and  this  expression  is  the  general  theorem.  By 
dropping  the  use  of  diagrams,  and  substituting,  in  the  demonstrations, 
general  phrases  for  the  letters  of  the  alphabet,  we  might  prove  the 
general  theorem  directly,  that  is,  we  might  demonstrate  all  the  cases 
at  once  ;  and  to  do  this  we  must,  of  course,  employ  as  our  premisses, 
the  axioms  and  definitions  in  their  general  form.  ]3ut  this  only  means, 
that  if  we  can  prove  an  individual  conclusion  by  assuming  an  individual 
fact,  then  in  Avhatever  case  we  are  waiTanted  in  making  an  exactly 
similar  assumption,  we  may  draw  an  exactly  similar  conclusion.  The 
definition  is  a  sort  of  notice  to  ourselves  and  others,  what  assumptions 
we  think  ourselves  entitled  to  make.  And  so  in  all  cases,  the  general 
propositions,  whether  called  definitions,  axioms,  or   laws  of  nature, 


FUNCTIONS  AND  VALUE  OF  THE  SYLLOGISM.        129 

which  we  lay  down  at  the  beginning  of  our  reasonings,  are  merely 
abi-idged  statements  in  a  kind  of  short  hand,  of  the  particular  facts, 
which,  as  occasion  aiises,  we  either  think  we  may  proceed  upon  as 
proved,  or  intend  to  assume.  In  any  one  demonstration  it  is  enough 
if  we  assume  for  a  particular  case,  suitably  selected,  what  by  the  state- 
ment of  the  definition  or  principle  we  announce  that  we  intend  to 
assume  in  all  cases  which  may  arise.  The  definition  of  the  circle, 
therefore,  is  to  one  of  Euclid's  demonstrations,  exactly  what,  according 
to  Stewart,  the  axioms  are  ;  that  is,  the  demonstration  does  not  depend 
upon  it,  but  yet  if  we  deny  it  the  demonstration  fails.  The  proof  does 
not  rest  upon  the  general  assumption,  but  upon  a  similar  assumption 
confined  to  the  particular  case  :  that  case,  however,  being  chosen  as  a 
specimen  or  paradigm  of  the  whole  class  of  cases  included  in  the  theo- 
rem, there  can  be  no  gi'ound  for  making  the  assumption  in  that  case 
which  does  not  exist  in  every  other  ;  and  if  you  deny  the  assumption  as 
a  general  truth,  you  deny  the  right  to  make  it  in  the  particular  instance. 
There  are,  undoubtedly,  the  most  ample  reasons  for  stating  both  the 
principles  and  the  theorems  in  their  general  fonn,  and  these  will  be 
explained  presently,  so  far  as  explanation  is  requisite.  But,  that  an 
unpractised  learner,  even  in  making  use  of ,  one  theorem  to  demon- 
strate another,  reasons  rather  from  particular  to  particular  tlian  from 
the  general  proposition,  is  manifest  from  the  difiiculty  he  finds  in  ap- 
plying a  theorem  to  a  case  in  which  the  configuration  of  the  diagram 
is  exti'emely  unlike  that  of  the  diagi'am  by  which  the  original  theorem 
was  demonstrated.  A  difficulty  which,  except  in  cases  of  unusual 
mental  power,  long  practice  can  alone  remove,  and  removes  chiefly  by 
rendering  us  familiar  with  all  the  configurations  consistent  with  the 
general  conditions  of  the  theorem. 

§  4.  From  the  considerations  now  adduced,  the  following  conclu- 
sions seem  to  be  established:  All  inference  is  from  particulars  to  par- 
ticulars :  General  propositions  are  mei-ely  registers  of  such  inferences 
already  made,  and  short  formulae  for  making  more :  The  major  premiss 
of  a  syllogism,  consequently,  is  a  formula  of  this  description :  and 
the  conclusion  is  not  an  inference  drawn  from  the  formula,  but  an  in- 
ference drawn  according  to  the  formula :  the  real  logical  antecedent, 
or  premisses,  being  the  particular  facts  firom  which  the  general  propo- 
sition was  collected  by  induction..  Those  facts,  and  the  individual  in- 
stances which  supplied  them,  may  have  been  forgotten  ;  but  a  record 
remains,  not  indeed  descriptive  of  the  facts  themselves,  but  showing 
how  those  cases  may  be  distinguished  respecting  which  the  facts,  when 
known,  were  considered  to  warrant  a  given  inference.  According  to 
the  indications  of  this  record,  we  draw  our  conclusion ;  which  is,  to  all 
intents  and  pui-poses,  a  conclusion  from  the  forgotten  facts.  For  this 
it  is  essential  that  we  should  read  the  rccoi-d  correctly :  and  the  rules 
of  the  syllogism  are  a  set  of  precautions  to  insure  our  doing  so. 

This  \dew  of  the  functions  of  the  syllogism  is  confinned  by  the  con- 
sideration of  precisely  those  cases  which  might  be  expected  to  be  least 
favorable  to  it,  namely,  those  in  which  ratiocination  is  independent  of 
any  previous  induction.  We  have  already  obsei-\'ed  that  the  syllogism, 
in  the  ordinary  course  of  our  reasoning,  is  only  the  latter  half  of  the 
process  of  ti-avelling  fi'om  premisses  to  a  conclusion.  There  are,  how- 
evex",  some  peculiai'  cases  in  which  it  is  the  whole  process.     Particu- 


130  REASONING. 

lars  alone  are  capable  of  being  subjected  to  observation  ;  and  all  knowl- 
edge which  is  derived  from  observation,  begins,  therefore,  of  necessity, 
in  particiilai-s ;  but  our  knowledge  may,  in  cases  of  a  certain  descrip- 
tion, be  conceived  as  coming  to  us  from  other  sources  than  observa- 
tion. It  may  pi'esent  itself  as  coming  from  revelation  ;  and  the  knowl- 
edore,  thus  supernaturally  communicated,  may  be  conceived  to  com- ' 
prise  not  only  particular  facts  "but  general  propositions,  such  as;  occur 
so  abundantly  in  the  A\Titings  of  Solomon  and  in  the  apostolic  epistles. 
Or  the  generalization  may  not  be,  in  the  ordinary  sense,  an  assertion  at 
all,  but  a  command  ;  a  law,  not- in  the  philosophical,  but  in  the  moral 
and  political  sense  of  the  term' :  an  .expression  of  the  desire  of  a  supe- 
rior, that  we,  or  any  number  of  other  persons,  shall  conform  our  con- 
duct to  certain  general  instriictions.  So  far  as  this  asserts  a  fact, 
namely,  a  volition  of  the  legislator,  that  fact  is  an  individual  fact,  and 
the  proposition,  therefore,  is  not  a  general  proposition.  But  the  de- 
scription therein  contained  of  the  conduct  which  it  is  the  Avill  of  the 
legislator  that  his  subjects  should  observe,  is  general.  The  proposi- 
tion asserts,  not  that  all  men  ore  anything,  but  that  all  men  sJiall  do 
something.  These  two  cases,  of  a  truth  revealed  in  general  terms,  and 
a  command  intimated  in  the  like  manner,  might  be  exchanged  for  the 
more  extensive  cases,  of  any  general  statement  received  upon  testimony, 
and  any  general  practical  precept.  But  the  more  limited  illustrations 
suit  us  better,  being  drawn  from  subjects  where  long  and  complicated 
trains  of  ratiocination  have  actually  been  grounded  upon  premisses 
which  came  to  mankind  from  the  first  in  a  general  form,  the  subjects 
of  Scriptural  Theology  and  of  positive  Law. 

In  both  these  cases  the  generalities  are  given  to  us,  and  the  pattic- 
ulars  are  elicited  from  them  by  a  process  which  correctly  resolves  itself 
into  a  series  of  syllogisms.  The  real  nature,  however,  of  the  supposed 
deductive  process,  is  evident  enough.  It  is  a  search  for  ti-uth,  no  doubt, 
but  through  the  medium  of  an  inquiry  into  the  meaning- of  a  fonn  of 
words.  The  only  point  to  be  determined  is,  whether  the  authority 
which  declared  the  general  proposition,  intended,  to  include  this  case 
in  it ;  and  whether  the  legislator  intended  his  command  to  apply  to  the 
presetit  case  among  others,  or  not.  This  is  a  question,  as  the  Gennans 
express  it,  of  hermeneutics  ;  it  relates  to  the  meaning  of  a  certain  fonn 
of  discourse.  The  operation  is  not  a  process  of  inference,  but  a  pro- 
cess of  interpretation. 

In  this  last  phrase  we  have  obtained  an  expression  which  appears  to 
me  to  characterize,  more  aptly  than  any  other,  the  functions  of  the 
syllogism  in  all  cases.  When  the  premisses  are  given  by  authority, 
the  function  of  Reasoning  is  to  ascertain  the  testimony  of  a  witness, 
or  the  will  of  a  legislator,  by  intei-preting  the  signs  in  which  the  one 
has  intimated  hife  assertion  and  the  other  his  command.  In  like  man- 
ner, when  the  premisses  are  derived  from  observation,  the  function  of 
Reasoning  is  to  ascertain  w'hat  we  (or  our  predecessors)  formerly 
thought  might  be  infen-ed  from  the  observed  facts,  and  to  do  this  by 
intei-preting  a  memorandum  of  ours,  or  of  theirs.  The  memorandum 
reminds  us,  that  from  evidence,  more  or  less  carefully  weighed,  it 
formerly  appeared  that  a  certain  attribute  might  be  infeiTed  wherever 
we  perceive  a  certain  mark.  The  proposition.  All  men  are  mortal, 
(for  instance,)  shows  that  we  have  had  experience  from  which  we 
thought  it  followed  that  the  attributes  connoted  by  the  tcnn  man,  aie 


FUNCTIONS  AND  VALUE  O^   THE  SYLLOGISM.        131 

a  mark  of  mortality.  But  wlicn  we  conclude  tliat  the  Duke  of  Wel- 
lington is  mortal,  we  Jo  not  infer  this  from  the  memorandum,  but  from 
the  former  experience.  All  that  we  infer  from  the  memorandum,  is 
our  own  previous  belief,  (or  that  of  those  who  transmitted  to  us  the 
pixiposition,)  concerning  the  inferences  which  that  former  experience 
would  waiTant. 

This  view  of  the  nature  of  the  syllogism  renders  consistent  and 
intelligible  what  otherwise  remains  obscure  and  confused  in  the  theory 
of  Archbishop  Whately  and  other  enlightened  defendei's  of  the 
syllogistic  doctrine,  respecting  the  limits  to  which  its  functions  are 
confined.  They  all  affirm,  in  as  explicit  terms  as  can  be  used,  that 
the  sole  office  of  general  reasoning  is  to  prevent  inconsistency  in  our 
opinions;  to  prevent  us  from  assenting  to  anything,  the  truth  of  which 
would  contradict  something  to  which  we  had  previously  on  good 
grounds  given  our  assent.  And  they  tell  us,  that  the  sole  gi'ound 
which  a  syllogism  aftbrds  for  assenting  to  the  conclusion,  is  that  the 
supposition  of  its  being  false,  combined  with  the  supposition  that  the 
premisses  are  true,  would  lead  to  a  contradiction  in  terms.  Now  this 
would  be  but  a  lame  account  of  the  real  grounds  which  we  have  for 
beheving  the  facts  which  we  leani  from  reasoning,  in  contradistinction 
to  observation.  The  true  reason  why  we  believe  that  the  Duke  of 
Wellington  ^\'ill  die,  is  that  his  fathers,  and  our  fathers,  and  all  other 
persons  wlio  were  contemporary  with  them,  have  died.  Those  facts 
are  the  real  premisses  of  the  reasoning.  But  we  are  not  led  to  infer 
the  conclusion  from  those  premisses,  by  the  necessity  of  avoiding  any- 
verbal  inconsistency.  There  is  no  contradiction  in  supposing  that  all 
those  persons  have  died,  and  that  the  Duke  of  Wellington  may,  not- 
withstanding, live  for  ever.  But  there  would  be  a  contradiction  if  we 
first,  on  the  gi'ound  of  those  same  premisses,  made  a  general  assertion 
including  and  covering  the  case  of  the  Duke  of  Wellington,  and  then 
refused  to  stand  to  it  in  the  individual  case.  There  is  an  inconsistency 
to  be  avoided  between  the  memorandum  we  make  of  the  inferences 
Avhich  may  be  justly  drawn  in  future  'cases,  and  the  inferences  we 
actually  draw  in  those  cases  when  they  arise.  With  this  vaew  we 
interpret  our  own  formula,  precisely  as  a  judge  intei-prets  a  law:  in 
order  that  we  may  avoid  drawing  any  inferences  not  confoi'mable  to 
our  former  intention,  as  a  judge  avoids  giving  any  decision' not  con- 
formable to  the  legislator's  intention.  The  rules  for  this  interpretation 
are  the  rules  of  the  syllogism :  and  its  sole  purpose  is  to  maintain 
consistency  between  the  conclusions  we  draw  in  every  particular  case, 
and  the  previous  general  directions  for  drawing  them ;  whether  those 
general  directions  were  framed  by  ourselves  as  the  result  of  induction, 
or  were  received  by  us  from  an  authority  competent  to  give  them. 

§  5.  In  the  above  observations  it  has,  I  think,  been  clearly  shown, 
that,  although  there  is  always  a  process  of  reasoning  or  inference 
where  a  syllogism  is  used,  the  syllogism  is  not  a  coiTect  analysis  of 
that  process  of  reasoning  or  inference ;  which  is,  on  the  contrary, 
(when  not  a  mere  inference  fi-ora  testimony,)  an  inference  from  partic- 
ulars to  particulars;  authoi-ized  by  a  previous  inference  from  particu- 
lars to  generals,  and  substantially  the  same  with  it ;  of  the  nature, 
therefore,  of  Induction.  But  while  these  conclusions  appear  to  me 
undeniable,  I  must  yet  enter  a  protest,  as  strong  as  that  of  Archbishop 


132  REASONING. 

Whately  himself,  against  the  doctrine  that  the  syllogistic  art  is  useless 
for  tiie  purposes  of  reasoning.  The  reasoning  lies  in  the  act  of  gen- 
eralization, not  in  intei-preting  the  record  of  that  act ;  but  the  syllogistic 
form  is  an  indispensable  collateral  security  for  the  con-ectness  of  the 
generalization  itself. 

It  has  already  been  seen,  that  if  we  have  a  collection  of  particulars 
sufficient  for  grounding  an  induction,  we  need  not  frame  a  general 
proposition ;  we  may  reason  at  once  from  those  particulars  to  other 
particulars.  But  it  is  to  be  remarked  withal,  that  whenever,  from  a 
set  of  particular  cases,  we  can  legitimately  draw  any  inference,  we 
may  legitimately  make  our  inference  a  general  one.  If,  from  obser- 
vation and  experiment,  we  can  conclude  to  one  new  case,  so  may  we 
to  an  indefinite  number.  If  that  which  has  held  true  in  our  past 
experience  will  therefore  hold  in  time  to  come,  it  will  hold  not  merely 
in  some  individual  case,  but  in  all  cases  of  a  given  description.  Every 
induction,  therefore,  which  suffices  to  prove  one  fact,  proves  an  indefi- 
nite multitude  of  facts :  the  expei'ience  which  justifies  a  single  predic- 
tion must  be  such  as  will  suffice  to  bear  out  a  general  theorem.  This 
theorem  it  is  extremely  important  to  ascertain  and  declare,  in  its 
broadest  form  of  generality ;  and  thus  to  place  before  our  minds,  in 
its  full  extent,  the  whole  of  what  our  evidence  must  prove  if  it  proves 
anything.  ^    ^. 

This  throwing  of  the  whole  body  of  possible  inferences  from  a  given 
set  of  particulars,  into  one  general  expression,  operates  as"  a  security 
for  their  being  just  inferences  in  more  ways  than  one. .  First,  the  gen- 
eral principle  presents  a  larger  object  to  the  imagination  than  any  of 
the  singular  propositions  which  it  contains.  A  process  of  thought  which 
leads  to  a  comprehensive  genei'ality,  is  felt  as  of  ,gi-eater  importance 
than  one  which  terminates  in  an  insulated  fact ;  and  the  mind  is,  even 
unconsciously,  led  to  bestow  greater  attention  upon  the  process,  and 
to  weigh  more  carefully  the  sufficiency  of  the  experience  appealed  to, 
for  supporting  the  inference  grounded  upon  it.  There  is  another,  and 
a  more  important,  advantage.  In  reasoning  from  a  coiu'se  of  individ- 
ual observations  to  some  new  and  unobserved  case,  which  we  are  but 
imperfectly  acquainted  with  (or  we  should  not  be  inquiring  into  it), 
and  in  which,  since  we  are  inquiring  into  it,  we  probably  feel  a  pecu- 
liar interest ;  there  is  very  little  to  prevent  us  from  giving  way  to 
negligence,  or  to  any  bias  which  may  affect  our  wishes  or  our  imagina- 
tion, and,  under  that  influience,  accepting  insufficient  evidence  as  suffi- 
cient. But  if,  instead  of  concluding  sfcfaight  to  the  particular  case,  we 
place  before  ourselves  an  entire  class  of  facts,  the  whole  contents  of  a 
general  proposition,  every  tittle  of  which  is  legitimately  inferable  from 
our  premisses,  if  that  one  particular  conclusion  is  so ;  there  is  then  a 
considerable  likelihood  that  if  the  premisses  are  insufficient,  and  the 
general  inference,  therefore,  groundless,  it  Avill  comprise  within  it  some 
fact  or  facts  the  reverse  of  which  we  already  know  to  be  true ;  and 
we  shall  thus  discover  the  eiTor  in  our  generalization,  by  what  the 
schoolmen  termed  a  reductio  ad  impossihile. 

Thus  if,  during  the  reign  of  Marcus  Aurelius,  a  subject  of  the  Roman 
empire,  under  the  bias  naturally  given  to  the  imagination  and  expec- 
tations by  the  lives  and  characters  of  the  Antonines,  had  been  disposed 
to  conclude  that  Commodus  would  be  a  just  ruler:  supposing  him  to 
Stop  there,  he  might  only  have  been  undeceived  by  sad  experience. 


FUNCTIONS    AND    VALUE    OF    TlIK    SYLLOGISM.  133 

But  if  lie  reflected  that  this  conclusion  could  not  be  justifi;il>lc  unless 
from  the  same  evidence  he  was  also  warranted  in  concluding  some  gen- 
eral proposition,  as,  for  instance,  that  all  Roman  emperors  are  just 
rulers ;  he  would  immediately  have  thought  of  Nero,  Domitian,  and 
other  instances,  which,  showing  the  falsity  of  the  general  conclusion,  and 
therefore  the  insufficiency  of  the  premisses,  would  have  warned  him 
that  those  premisses  could  not  prove  in  the  instance  of  Commodus, 
what  they  were  inadequate  to  prove  in  any  collection  of  cases  in  which 
his  was  included. 

The  advantage,  in  judging  whetlier  any  controvei'ted  inference  is 
legitimate,  of  referring  to  a  parallel  case,  is  universally  acknowledged. 
But  by  ascending  to  the  general  proposition,  we  bring  under  our  view 
not  one  parallel  case  only,  but  all  possible  parallel  cases  at  once;  all 
cases  to  which  the  same  set  of  evidentiary  considerations  are  applicable. 

When,  therefore,  we  argue  from  a  number  of  known  cases  to  another 
case  supposed  to  be  analogous,  it  is  always  possible,  and  generally  ad- 
vantageous, to  divert  our  argument  into  the  circuitous  channel  of  an 
induction  from  those  known  cases  to  a  general  proposition,  and  a  subse- 
quent application  of  the  general  proposition  to  the  unknown  case. 
This  second  part  of  the  operation,  which,  as  before  observed,  is  essen- 
tially a  process  of  intei-pretation,  will  be  resolvable  into  a  syllogism  or 
a  series  of  syllogisms,  the  majors  of  which  will  be  general  propositions 
embracing  whole  classes  of  cases;  every  one  of  which  propositions 
must  be  true  in  all  its  extent,  if  our  argument  is  maintainable.  If, 
therefore,  any  fact  fairly  coming  within  the  range  of  one  of  these  general 
propositions,  and  consequently  asserted  by  it,  is  known  or  -suspected 
to  be  other  than  the  proposition  asserts  it  to  be,  this  mode  of  stating 
the  argument  causes  us  to  know  or  to  suspect  that  the  original  obser- 
vations, which  are  the  real  grounds  of  our  conclusion,  are  not  sufficient 
to  support  it.  And  in  proportion  to  the  greater  chance  of  our  detecting 
the  inconclusiveness  of  our  evidence,  will  be  the  increased  reliance  we' 
ai'e  entitled  to  place  in  it  if  no  such  evidence  of  defect  shall  appear. 

The  value,  therefore,  of  the  syllogistic  form,  and  of  the  rules  for 
using  it  coiTectly,  does  not  consist  in  their  being  the  form  and  the  rules 
according  to  which  our  reasonings  are  necessarily,  or  even  usually, 
made ;  but  in  their  furnishing  us  with  a  mode  in  which  those  reason- 
ings may  always  be  represented,  and  which  is  admirably  calcu- 
lated, if  they  are  inconclusive,  to  bring  their  inconclusiveness  to  light. 
An  induction  from  particulars  to  generals,  followed  by  a  syllogistic 
process  from  those  generals  to  other  particulars,  is  a  form  in  which  we 
may  always  state  our  reasonings  if  we  please.  It  is  not  a  form  in 
which  we  must  reason,  but  it  is  a  form  in  which  we  may  reason,  and 
into  which  it  is  indispensable  to  throw  our  reasoning,  when  there  is 
any  doubt  of  its  validity ;  though  when  the  case  is  familiar  and  little 
complicated,  and  there  is  no  suspicion  of  eiTor,  we  may,  and  do,  reason 
at  once  from  the  known  particular  cases  to  unknown  ones. 

These  are  the  uses  of  the  syllogism,  as  a  mode  of  verifying  any 
given  argument.  Its  ulterior  uses,  as  respects  the  general  course  of 
our  intellectual  operations,  hardly  require  illustration,  being  in  fact  the 
acknowledged  uses  of  general  language.  They  amount  substantially 
to  this,  that  the  inductions  may  be  made  once  for  all :  a  single  careful ; 
inten'ogation  of  experience  may  suffice,  and  the  result  may  be  regis- 
tered in  the  form  of  a  general  proposition,  which  is  committed  to 


134  KEASONING. 

memory  or  to  writing,  and  fi'om  wliicli  afterwards  we  have  only  to  syl- 
loo-ize.  The  particulars  of  om-  experiments  may  then  be  dismissed 
from  the  memory,  in  which  it  woulcl  be  impossible  to  retain  so  great 
a  multitude  of  details ;  while  the  knowledge  which  those  details  afforded 
for  future  use,  and  which  would  otherwise  be  lost  as  soon  as  the  obser- 
vations were  forgotten,  or  as  their  record  became  too  bulky  for  refer- 
ence, is  retained  in  a  commodious  and  immediately  available  shape  by 
means  of  general  language. 

A.fainst  this  advantage  is  to  be  set  the  countei-vailing  inconvenience, 
that  inferences  originally  made  on  insufficient  evidence,  become  conse- 
crated, and,  as  it  were,  hardened  into  general  maxims ;  and  the  mind 
cleaves  to  them  from  habit,  after  it  has  outgi'own  any  liability  to  be 
misled  by  similar  fallacious  appearances  if  they  were  now  for  the  first 
time  presented;  but  having  forgotten  the  particulars,  it  does  not  think 
of  revising  its  own  former  decision.  An  inevitable  drawback,  which, 
however  considerable  in  itself,  forms  evidently  but  a  trifling  deduction 
from  the  immense  advantages  of  general  language. 

The  use  of  the  syllogism  is  in  truth  no  other  than  the  use  of  general 
propositions  in  reasoning.  AVe  can  reason  without  them ;  in  simple 
and  obvious  cases  we  habitually  do  so ;  minds  of  great  sagacity  can 
do  it  in  cases  not  simple  aiid  obvious,  provided  their  exj^erience 
supplies  them  with  instances  essentially  similar  to  every  combination 
of  circumstances  likely  to  arise.  But  other  men,  or  the  same  men 
when  without  the  same  preeminent  advantages  of  personal  experience, 
are  quite  helpless  without  the  aid  of  general  propositions,  wherever 
the  case  presents  the  smallest  complication  ;  and  if  we  made  no  general 
propositions,  few  of  us  would  get  hiuch  beyond  those  simple  infer- 
ences which  are  drawn  by  the  more  intelligent  of  the  brutes.  Though 
not  necessary  to  reasoning,  general  propositions  are  necessary  to  any 
considerable  progress  in  reasoning.  It  is,  therefore,  natural  and 
indispensable  to  separate  the  process  of  investigation  into  two  parts ; 
and  obtain  general  formulae  for  determining  what  inferences  may  be 
drawn,  before  the  occasion  arises  for  drawing  the  inferences.  The 
work  of  drawing  them  is  then  that  of  applying  the  fbniiulce ;  and  the 
rules  of  the  syllogism  are  a  system  of  securities  for  the  con-ectness  of 
the  application. 

§  6.  To  complete  the  series  of  considerations  connected  with  the 
pnilosophical  character  of  the  syllogism,  it  is  requisite  to  consider, 
since  the  syllogism  is  not  the  universal  type  of  the  reasoning  process, 
what  is  the  real  type.  This  resolves  itself  into  the  question,  what  is 
the  nature  of  the  minor  premiss,  and  in  what  manner  it  contributes  to 
establish  the  conclusion  ;  for  as  to  the  major,  we  now  fully  understand, 
that  the  place  which  it  nominally  occupies  in  our  reasonings,  properly 
belongs  to  the  individual  facts  or  observations  of  which  it  expresses 
the  general  result ;  the  major  itself  being  no  real  part  of  the  argument, 
but  an  inteiTuediate  halting  place  for  the  mind,  interposed  by  an  artifice 
of  language  between  the  real  premisses  and  the  conclusion,  by  way 
of  a  security,  which  it  is  in  a  most  material  degree,  for  the  correctness 
of  the  process.  The  minor,  however,  being  an  indispensable  part  of 
the  syllogistic  expression  of  an  argument,  without  doubt  either  is,  or 
corresponds  to,  an  equally  indispensable  part  of  the  argument  itself, 
and  we  have  only  to  inquire  what  pait. 


FUNCTIONS  AND  VALUE  OF  THE  SYLLOGISM.        135 

It  is  perhaps  worth  while  to  notice  here  a  speculation  of  one  of  the 
philosophers  to  whom  mental  science  is  must  indebted,  hut  who, 
though  a  very  penetrating,  was  a  very  hasty  thinker,  and  whose  want 
of  due  circumspection  rendered  him  fully  as  remarkable  for  what  he 
did  not  see,  as  for  what  he  saw.  I  allude  to  Dr.  Thomas  Brown, 
whose  theory  of  ratiocination  is  peculiar.  He  saw  the  "pctltio  principii 
which  is  inherent  in  every  syllogism,  if  we  consider  the  major  to  be 
itself  the  evidence  by  which  the  conclusion  is  proved,  instead  of  being, 
what  in  fact  it  is,  an  assertion  of  the  existence  of  evidence  sufficient 
to  prove  any  conclusion  of  a  given  description.  Seeing  this.  Dr. 
Brown  not  only  failed  to  see  the  imnrense  advantage,  in  point  of 
secmity  for  coiTectness,  which  is  gained  by  interposing  this  step 
between  the  real  evidence  and  the  conclusion ;  but  he  thought  it 
incumbent  upon  him  to  strike  out  the  major  altogether  from  the  reason- 
ing process,  without  substituting  anything  else  ;  and  maintained  that 
our  reasonings  consist  only  of  the  minor  premiss  and  the  conclusion, 
Socrates  is  a  man,  therefore  Socrates  is  mortal :  thus  actually  suppress- 
ing, as  an  unnecessary  step  in  the  argument,  the  appeal  to  foniier 
experience.  The  absurdity  of  this  was  disguised  from  him  by  the 
opinion  he  adopted,  that  reasoning  is  merely  analyzing  our  own  general 
notions,  or  abstract  ideas  ;  and  that  the  proposition,  Socrates  is  mortal, 
is  evolved  from  the  proposition,  Socrates  is  a  man,  simply  by  recog- 
nizing the  notion  of  mortality,  as  al^-eady  contained  in  the  notion  we 
form  of  a  man. 

After  the  explanations  so  fully  entered  into  on  the  subject  of 
propositions,  much  further  discussion  cannot  be  necessary  to  make  the 
radical  error  of  this  view  of  ratiocination  apparent.  If  the  word  man 
connoted  mortality ;  if  the  meaning  of  "  mortal"  were  involved  in  the 
meaning  of  "  man ;"  we  might,  undoubtedly,  evolve  the  conclusion 
fi-om  the  minor  alone,  because  the  minor  would  have  distinctly  asserted 
it.  But  if,  as  is  in  fact  the  case,  the  word  man  does  not  connote  mortality, 
how  does  it  appear  that  in  the  mind  of  every  person  who  admits 
Socrates  to  be  a  man,  the  idea  of  man  must  include  the  idea  of  mor- 
tality 1  Dr.  Brown  could  not  help  seeing  this  difficulty,  and  in  order 
to  avoid  it,  was  led,  contrary  to  his  intention,  to  reestablish,  under 
another  name,  that  step  in  the  argument  which  corresponds  to  the 
major,  by  affinning  the  necessity  oi  'previously  perceiving  the  relation 
between  the  idea  of  man  and  the  idea  of  mortal.  If  the  reasbner  has 
not  previously  perceived  this  relation,  he  will  not,  says  Dr.  Brown, 
infer  because  Socrates  is  a  man,  that  Socrates  is  mortal.  But  even 
this  admission,  though  amounting  to  a  surrender  of  the  doctrine  that 
an  argument  consists  of  the  minor  and  the  conclusion  alone,  will  not 
save  the  remainder  of  Dr.  Brown's  theory.  The  failure  of  assent  to 
the  argument  does  not  take  place  merely  because  the  reasoner,  for 
want  of  due  analysis,  does  not  perceive  that  his  idea  of  man  includes 
the  idea  of  mortality ;  it  takes  place,  much  more  commonly,  because 
in  his  mind  that  relation  between  the  two  ideas  has  never  existed. 
And  in  truth  it  never  does  exist,  except  as  the  result  of  experience. 
Consenting,  for  the  sake  of  the  argument,  to  discuss  the  question  upon 
a  supposition  of  which  we  have  recognized  the  radical  incoiTectness, 
namely,  that  the  meaning  of  a  proposition  relates  to  the  ideas  of  the 
things  spoken  of,  and  not  to  the  things  themselves ;  and  conceding  for 
a  moment,  the  existence  of  abstract  ideas,  I  must  yet  observe,  that  the 


136  REASONING. 

idea  of  man,  as  an  universal  idea,  the  common  property  of  all  rational 
crealures,  cannot  involve  anything  but  what  is  strictly  implied  in  the 
name.  If  any  one  includes  in  his  own  private  idea  of  man,  as  no 
doubt  is  almost  always  the  case,  some  other  attributes,  such  for 
instance  as  mortality,  he  does  so  only  as  the  conseqvxence  of  experi- 
ence after  having  satisfied  himself  that  all  men  possess  that  attribute : 
so  that  wiiatever  the  idea  contains,  in  any  person's  mind,  beyond  what 
is  included  iu  the  conventional  signification  of  the  Avord,  has  been  added 
to  it  as  the  result  of  assent  to  a  proposition ;  while  Dr,  Brown's  theory 
requires  us  to  suppose,  on  the  contrary,  that  assent  to  the  proposition 
is  produced  by  evolving,  through  an  analytic  process,  this  very  element 
out  of  the  idea.  This  theory,  therefore,  may  be  considered  as 
sufficiently  refuted,  and  the  minor  premiss  must  be  regarded  as  totally 
insufficient  to  prove  the  conclusion,,  except  with  the  assistance  of  the 
major,  or  of  that  which  the  major  represents,  namely,  the  various 
singular  propositions  expressive  of  the  series  of  obsei'vations,  of  which 
the  generalization  called  the  major  premiss  is  the  result. 

In  the  argument,  then,  which  proves  that  Socrates  is  mortal,  one 
indispensable  part  of  the  premisses  will  be  as  follows :  "  My  father, 
and  my  father's '  father,  A,  B,  C,  and  an  indefinite  number  of  other 
persons,  were  mortal;"  which  is  only  an  exjjression  in  different  words 
of  the  observed  fact  that  they  have  died.  This  is  the  major  premiss, 
divested  of  the  petitio  princ'qni,  and  cut  down  to  as  much  as  is  really 
known  by  direct  evidence. 

In  order  to  connect  this  proposition  with  the  conclusion,  Socrates  is 
mortal,  the  additional  link  necessary  is  such  a  proposition  as  the  fol- 
lowing :  "  Socrates  resembles  my  father,  and  my  father's  father,  and 
the  other  individuals  specified."  This  proposition  we  assert  when  we 
say  that  Socrates  is  a  man.  .By  saying  so  we  likewise  assert  in  what 
respect  he  resembles  them,  namely,  in  the  attribvites  connoted  by  the 
word  man.  And  fi-om  this  we  conclude  that  he  further  resembles 
them  in  the  attribute  mortality. 

§  7.  We  -have  thus  obtained  what  we  were  seeking,  an  universal 
type  of  the  reasoning  process.  We  find  it  resolvable  in  all  cases  into 
the  following  elements :  Certain  individuals  have  a  given  attribute ; 
an  indixddual  or  individuals  resemble  the  former  in  certain  other  attri- 
butes ;  therefore  they  resemble  them  also  in  the  given  attribute.  This 
type  of  ratiocination  does  not  claim,  like  the  syllogism,  to  be  conclu- 
sive from  the  mere  form  of  the  expression ;  nor  can  it  possibly  be  so. 
That  one  proposition  does  or  does  not  assert  the  very  fact  which  was 
already  asserted  in  another,  may  appear  from  the  form  of  the  expres- 
sion, that  is,  from  a  comparison  of  the  language ;  but  when  the  two 
propositions  assert  facts  which  are  bonajide  different,  whether  the  one 
fact  proves  the  other  or  not  can  never  appear  from  the  language,  but 
must  depend  upon  other  considerations.  Whether,  from  the  attributes 
in  which  Socrates  resembles  those  men  who  have  heretofore  died,  it 
is  allowable  to  infer  that  he  resembles  them  also  in  being  mortal,  is  a 
question  of  Induction  ;  and  is  to  be  decided  by  the  principles  or  canons 
which  we  shall  hereafter  recognize  as  tests  of  the  coirect  performance 
of  that  great  mental  operation. 

Meanwhile,  however,  it  is  certain,  as  before  remarked,  that  if  this 
inference  can  be  drawn  as  to  Socrates,  it  can  be  drawn  as  to  all  others 


TRAINS    OF    BEASONING.  137 

who  resemble  the  observetl  iiulividiuvls  in  the  same  attributes  in  which 
lie  resembles  them  ;  that  is  (to  express  t,he  thing  concisely),  of  all  men. 
It"  thert^tbre,  the  argument  be  conclusive  in  the  case  of  Socrates,  we 
are  at  liberty,  once  for  all,  to  treat  the  possession  of  tlie  attributes  of 
man  as  a  mark,  or  satisfactory  evidence,  of  the  attribute  of  mortality. 
This  we  do  by  laying  down  tlie  universal  proposition.  All  men  are 
mortal,  and  interpreting  this,  as  occasion  arises,  in  its  application  to 
Socrates  and  others.  By  this  means  we  establish  a  very  convenient 
di\-ision  of  the  jentire  logical  operation  into  two  steps  ;  first,  that  of 
ascertaining  what  attributes  are  marks  of  mortality  ;  and,  secondly, 
A\'hether  any  given  individuals  possess  those  marks.  And  it  will,  gener- 
ally be  ad\-isable,  in  our  speculations  on  the  reasoning  process,  to 
consider  this  double  operation  as  in  fact  taking  place,  and  all  rfeason- 
ing  as  carried  on  in  the  form  into  which  it  must  necessarily  be  thrown 
to  enable  us  to  apply  to  it  any  test  of  its  coiTect  performance. 

Although,  therefore,  all  processes  of  thought  in  which  the  ultimate 
premisses  are  particulars,  whether  we  conclude  from  particulars  to  a 
general  formula,  or  from  particulars  to  other  particulars  according  to 
that  formula,  are  equally  Induction ;  we  shall  yet,  confonoiably  to 
usage,  consider  the  name  Induction  as  more  peculiarly  belonging  to 
the  process  of  establishing  the  general  proposition  ;  and  the  remaining 
operation,  which  is  substantially  that  of  intei-}5reting  the  general  pro- 
position, we  shall  call  by  its  usual  name,  Deduction.  And  we  shall 
consider  every  process  by  which  anything  is  inferred  respecting  an 
unobserved  case,  as  consisting  of  an  Induction  followed  by  a  Deduc- 
tion ;  because,  although  the  process  needs  not  necessarily  be  earned 
on  in  this  form,  it  is  always  susceptible  of  the  form,  and  must  be 
thrown  into  it  when  assurance  of  scientific  accuracy  is  needed  and 
desired. 


CHAPTER  IV. 

OF  TRAINS  OF  REASONING,  AND  DEDUCTIVE  SCIENCES. 

§  1.  In  our  analysis  of  the  syllogism  it  appeared  that  the  minor  prem- 
iss always  affirms  a  resemblance  between  a  new  case,  and  some  cases 
previously  known  ;  while  the  major  premiss  asserts  something  which, 
having  been  found  true  of  those  known  cases,  we  consider  ourselves 
warranted  in  holding  true  of  any  other  case  resembling  the  former  in 
certain  given  particulars. 

If  all  ratiocinations  resembled,  as  to  the  minor  premiss,  the  examples 
which  we  exclusively  employed  in  the  pi'eceding  chapter;  if  the  Te-~ 
semblance,  which  that  premiss  asserts,  were  obvious  to  the  senses,  as  in 
the  proposition,  "  Socrates  is  a  man,"  or  were  at  once  ascertainable  by 
direct  observation  ;  there  would  be  no  necessity  for  trains  of  reasoning, 
and  Deductive  or  Ratiocinative  Sciences  would  not  exist.  Trains  of 
reasoning  exist  only  for  the  sake  of  extending  an  induction,  founded  as 
all  inductions  must  be  upon  observed  cases,  to  other  cases  in  which  we 
not  only  cannot  directly  observe  what  is  to  be  proved,  but  cannot  di- 
rectly observe  even  the  mark  which  is  to  prove  it. 
S 


13S  REASONING. 

§  2.  Suppose  tlie  syllogism  to  be,  All  cows  ruminate,  tlie  animal  wliicli 
is  before  me  is  a  cow,  therefore  it  ruminates.  The  minor,  if  true  at  all, 
is  obviously  so  :  the  only  premiss  the  establishment  of  which  requires 
any  anterior  process  of  iiujuiry,  is  the  major;  and  provided  the  induc- 
tion of  which  that  premiss  is  the  expression  was  correctly  performed, 
the  conclusion  resj^ectiiig  the  animal  now  present  will  be  instantly 
drawn ;  because  as  soon  as  she  is  compared  with  the  formula,  she  will 
be  identified  as  being  included  in  it.  But  suppose  the  syllogism  to  be 
the  following : — All  arsenic  is  poisonous,  the  substance  which  is  before 
me  is  arsenic,  therefore  it  is  poisonous.  The  truth  of  the  minor  may  not 
here  be  obvious  at  first  sight ;  it  may  not  be  intuitively  evident,  but  may 
itself  be  known  only  by  inference.  It  may  be  the  conclusion  of  another 
argument,  which,  thrown  into  the  syllogistic  form,  would  stand  thus: — 
Whatever  forms  a  compound  with  hydrogen,  which  yields  a  black  pre- 
cipitate with  nitrate  of  silver,  is  arsenic ;  the  substance  before  me  con- 
forms to  this  condition  ;  therefore  it  is  arsenic.  To  establish,  therefore, 
the  ultimate  conclusion.  The  substance  before  me  is  poisonous,  requires 
a  process  which,  in  order  to  be  syllogistically  expressed,  stands  in  need 
of  two  syllogisms  :  and  we  have  a  Train  of  Reasoning. 

When,  however,  we  thus  add  syllogism  to  syllogism,  we  are  really 
adding  induction  to  induction.  Two  separate  inductions  must  have  ta- 
ken place  to  render  this  chain  of  inference  possible  ;  inductions  founded, 
probably,  on  different  sets  of  individual  instances,  but  which  converge  in 
their  results,  so  that  the  instance  which  is  the  subject  of  inquiry  comes 
within  the  range  of  them  both.  The  record  of  these  inductions  is  con- 
tained in  the  majors  of  the  two  syllogisms.  First,  we,  or  others  before 
us,  have  examined  various  objects  which  yielded  under  the  given  cir- 
cumstances the  given  precipitate,  and  found  that  they  possessed  the 
properties  connoted  by  the  word  arsenic ;  they  were  metallic,  volatile, 
their  vapor  had  a  smell  of  garlic,  and  so  forth.  Next,  we,  or  others  be- 
fore us,  have  examined  various  specimens  which  possessed  this  metallic 
and  volatile  character,  whose  vapor  had  this  smell,  &c.,  and  have  inva- 
riably found  that  they  were  poisonous.  The  first  observation  we  judge 
that  we  may  extend  to  all  substances  whatever  which  yield  the  precipi- 
tate :  the  second,  to  all  metallic  and  volatile  substances  resembling 
those  we  examined ;  and  consequently,  not  to  those  only  which  ai'e 
seen  to  be  such,  but  to  those  Avhich  are  concluded  to  be  such  by  the 
prior  induction.  The  substance  before  us  is  only  seen  to  come  within 
one  of  these  inductions  ;  but  by  means  of  this  one,  it  is  brought  within 
the  other.  We  are  still,  as  before,  concluding  from  particulars  to  par- 
ticulars,; but  we  are  now  concluding  from  particulars  observed,  to  other 
particulars  which  are  not,  as  in  the  simple  case,  seen  to  resemble  them 
in  the  material  points,  but  inferred  to  do  so,  because  resembling  them 
in  something  else,  which  we  have  been  led  by  quite  a  different  set  of 
instances  to  consider  as  a  mark  of  the  former  resemblance. 

This  first  example  of  a  train  of  reasoning  is  still  extremely  simple, 
the  series  consisting  of  only  two  syllogisms.  The  following  is  some- 
what more  complicated : — No  government,  which  earnestly  seeks  the 
good  of  its  subjects,  is  liable  to  revolution ;  the  Prussian  government 
earnestly  seeks  the  good  of  its  subjects,  therefore  it  is  not  in  danger 
of  revolution.  The.  major  premiss  in  this  argument  we  shall  suppose 
not  to  be  derived  from  considerations  a  priori,, hut  to  be  a  generaliza- 
tion from  history,  which,  whether  correct  or  erroneous,  must  have 


TRAINS    OF    REASONING.  139 

been  founded  upon  observation  of  governments  concerning  wlioso 
desii'o  of  the  good  of  their  subjects  there  was  no  doubt.  It  has  been 
found,  or  thought  to  be  found,  that  these  were  not  liable  to  revolution, 
and  it  has  been  deemed  that  those  instances  wari'anted  an  extension 
of  the  same  predicate  to  any  and  every  government  which  resembles 
them  in  the  attribute  of  desiring  earnestly  the  good  of  its  subjects. 
But  does  the  Pinissian  government  thus  resemble  them  1  This  may  be 
debated  pro  and  con  by  many  arguments,  and  must,  in  any  case,  be 
proved  by  another  induction ;  for  we  cannot  directly  observe  the  sen- 
timents and  desires  of  the  persons  who  conduct  the  government  of 
that  country.  To  prove  the  minor,  therefore,  we  require  an  argument 
in  this  form :  Every  government  which  acts  in  a  certain  manner,  de- 
sires the  good  of  its  subjects ;  the  Prussian  government  acts  in  that 
particular  manner,  therefore  it  desires  the  good  of  its  subjects.  But 
is  it  true  that  the  Prussian  government  acts  in  the  manner  supposed? 
This  minor  also  may  require  proof;  still  another  induction,  as  thus  :■ — . 
What  is  asserted  by  many  disinterested  witnesses,  must  be  believed 
to  be  true ;  that  the  Prussian  government  acts  in  this  manner,  is  as- 
serted by  many  disinterested  witnesses,  therefore  it  must  be  believed 
to  be  true.  The  argument  hence  consists  of  three  steps.  Having  the 
evidence  of  our  senses  that  the  case  of  the  Prussian  government  re- 
sembles a  number  of  fonner  cases,  in  the  circumstance  of  having 
something  asserted  respecting  it  by  many  disinterested  witnesses,  we 
infer,  first,  that  as  in  those  former  instances,  so  in  this  instance  the  asser- 
tion is  true.  Secondly,  what  was  asserted  of  the  Prussian  government 
being  that  it  acts  in  a  particular  manner,  and  other  governments  or 
persons  having  been  observed  to  act  in  the  same  manner,. the  Prussian, 
government  is  brought  into  kno^vn  resemblance  with  those  other  gov- 
ernments or  persons ;  and  since  they  were  known  to  desire  the  good 
of  the  people,  we  thereupon,  by  a  second  induction,  infer  that  the 
Prussian  government  desires  the  good  of  the  people.  This  brings  that 
government  into  known  resemblance  -with,  the  other  governments  which 
were  observed  to  escape  revolution,  and  thence,  by  a  third  induction, 
we  predict  that  the  Prussian  government  will  in  like  manner  escape. 
And  thus  we  are  enabled  to  reason  from  the  well-intentioned  govern- 
ments which  we  historically  know  as  having  escaped  revolution,  to 
other  governments  which,  when  we  made  the  induction,  we  may  have 
known  nothing  about :  yet  if  the  induction  was  good,  and  therefore 
applicable  to  all  governments  of  which  we  know  the  intentions  but  do 
not  know  the  fortunes,  it  must  be  no  less  applicable  to  those  whos6 
intentions  we  do  not  know,  but  can  only  infer,  provided  this  inference 
also  rests  upon  a  good  induction.  We  ai-e  still  reasoning  from  particu- 
lars to  particulars,  but  we  now  reason  to  the  new  instance  from  three 
distinct  sets  of  fonner  instances :  to  one  only  of  those  sets  of  instances 
do  we  directly  perceive  the  new  one  to  be  similar ;  but  from  that  sim- 
ilarity we  inductively  infer  that  it  has  the  attribute  by  which  it  is  as- 
similated to  the  next  set,  and  brought  within  the  corresponding  induc- 
tion ;  when  by  a  repetition  of  the  same  operation  we  infer  it  to  be 
similar  to  the  third  set,  and  hence  a  third  induction  conducts  us  to  the 
ultimate  ccmclusion. 

§  3.  Notwithstanding  the  superior  complication  of  these  examples, 
compared  with  those  by  which  in  the  preceding  chapter  we  illustrated 


140  REASONING. 

the  general  theory  of  reasoning,  every  doctrine  which  we  then  laid 
down  holds  equally  true  in  these  more  intricate  cases.  '  The  succes- 
sive general  propositions  are  not  steps  in  the  reasoning,  are  not  inter- 
mediate links  in  the  chain  of  inference,  between  the  particulars  observed, 
and  those  to  which  we  apply  the  observation.  If  we  had  sufficiently 
capacious  memories,  and  a  sufficient  power  of  maintaining  order  among 
a  huge  mass  of  details,  the  reasoning  could  go  on  without  any  general 
jjropositions ;  they  are  mere  formula?  for  infemng  particulars  from 
particulars.  The  principle  of  general  reasoning  is  (as  before  explained), 
that  if  from  observation  of  certain  kno^^^l  particulars,  what  was  seen  to 
be  true  of  them  can  be  infeiTod  to  be  time  of  any  others,  it  may  be  in^ 
fened  of  all  others  which  are  of  a  certain  description.  And  in  order 
that  we  may  never  fail  to  draw  this  conclusion  in  a  new  case  when  it 
can  be  dra^vTi  coiTectly,  and  may  avoid  drawing  it  when  it  cannot,  we 
determine  once  for  all  what  are  the  distinguishing  marks  by  which 
such  cases  may  be  recognized.  The  subsequent  process  is  merely 
that  of  identifying  an  object,  and  ascertaining  it  to  have  those  marks; 
whether  we  identify  it  by  the  very  marks  themselves,  or  by  others 
which  we  have  ascertained  (through  another  and  a  similar  process)  to 
be  marks  of  those  marks.  The  real  inference  is  always  fi-om  particu- 
lars to  particulars,  from  the  observed  instances  to  an  unobserved  one  : 
but  in  drawing  this  inference,  we  conform  to  a  formula  which  we  have 
adopted  for  our  guidance  in  such  operations,  and  which  is  a  record  of 
the  criteria  by  which  we  thought  we  had  ascertained  that  we  might 
distinguish  when  the  inference  could  and  when  it  could  not  be  drawai. 
The  real  premisses  are  the  individual  observations,  even  though  they 
may  have  been  forgotten,  or  being  the  observations  of  others  and  not 
of  ourselves,  may,  to  us,  never  have  been  known :  but  we  have 
before  us  proof  that  we  or  others  once  thought  them  sufficient  for  an 
induction,  and  we  have  marks  to  show  whether  any  new  case  is 
one  of  those  to  which,  if  then  knowTi,  the  induction  would  have  been 
deemed  to  extend.  These  marks  we  either  recognize  at  once,  or  by 
the  aid  of  other  marks,  which  by  another  previous  induction  we  col- 
lected to  be  marks  of  f/icm.  Even  these  marks  of  marks  may  only  be 
recognized  through  a  third  set  of  marks  ;  and  we  may  have  a  train  of 
reasoning,  of  any  length,  to  bring  a  new  case  within  the  scope  of  an 
induction  gi-ounded  on  particulars  its  simifarity  to  which  is  only  ascer- 
tained in  this  indirect  manner. 

Thus,  in  the  argument  concerning  the  Prussian  government,  the 
ulthnate  inductive  inference  was,  that  it  was  not  liable  to  revolution  : 
this  inference  was  drawn  according  to  a  formula  in  which  desire  of  the 
public  good  was  set  down  as  a  mark  of  not  being  liable  to  revolution ; 
a  mark  of  this  mark  was,  acting  in  a  particular  manner  ;  and  a  mark  of 
acting  in  that  manner,  was,  being  asserted  to  do  so  by  many  disinter- 
ested witnesses :  this  mark,  the  Prussian  government  was  recognized 
by  the  senses  as  possessing.  Hence  that  government  fell  within  the 
last  induction,  and  by  it  was  brought  within  all  the  others.  The  per- 
ceived resemblance  of  the  case  to  one  set  of  observed  particular  cases, 
brought  it  into  known  resemblance  with  another  set,  and  that  with  a 
third. 

In  the  more  complex  branches  of  knowledge,  the  deductions  seldom 
consist,  as  in  the  examples  hitherto  exhibited,  of  a  single  chain,  k  a 
mark  of  b,  i  of  c,  c  of  d,  therefore  a  a  mark  of  d.      They  consist  (to 


TRAINS    OF    REASONING.  141 

caiTy  on  tlve  same  metaplior)  of  several  chains  united  at  the  extremity, 
as  thus  :  a  a  mark  of  d,  h  of  e,  c  o^f,  d  ef  of  n;  therefure  ahc  a  mark 
of«.  Suppose,  for  example,  the  following  combination  of  circum- 
stances:  1st,  rays  of  light  impinging  on  a  reflecting  surface;  2(1,  that 
sijrface  parabolic ;  3d,  those  rays  parallel  to  each  other  and  to  the 
axis  of  the  surface.  It  is  to  be  proved  that  the  concourse  of  these 
three  circumstances  is  a  mark  that  the  reflected  rays  will  pass  through 
the  focus  of  the  parabolic  surface.  Now  each  of  the  three  circum- 
stances is  singly  a  mark  of  somQthing  material,  to  the  case.  Rays  of 
light  impinging  on  a  reflecting  surface,  are  a  mark  that  those  rays  will 
be  reflected  at  an  angle  equal  to  the  angle  of  incidence.  The  para- 
bolic form  of  the  surface  is  a  mark  that,  fi'om  any  point  of  it,  a  line 
drawn  to  the  focus  and  a  line  parallel  to  the  axis  will  make  equal  an- 
gles with  the  surface.  And  finally,  the  parallelism  of  the  rays  to  the 
axis  is  a  mark  that  theu-  angle  of  incidence  coincides  with  one  of  these 
equal  angles.  The  three  marks  taken  together  are  therefore  a  mark 
of  .all  these  three  things  united.  But  the  three  United  are  evidently  a 
mark  that  the  angle  of  reflection  must  coincide  with  the  other  of  the 
two  equal  angles,  that  fonned  by  a  line  drawn  to  t!ie  focus ;  and  this 
again,  by  the  fundamental  axiom  concerning  sti'aight  lines,  is  a  mark 
that  the  reflected  rays  pass  through  the  focus.  Most  chains  of  physical 
deduction- are  of  this  more  complicated  type  ;  and  even  in  mathematics 
such  ai'e  abundant,  as  in  all  propositions  where  the  hypothesis  includes 
numerous  conditions  :  "  If  a  circle  be  taken,  and  //"within  that  circle 
a  point  be  taken,  not  the  centre,  and  //"straight  lings  be  drawn  from 
that  point  to  the  circumference,  then,"  &c. 

§  4.  The  considerations  now  stated  remove  a  serious  difficulty  from 
the  view  we  have  taken  of  reasoning ;  which  view  might  othervidse 
have  seemed  not  easily  reconcilable  with  the  fact  that  there  are  De- 
ductive or  Ratiocinative  Sciences.  It  might  seem  to  follow,  if  all  rea- 
soning be  induction,  that  the  difficulties  of  philosophical  investigation 
must  lie  in  the  inductions  exclusively,  and  that  when  these  were  easy, 
and  susceptible  of  no  doubt  or  hesitation,  there  could  be  no  science,  or, 
at  least,  no  difficvilties  in  science.  The  existence,  for  example,  of  an 
extensive  Science  of  Mathematics,  requiring  the  highest  scientific  ge- 
nius in  those  who  contributed  to  its  creation,  and  calling  for  a  most 
continued  and  vigorous  exertion  of  intellect  in  order  to  appropriate  it 
when  created,  may  seem  hard  to  be  accounted  for  on  the  foregoing 
theory.  But  the  considerations  more  recently  adduced  remove  the 
mystery,  by  showing,  that  even  when  the  inductions  themselves  are 
obvious,  there  may  be  much  difficulty  in  finding  whether  the  partic- 
.ular  case  which  is  the  subject  of  inquiry  comes  within  them  ;  and  am-, 
pie  room  for  scientific  ingenuity  in  so  combining  various  inductions, 
as,  by  means  of  one  within  which  the  case  e^^dently  falls,  to  bring  it 
within  others  in  which  it  cannot  be  directly  seen  to  be  included. 

When  the  more  obvious  of  the  inductions  which  can  be  made  in 
any  science  from  direct  observations,  have  been  made,  and  general 
formulas  have  been  framed,  detennining  the  limits  within  which 
these  inductions  are  applicable;  as  often  as  a  new  case  can  be  at 
once  seen  to  come  within  one  of  the  formulas,  the  induction  is  ap- 
plied to  the  new  case,  and  the  business  is  ended.  But  new  cases 
ai'e  continually  arising,   which    do   not  obviously   come    within    any 


142  REASONING. 

formula  whereby  the  questions  we  want  solved  in  respect  of  them 
could  be  answered.  Let  us  take  an  instance  from  geometry  ;  and 
as  it  is  taken  only  for  illustration,  let  the  reader  concede  to  us  for 
the  present,  what  we  shall  endeavor  to  prove  in  the  next  chapter, 
that  the  first  principles  of  geometry  are  results  of  induction.  Our 
example  shall  be  the  fifth  proposition  of  the  first  book  of  Euclid. 
The  inquiry  is,  Are  the  angles  at  the  base  of  an  isosceles  triangle 
equal  or  unequal  ]  The  first  thing  to  be  considered  is,  what  induc- 
tions we  have,  from  which  we  can  infer  equality  or  inequalit}'.  For 
iufen-ing  equality  we  have  the  following  fonnulae  :  —  Things  which 
being  applied  to  each  other  coincide,  are  equals.  Things  which  are 
equal  to  the  same  thing  are  equals.  A  whole  and  the  sum  of  its 
parts  are  equals.  The  sums  of  equal  things  are  equals.  The  dif- 
ferences of  equal  things  are  equals.  There  are  no  other  fonnulse  to 
prove  equality.  For  inferring  inequality  we  have  the  following : — 
A  whole  and  its  parts  are  unequals.  The  sums  of  equal  things  and 
unequal  things  are  unequals.  The  differences  of  equal  things  and 
unequal  things  are  unequals.  In  all,  eight  formulae.  The  angles  at 
the  base  of  an  isosceles  triangle  do  not  ob\-iously  come  within  any  of 
these.  The  formulas  specify  certain  marks  of  equality  and  of  in- 
equality, but  the  angles  cannot  be  perceived  intuitively  to  have  any 
of  those  marks.  We  can,  however,  examine  whether  they  have 
properties  which,  in  any  other  formulae,  are  set  down  as  marks  of 
those  marks.  On  examination  it  appears  that  they  have;  and  we 
ultimately  succeed  in  bringing  them  within  this  formula,  "  The 
differences  of  equal  things  are  equal."  Whence  comes  the  difficulty 
in  recognizing  these  angles  as  the  differences  of  equal  things'?  Be- 
cause each  of  them  is  the  difference  not  of  one  pair  only,  but  of  in- 
numerable pairs  of  angles;  and  out  of  these  we  had  to  imagine  and 
select  two,  which  could  either  be  intuitively  perceived  to  be  equals, 
or  possessed  some  of  the  marks  of  equality  set  down  in  the  various 
formulcB.  By  an  exercise  of  ingenuity,  which,  on  the  part  of  the  first 
inventoi,  deserves  to  be  regarded  as  considerable,  two  pairs  of  angles 
were  hit  upon,  which  united  these  requisites.  First,  it  could  be  per- 
ceived intuitively  that  their  differences  were  the  angles  at  the  base; 
and,  secondly,  they  possessed  one  of  the  marks  of  equality,  namely, 
coincidence  when  applied  to  one  another.  This  coincidence,  how- 
ever, was  not  peiceived  intuitively,  but  infeired,  in  conformity  to 
another  formula. 

To  make  all  clear,  we  subjoin  an  analysis  of  the  demonstration. 
Euclid,  it  ^^■^.\l  be  remembered,  demon- 
strates his  fifth  proposition  by  means  of 
the  fourth.  This  it  is  not  allov.'able  for  us 
to  do,  because  we  are  undertaking  to  ti-ace 
deductive  truths  not  to  prior  deductions, 
but  to  their  original  inductive  foundation. 
We  must  therefore  use  the  premisses  of 
the  fourth  proposition  instead  of  its  con- 
clusion, and  prove  the  fifth  directly  from 
first  principles.  To  do  so  requires  six  for- 
mulas. (We  must  begin,  as  in  Euclid, 
by  prolonging  the  equal  sides  A B,  AC,  to  equal  distances,  and  join- 
ing the  extremities  B  E,  D  C.) 


TRAINS    OF    REASONING.  143 

First  Formula.   The  sums  of  equals  arc  equal. 
A  D  and  A  E  arc  sums  of  equals  by  the  supposition.     Having  that 
niai-k  of  equahty,  they  are  concluded  by  this  formula  to  be  equal. 

Second  Formula.  Equal  straight  Inics  being  aj)j)licd  to  one  another 
coincide. 

AC,  AB,  are  within  this  formula  by  supposition;  AD,  AE,  have 
been  brought  within  it  by  the  preceding  step.  Both  these  pairs  of 
sti'aight  lines  have  the  property  of  e(}uality ;  which,  according  to  the 
second  formula,  is  a  mark  that,  if  applied  to  each  otlier,  they  will  coin- 
cide. Coinciding  altogether  means  coinciding  in  every  part,  and  of 
coui'se  at  their  extremities,  DE  and  BC. 

Third  Formula.  Straight  lines,  having  their  extremities  coincident, 
coincide. 
BE  and  DC  have  been  brought  within  this  formula  by  the  preceding 
induction ;  they  will  therefore  coincide. 

Fourth  Formula.  Angles,  having  their  sides  coincident,  coincide. 

The  two  previous  inductions  having  shown  that  BE  and  DC  coin- 
cide, and'that  AD,  AE,  coincide,  the  angles  ABE  and  ACD  are 
thereby  brought  within  the  fourth  formula,  and  accordingly  coincide. 

Fifth  Formula.    Things  which  coincide  are  equal. 

The  angles  ABE  and  ACD  are  brought  within  this  formula  by  the 
induction  immediately  preceding.  This  train  of  reasoning  being  also 
applicable,  mutatis  mutandis,  to  the  angles  E  BC,  D  CB,  these  also  are 
brought  within  the  fifth  formula.     And,  finally. 

Sixth  Formula.    The  differences  of  equals  are  equal. 

The  angle  ABC  being  the  difference  of  ABE,  C  BE,  and  the  angle 
ACB  being  the  difference  of  ACD,  DCB;  which  have  been  proved 
to  be  equals ;  ABC  and  ACB  are  brought  within  the  last  formula  by 
the  whole  of  the  previous  process. 

The  difficulty  here  encountered  is  chiefly  that  of  figuring  to  ourselves 
the  two  angles  at  the  base  of  the  triangle  ABC,  as  remainders  made 
by  cutting  one  pair  of  angles  out  of  another,  while  each  pair  shall  be 
con-esponding  angles  of  ti'iangles  which  have  two  sides  and  the  inter- 
vening angle  equal.  It  is  by  this  happy  contrivance  that  so  many  dif- 
ferent inductions  are  brought  to  bear  upon  the  same  particular  case. 
And  this  not  being  at  all  an  obvious  idea,  it  may  be  seen  from  an 
example  so  near  the  threshold  of  mathematics,  how  much  scope  there 
may  well  be  for  scientific  dexterity  in  the  higher  branches  of  that  and 
other  sciences,  in  order  so  to  combine  a  few  simple  inductions,  as  to 
bring  within  each  of  them  innumerable  cases  which  arc  not  obyiou,sly 
included  in  it ;  and  how  long,  and  numerous,  and  complicated,  may  be 
the  processes,  necessary  for  bringing  the  inductions  together,  even  wheu 
each  induction  may  itself  be  very  easy  and  simple.  All  the  inductions 
involved  in  all  geometry  are  comprised  in  those  simj^le  ones,  the  for- 
mula of  which  are  the  Axioms,  and  a  few  of  the  so-called  Definitions. 
The  remainder  of  the  science  is  made  up  of  the  processes  employed 
for  bringing  unforeseen  cases  within  these  inductions  ;  or  (in  syllogistic 


144  REASONING. 

language)  for  proving  the  minors  necessary  to  complete  the  syllogisms; 
the  majors  being  the  definitions  and  axioms.  In  ^hose  definitions  and 
axioms  are  laid  down  the  whole  of  .the  marks,  by  an  artful  combina- 
•tion  of  which  men  have  been  able  to  discover  and  prove  all  that  is 
proved  in  geometry.  The  marks  being  so  few,  and  the  inductions 
which  furnish  them  being  so  obvious  and  familiar ;  the  connecting  of 
several  of  them  together,  which  constitutes  Deductions,  or  Trains  of 
Reasoning,  forms  the  whole  diflftculty  of  the  science,  and,  with  a  trifling 
exception,  its  whole  bulk  ;  'and  hence  Geometry  is  a  Deductive  Science. 

§  5.  It  will  be  seen  hereafter  that  there  are  weighty  scientific 
reasons  for  giving  to  every  science  as  much  of  the  character  of  a  De- 
ductive Science  as.  possible ;  for  endeavoring  to  construct  the  science 
from  the  fewest  and  the  simplest  possible  inductions,  and  to  njake 
these,  by  any  combinations  however  complicated,  suffice  for  pro^dng 
even  such  truths,  relating  to  complex  cases,  as  could  be  proved,  if  we 
chose,  by  inductions  from  specific  experience.  Every  branch  of  nat- 
ural philosophy  was  originally  experimental ;  each  generalization, 
rested  upon  a  special  induction,  and  was  derived  from  its  own  distinct 
set  of  observations  and  experiments.  From  being  sciences  of  pure 
experiment,  as  the  phrase  is, -or,  to  speak  more  correctly,  sciences  in 
which  the  reasonings  consist  of  no  more  than  one  step,  and  are  ex- 
pressed by  single  syllogisms,  all  these  sciences  have  become  to  some 
extent  and  some  of  them  in  nearly  the  whole  of  their  extent,  sciences 
of  pure  reasoning ;  whereby  multitudes  of  truths,  already  knowta  by 
induction  from  as  many  different  sets  of  experiments,  have  come  to  be 
exhibited  as  deductions  or  corollaries  from  inductive  propositions  of  a 
simpler  and  more  universal  character.  Thus  mechanics,  hydrostatics, 
optics,  acoustics,  and  thermology,  have  successively  been  rendered 
mathematical;  and  astronomy  was  brought  by  Newton  within  the 
laws  of  general  mechanics.  Why  it  is  that  the  substitution  of  this  cir- 
cuitous mode  of  proceeding,  for  a  process  apparently  much  easier  and 
more  natural,  is  held,  and  justly,  to  be  the  greatest  triumph  of  the  in- 
vestigation of  nature,  we  are  not,  in  this  stage  of  our  inquiry,  .prej)ared 
to  examine.  But  it  is  necessary  to'  remark,  that  although,  by  this 
progi-essive  transformation,  all  sciences  tend  to  become  more  and  more 
Deductive,  they  are  not  therefore  the  less  Inductive  ;  every  step  in  the 
Deduction  is  still  an  Induction.  The  opposition  is  not  between  the 
terms  Deductive  and  Inductive,  but  between  Deductive  and  Experi- 
mental. .  A  science  is  Experimental,  in  proportion  as  every  new  case, 
which  presents  any  peculiar  features,  stands  in  need  of  a  new-set  of 
observations  and  experiments,  a  fresh  induction.  It  is  Deductive,  in 
proportion  as  it  can  draw  conclusions,  respecting  cases  of  a  new  kind, 
by  processes  which  bring  those  cases  under  old  inductions;  by  ascer- 
taining that  cases  which  cannot  be  observed  to'  have  the  requisite 
marks,  have,  however,  marks  of  those  marks. 

We  can  now,  therefore,  perceive  what  is  the  generic  distinction  be- 
tween sciences  which  can  be  made  Deductive,  and  those  which  must 
as  yet  remain  Experimental.  The  difference  consists  iji  our  having 
been  able,  or  not  yet  able,  to  discover  marks  of  marks;  If  by  our 
various  inductions  we  have  been  able  to  proceed  no  further  'than  to 
such  propositions  as  these,  a  a  mark  of  b,  or  a  and  h  marks  of  one 
another,  c  a  mark  of  d,  or  c  and  d  marks  of  one  another,  vnthout  any- 


TRAINS    OF    REASONING.  115 

thing  to  connect  a  or  b  with  c  or  d:  we  have  a  science  of  detached 
and  mutally  independent  generalizations,  such  as  these,  that  acids 
redden  vegetable  blues,  and  that  alkalis  color  them  green ;  from 
neither  of  which  propositions  could  we,  directly  or  indirectly,  infer 
the  other :  and  a  science,  so  far  as  it  is  composed  of  such  propositions, 
is  purely  experimental.  Chemistry,  in  the  present  state  of  our  knowl- 
edge, has  not  yet  thrown  oft"  this  character.  There  are  other  sciences, 
however,  of  which  the  propositions  are  of  this  kind  :  a  a  mark  of  Z»,  i  a 
mark  of  c,  c  of  d,  d  of  e,  &c.  In  these  sciences  we  can  mount  the 
ladder  from  a  to  e  by  a  process  of  ratiocination ;  we  can  conclude 
that  a  is  a  mark  of  e,  and  that  every  object  which  has  the  mark  a  has 
the  property  e,  although,  perhaps,  we  never  were  able  to  observe  a 
and  e  together,  and  although  even  d,  our  only  direct  mark  of  e,  may 
be  not  perceptible  in  those  objects,  but  only  inferrible.  Or  varying 
the  first  metaphor,  we  may  be  said  to  get  from  a  to  e  underground  :  the 
marks  b,  c,  d,  which  indicate  the  route,  must  all  be  possessed  somewhere 
by  tlie  objects  concerning  which  we  are  inquiring ;  bat  they  are  below 
the  surface  :  a  is  the  only  mark  that  is  visible,  and  by  it  we  are  able 
to  trace  in  succession  all  the  rest. 

§  6.  We  can  now  understand  how  an  experimental  transforms  itself 
into  a  deductive  science  by  the  mere  progress  of  experiment.  In  an 
experimental  science,  the  inductions,  as  we  have  said,  lie  detached, 
as,  a  a  mark  of  6,  c  a  mark  of  <Z,  e  a  mark  oif,  and  so  on :  now,  a  new 
set  of  instances,  and  a  consequent  new  induction,  may  at  anytime 
bridge  over  the  interval  between  two  of  these  unconnected  arches ;  b, 
for  example,  may  be  ascertained  to  be  a  mark  of  c,  which  enables  us 
thenceforth  to  prove  deductively  that  a  is  a  mark  of  c.  Or,  as  some- 
times happens,  some  grand  comprehensive  induction  may  raise  an  arch 
high  in  the  air,  which  bridges  over  hosts  of  them  at  once  :  b,  d,f,  and 
all  the  rest,  turning  out  to  be  marks  of  some  one  thing,  or  of  things 
between  which  a  connexion  has  already  been  traced.  As  when  New- 
ton discovered  that  the  motions,  whether  regular  or  apparently  anom- 
alous, of  all  the  bodies  of  the  solar  system,  (each  of  which  motions  had 
been  infeiTed  by  a  separate  logical  operation,  from  separate  marks,) 
were  all  marks  of  moving  round  a  common  centre,  with  a  centripetal 
force  varying  directly  as  the  mass  and  inversely  as  the  square  of  the 
distance  from  that  centre.  This  is  the  greatest  example  which  has  yet 
occun-ed  of  the  transformation,  at  one  stroke,  of  a  science  which  was 
still  to  a  gieat  degi-ee  merely  experimental,  into  a  deductive  science. 

Transfonnations  of  the  same  nature,  but  on  a  smaller  scale,  contin- 
ually take  place  in  the  less  advanced  branches  of  physical  knowledge, 
without  cna1)ling  them  to  throw  off  the  character  of  experimental 
sciences.  Thus  with  regard  to  the  two  unconnected  propositions  be- 
fore cited,  namely,  Acids  redden  vegetable  blues,  Alkalis  make  them 
green ;  it  is  remarked  by  Liebig,  that  all  blue  coloring  matters  which 
are  reddened  by  acids  (as  well  as,  reciprocally,  all  red  coloring  matters 
which  are  rendered  blue  by  alkalis)  contain  nitrogen  :  and  it  is  cjuite 
possible  to  conceive  that  this  circumstance  may  one  day  funiish  a  bond 
of  connexion  bet^vcen  the  two  propositions  in  question,  by  showing 
that  the  antagonist  action  of  acids  and  allcalis  in  producing  or  destroy- 
ing the  color  blue,  is  the  result  of  some  one  more  general  law. 
Although  this  connecting  of  detached  generalizations  is  so  much  gain, 
T 


146  REASONING. 

it  tends  but  little  to  give  a  deductive  character  to  any  science  as  a 
w^hole  ;  because  the  new  courses  of  observation  and  experiment,  which 
thus  enable  us  to  connect  together  a  few  general  truths,  usually  make 
known  to  us  a  still  greater  number  of  unconnected  new  ones.  Hence 
chemistry,  though  similar  extensions  and  simplifications  of  its  general- 
izations are  continually  taking  place,  is  still  in  the  main  an  experimen- 
tal science ;  and  is  likely  so  to  continue,  unless  some  comprehensive 
induction  should  be  hereafter  arrived  at,  which,  like  Newton's,  shall 
connect  a  vast  number  of  the  smaller  known  inductions  together,  and 
change  the  whole  method  of  the  science  at  once.  Chemistry  has 
already  one  great  generalization,  which,  though  relating  to  one  of  the 
subordinate  aspects  of  chemical  phenomena,  possesses  within  its  limited 
sphere  this  comprehensive  character ;  the  principle  of  Dalton,  called 
the  atomic  theory,  or  the  doctrine  of  chemical  equivalents  :  which  by 
enabling  us  to  a  certain  extent  to  foresee  the  proportions  in  which  two 
substances  will  combine,  before  the  experiment  has  been_  tried,  con- 
stitutes undoubtedly  a  source  of  new  chemical  truths  obtainable  by 
deduction,  as  well  as  a  connecting  principle  for  all  truths  of  the  same 
description  previously  obtained  by  experiment. 

§  7.  The  discoveries  which  change  the  method  of  a  science  from  ex- 
perimental to  deductive,  mostly  consist  in  establishing,  either  by  de- 
duction or  by  direct  experiment,  that  the  varieties  of  a  particular 
phenomenon  unifonnly  accompany  the  varieties  of  some  other  phe- 
nomenon better  known.  Thus  the  science  of  sound,  which  pre-^dously 
stood  in  the  lowest  rank  of  merely  experimental  science,  became  de- 
ductive when  it  was  proved  by  experiment  that  every  variety  of  sound 
was  consequent  upon,  and  therefore  a  mark  of,  a  distinct  and  definable 
variety  of  oscillatory  motion  among  the  particles  of  the  transmitting 
medium.  When  this  was  ascertained,  it  followed  that  every  relation 
of  succession  or  coexistence  which  obtained  between  phenomena  of  the 
more  known  class,  obtained  also  between  the  phenomena  vvhich  cor- 
responded to  them  in  the  other  class.  Every  sound,  being  a  mark  of 
a  particular  oscillatory  motion,  became  a  mark  of  everything  which,  by 
the  laws  of  dynamics,  was  known  to  be  inferrible  from  that  motion  ; 
and  evei'ything  which  by  those  same  laws  was  a  mark  of  any  oscilla- 
tory motion,  became  a  mark  of  the  corresponding  sound:  And  thus 
many  truths,  not  before  suspected,  concerning  sound,  became  deduci- 
ble  from  the  known  laws  of  the  propagation  of  motion  through  an  elas- 
tic medium ;  while  facts  already  empirically  known  respecting  sound, 
became  an  indication  of  corresponding  properties  of  vibrating^  bodies, 
previously  undiscovered. 

But  the  grand  agent  for  transforming  experimental  into  deductive 
sciences,  is  the  science  of  number.  The  properties  of  nujnbers,  alone 
among  all  known  phenomena,  are,  in  the  most  rigorous  sense,  jiroper- 
ties  of  all  things  whatever.  All  things  are  not  colored,  or  ponderable, 
or  even  extended  ;  but  all  things  are  numerable.  And  if  we  consider 
this  science  in  its  whole  extent,  from  common  arithmetic  up  to  the 
calculus  of  variations,  the  truths  already  ascertained  seem  all  but  infi- 
nite, and  admit  of  indefinite  extension. 

These  truths,  although  afiirmable  of  all  things  whatever,  of  coiirse 
apply  to  them  only  in  respect  of  their  quantity.  But  if  it  comes  to  be 
discovered  that  variations  of  quality  in  any  class  of  phenomena,  corre- 


TRAINS    OF    REASONING.  147 

spend  regulai-ly  to  variations  of  quantity  either  in  those  same  or  in 
some  other  phenomena ;  every  formula  of  mathematics  applicable  to 
quantities  which  vary  in  that  paiticular  manner,  becomes  a  mark  of  a 
corresponding  general  truth  respecting  the  variations  in  quality  which 
accompany  them  :  and  the  science  of  quantity  being  (as  far  as  any 
science  can  be)  altogether  deductive,  the  theory, of  that  particular  kind 
of  qualities  becomes,  to  this  extent,  deductive  likewise. 

The  most  striking  instance  in  poiut  which  history  affords,  (though 
not  an  example  of  an  experimental  science  rendered  deductive,  but  of 
an  unparalleled  extension  given  to  the  deductive  process  in  a  science 
which  was  deductive  already,)  is  the  revolution  in  geometry  which 
originated  with  the  illustrious  Descartes,  and  was  completed  by  Clai- 
raut.  These  philosophers  remarked,  that  to  every  variety  of  position 
in  points,  direction  in  lines,  or  form  in  curves  or  surfaces,  (all  of  which 
are  Qualities,)  there  corresponds  a  peculiar  relation  of  quantity  between 
either  two  or  three  rectilineal  coordinates ;  insomuch  that  if  the  law 
were  known  according  to  which  those  coordinates  vary  relatively  to 
one  another,  every  other  geometrical  property  of  the  line  or  surface  in 
question,  whether  relating  to  quantity  or  quality,  would  be  capable  of 
being  infen-ed.  Hence  it  followed  that  every  geometrical  question 
could  be  solved,  if  the  corresponding  algebraic^al  one  could ;  and 
geometry  received  an  accession  (actual  or  potential)  of  new  tiTiths,  cor- 
responding to  every  property  of  numbers  which  the  prf)gress  of  the 
calculus  had  brought,  or  might  in  future  bring,  to  light.  In  the  same 
general  manner,  mechanics,  astronomy,  and  in  a  less  degree,  every 
branch  of  natural  philosophy  commonly  so  called,  have  been  made 
algebraical.  The  varieties  of  physical  phenomena  with  which  those 
sciences  are  conversant,  have  been  found  to  answer  to  determinable 
varieties  in  the  quantity  of  some  circumstance  or  other ;  or  at  least  to 
varieties  of  form  or  position,  for  which  corresponding  equations  of 
quantity  had  already  been,  or  were  susceptible  of  being,  discovered 
by  geometers. 

In  these  various  transformations,  'the  propositions  of  the  science  of 
number  do  but  fulfil  the  function  proper  to  all  propositions  forming  a 
train  of  reasoning,  viz.,  that  of  enabUng  us  to  arrive  in  an  indirect 
method,  by  marks  of  marksj,  at  such  of  the  propeities  of  objects  as  we 
cannot  directly  ascertain  (or  not  so  conveniently)  by  experiment. 
We  travel  from  a  given  visible  or  tangible  fact,  throuo-h  the  truths 
of  numbers,  to  the  fact  sought.  The  given  fact  is  a  mark  that  a  cer- 
tain relation  subsists  between  the  quantities  of  some  of  the  elements 
concerned ;  while  the  fact  sought  presupposes  a  ceitain  relation 
between  the  quantities  of  some  other  elements :  now,  if  these  last 
quantities  are  dependent  in  some  known  manner  upon  the  former,  or 
vice  versa,  we  can  argue  from  the  numeiical  relation  between  the  one 
set  of  quantities,  to  detennine  that  which  subsists  between  the  other 
set ;  the  theorems  of  the  calculus  affording  the  intermediate  links. 
And  thus  the  one  of  the  two  physical  facts  becomes  a  mark  of  the 
other,  by  being  a  mark  of  a  mark  of  a  mark  of  it. 


14S  REASONING. 

CHAPTER  V. 

OF  DEMONSTRATION,  AND  NECESSARY  TRUTHS. 

§  1.  If,  as  laid  down  in  .the  two  preceding  chapters,  the  foundation 
of  all  sciences,  even  deductive  or  demonstrative  sciences,  is  Induction; 
if  every  step  in  the  ratiocinations  even  of  geometry  is  an  act  of  induc- 
tion ;  and  if  a  train  of  reasoning  is  but  bringing  many  inductions  to 
bear  upon  the  same  subject  of  inquiry,  and  dravsdng  a  case  within  one 
induction  by  means  of  another;  wherein  lies  the  peculiar  certainty 
always  ascribed  to  the  sciences  which  are  entirely,  or  almost  entirely, 
deductive"?  Why  are  they  called  the  Exact  Sciences'?  Why  are 
mathematical  certainty,  and  the  evidence  of  demonstration,  common 
phrases  to  express  the  very  highest  degree  of  assurance  attainable  by 
reason  1  Why  are  mathematics  by  almost  all  philosophers,  and  (by 
many)  even  those  branches  of  natural  philosophy  which,  through  the 
medium  of  mathematics,  have  been  converted  into  deductive  sciences, 
considered  to  be  independent  of  the  evidence  of  experience  and  ob- 
servation, and  characterized  as  systems  of  Necessary  Truth  1 

The  answer  I  conceive  to  be,  that  this  character  of  necessity, 
ascribed  to  the  truths  of  mathematics,  and  even  (with  some  reserva- 
tions to  be  hereafter  made)  the  peculiar  certainty  attributed  to  them, 
is  an  illusion;  in  order  to  sustain  which,  it  is  necessary  to  suppose 
that  those  truths  relate  to,  and  express  the  properties  of,  purely 
imaginary  objects.  It  is  acknowledged  that  the  conclusions  of  ge- 
ometry are  deduced,  partly  at  least,  from  the  so-called  Definitions,  and 
that  those  definitions  are  assumed  to  be  correct  descriptions,  as  far  as 
they  go,  of  the  objects  with  which  geometry  is  conversant.  Now  we 
have  pointed  out  that,  from  a  definition  as  such,  no  proposition,  unless 
it  be  one  concerning  the  meaning  of  a  word,  can  ever  follow ;  and 
that  what  apparently  follows  fi-om  a  definition,  follows  in  reality  from 
an  implied  assumption  that  there  exists  a  real  thing  conformable 
thereto.  This  assumption,  in  the  case  of  the  definitions  of  geometry, 
is  false  :  there  exist  no  real  things  exactly  conformable  to  the  defini- 
tions. There  exist  no  points  withowt  magnitude  ;  no  lines  ^\dthout 
breadth,  nor  perfectly  straight ;  no  circles  with  all  their  radii  exactly 
equal,  nor  squares  with  all  their  angles  perfectly  right.  It  will  per- 
haps be  said  that  the  assumption  does  not  extend  to  the  actual,  but 
only  to  the  possible,  existence  of  such  things.  I  answer  that,  accord- 
ing to  any  test  we  have  of  possibility,  they  are  not  even  possible. 
Their  existence,  so  far  as  we  can  form  any  judgment,  would  seem  to 
be  inconsistent  with  the  physical  constitution  of  our  planet  at  least,  if 
not  of  the  universe.  To  get  rid  of  this  difficulty,  and  at  the  same 
time  to  save  the  credit  of  the  supposed  systems  of  necessary  truth,  it 
is  customary  to  say  that  the  points,  lines,  circles,  and  squares  which 
are  the  subject  of  geometry,  exist  in  our  conceptions  merely,  and  are 
part  of  our  minds ;  which  minds,  by  working  on  their  own  materials, 
construct  an  a  priori  science,  the  evidence  of  which  is  purely  mental, 
and  has  nothing  whatever  to  do  with  outward  experience.  By 
howsoever  high  authorities  this  doctrine  may  have  been  sanctioned, 
it  appears  to  me  psychologically  incorrect.  The  points,  lines,  circles, 
and  squares,  which  any  one  has  in  his  mind,  are  (I  apprehend)  simply 


DEMONSTRATION,    AND    NECESSARY    TRUTHS.  149 

copies  of  the  points,  lines,  circles,  and  squares  which  he  has  known  in 
his  experience.  A  line  as  defined  by  geometers  is  wholly  inconceiva- 
ble. We  can  reason  about  a  line  as  if  it  had  no  breadth;  because  we 
have  a  power,  which  is  the  foundation, of  all  the  control  we  can  exer- 
cise over  the  operations  of  our  minds ;  the  power,  when  a  perception 
is  present  to  our  senses,  or  a  conception  to  our  intellects,  of  attending 
to  a  part  only  of  that  perception  or  conception,  instead  of  the  whole. 
But  we  cannot  conceive  a  line  without  breadth ;  we  can  form  no 
mental  picture  of  such  a  line  :  all  the  lines  which  we  have  in  our 
minds  are  lines  possessing  breadth.  If  any  one  doubts  this,  we  may 
refer  him  to  his  own  experience.  I  much  question  if  any  one  who 
fancies  that  he  can  conceive  what  is  called  a  mathematical  line,  thinks 
so  from  the  evidence  of  his  consciousness  :  I  suspect  it  is  rather  be- 
cause he  supposes  that  unless  such  a  conception  were  possible,  mathe- 
matics could  not  exist  as  a  science  :  a  supposition  which  there  will  be 
no  difficulty  in  showing  to  be  entirely  groundless. 

Since  then  neither  in  nature,  nor  in  the  human  mind,  do  there  ex- 
ist any  objects  exactly  coiTesponding  to  the  definitions  of  geometry, 
while  yet  that  science  cannot  be  supposed  to  be  conversant  about  non- 
entities ;  nothing  remains  but  to  consider  geometry  as  conversant  with 
such  lines,  angles,  and  figures  as  really  exist ;  and  the  definitions,  as 
they  are  called,  must  be  regarded  as  some  of  our  first  and  most  obvi- 
ous generalizations  concerning  those  natural  objects.  The  correctness 
of  those  generalizations,  as  generalizations,  is  without  a  flaw :  the 
equality  of  all  the  radii  of  a  circle  is  true  of  all  circles,  so  far  as  it  is 
true  of  any  one :  but  it  is  not  exactly  true  of  any  circle :  it  is  only 
nearly  true  :  so  nearly  that  no  error  of  any  importance  in  practice  will 
be  incurred  by  feigning  it  to  be  exactly  true.  When  we  have  occa- 
sion to  extend  these  inductions,  or  their  consequences,  to  cases  in  which 
the  error  would  be  appreciable — to  lines  of  perceptible  breadth  or 
thickness,  parallels  which  deviate  sensibly  from  equidistance,  and  the 
like — we  correct  our  conclusions,  by  combining  with  them  a  fresh  set 
of  propositions  relating  to  the  abeiTation;  just  as  we  also  take  in 
propositions  relating  to  the  physical  or  chemical  propeities  of  the  ma- 
terial, if  those  properties  happen  to  introduce  any  modification  into  the 
result,  which  tliey  easily  may,  even  with  respect  to  figure  and  magni- 
tude, as  in  the  case,  for  instance,  of  expansion  by  heat.  So  long,  how- 
ever, as  there  exists  no  practical  necessity  for  attending  to  any  of  the 
properties  of  the  object  except  its  geometrical  properties,  or  to  any  of 
the  natural  irregularities  in  those,  it  is  convenient  to  neglect  the  con- 
sideration of  the  other  properties  and  of  the  iri-egularities,  and  to  rea- 
son as  if  these  did  not  exist :  accordingly,  we  formally  announce,  in 
the  definitions,  that  we  intend  to  proceed  on  this  plan.  But  it  is  an 
eiTor  to  suppose,  because  we  resolve  to  confine  our  attention  to  a  cer- 
tain number  of  the  properties  of  an  object,  that  we  therefore  conceive, 
or  have  an  idea  of,  the  object,  denuded  of  its  other  properties.  We 
are  thinking,  all  the  time,  of  precisely  such  objects  as  we  have  seen 
and  touched,  and  with  all  the  properties  which  naturally  belong  to 
them ;  but,  for  scientific  convenience,  we  feign  them  to  be  divested  of 
all  properties,  except  those  in  regard  to  which  we  design  to  consider 
them. 

The  peculiar  accuracy,  supposed  to  be  characteristic  of  the  first 
principles  of  geometry,  thus  appears  to  be  fictitious.     The  assertions 


150  REASONING 

on  which  the  reasonings  of  the  science  are  founded,  do  not,  any  more 
than  in  other  sciences,  exactly  coiTespond  with  the  fact ;  t>ut  we  srip- 
pose  that  they  do  so,  for  the  sake  of  tracing  the  consequences  which 
follow  fiom  the  supposition.  The  opinion  of  Dugald  Stewart  respect- 
ing the  foundations  of  geometry,  is,  I  conceive,  substantially  correct ; 
that  it  is  built  upon  hypotheses ;  that  it  owes  to  this  alone  the  peculiar 
certainty  supposed  to  distinguish  it ;  and  that  in  any  science  whatever, 
by  reasoning  from  a  set  of  hypotheses,  we  may  obtain  a  body  of  con- 
clusions as  certain  as  those  of  geometiy,  that  is,  as  strictly  in  accord- 
ance with  the  hypotheses,  and  as  in'esistibly  compelling  assent  07i 
condition  that  those  hypotheses  are  true. 

When,  therefore,  it  is  affirmed  that  the  conclusions  of  geometry  are 
necessary  truths,  the  necessity  consists  in  reality  only  in  this,  that  they 
necessarily  follow  from  the  suppositions  from  which  they  are  deduced. 
Those  suppositions  are  so  far  from  being  necessary,  that  they  are  not 
even  true  ;  they  purposely  depart,  more  or  less  widely,  from  the  truth. 
The  only  sense  in  which  necessity  can  be  ascribed  to  the  conclusions 
of  any  scientific  investigation,  is  that  of  necessarily  following  from  some 
assumption,  which,  by  the  conditions  of  the  inquiry,  is  not  to  be  ques- 
tioned. In  this  relation,  of  course,  the  derivative  truths  of  every  de- 
ductive science  must  stand  to  the  inductions,  or  assumptions,  on  which 
the  science  is  founded,  and  which,  whether  true  or  untrue,  certain  or 
doubtful  in  themselves,  are  always  svipposed  certain  for  the  purposes 
of  the  particular  science.  And  therefore  the  conclusions  of  all  deduc- 
tive sciences  were  said  by  the  ancients  to  be  necessary  propositions. 
We  have  obsei-^'ed  already  that  to  be  predicated  necessarily  was  char- 
acteristic of  the  predicable  Propiium,  and  that  a  proprium  was  any 
property  of  a  thing  which  could  be  deduced  from  its  essence,  that  is, 
from  the  properties  included  in  its  definition. 

§  2.  The  important  doctrine  of  Dugald  Stewart,  which  I  have  en-  . 
deavored  to  enforce,  has  been  contested  by  a  living  philosopher,  Mr. 
Whewell,  both  in  the  dissertation  appended  to  his  excellent  Mechani- 
cal Enclid,  and  in  his  more  recent  elaborate  work  on  the  Philosophy 
of  the  Inductive  Sciences;  in  which  last  he  also  replies  to  an  article 
in  the  Edinburgh  Review  (ascribed  to  a  writer  of  gi'eat  scientific  emi- 
nence), in  which  Stewart'^  opinion  was  defended  against  his  foirner 
strictures.  Mr.  Whewell's  mode  of  refuting  Stewart  is  to  prove  against 
him  (as  has  also  been  done  in  this  work),  that  the  premisses  of  geom- 
etry are  not  definitions,  but  assumptions  of  the  real  existence  of  things 
corresponding  to  those  definitions.  This,  however,  is  doing  little  for 
Mr.  Whewell's  purpose,  for  it  is  these  very  assixmptions  which  we  say 
are  hypotheses,  and  which  he,  if  he  denies  that  geometry  is  founded  on 
hypotheses,  must  show  to  be  absolute  truths.  All  he  does,  however, 
is  to  observe,  that  they  at  any  rate  are  not  arbitrary  hypotheses ;  that 
we  should  not  be  at  liberty  to  substitute  other  hypotheses  for  them; 
that  not  only  "  a  definition,  to  be  admissible,  must  necessarily  refer  to 
and  agree  with  some  conception  which  we  can  distinctly  frame  in  our 
thoughts,"  but  that  the  straight  lines,  for  instance,  which  we  define, 
must  be  "those  by  which  angles  are  contained,  those  by  which  trian- 
gles are  bounded,  those  of  which  jiarallelism  may  be  predicated,  and 
the  like."*  And  this  is  true;  but  this  has  never  been  contradicted. 
*  Whewell's  Mechanical  Euclid,  p.  149,  et  segq. 


DEMONSTKATION,   AND    NECESSARY    TRUTHS.  151 

Those  who  say  that  the  premisses  of  geometry  are  hypotheses,  arc  not 
bound  to  maintain  them  to  be  hypotlieses  which  have  no  r^jlation  what- 
ever  to  fact.  Since  an  hypothesis  framed  for  the  purpose  of  scientific 
inquiry  must  relate  to  something  whicli  has  real  existence  (for  there 
can  be  no  science  respecting  non-entities),  it  folliows  that  any  hypothe- 
sis we  make  respecting  an  object,  to  faciUtatc  onr  study  of  it,  must,  not 
involve  anything  which  is  distinctly  false,  and  repugnant  to  its  real 
nature  :  we  must  not  ascrilx)  to  the  thing  any  property  which  it  has 
not ;  ^our  liberty  extends  only  to  suppressing  some  of  those  which  it 
has,  under  the  indispensable  obligation  of  restoring  them  whenever, 
and  in  as  far  as,  their  presence  or  absence  would  make  any  material 
diilerence  in  the  truth  of  our  conclusions.  Of  this  nature,  accordingly, 
are  the  fir^it  principles  involved  in  the  definitions  of  geometry.  In 
their  positive  part  they  are  observed  facts ;  it  is  only  in  their  negative 
part  that  they  are  hypothetical.  That  the  hypotheses  should  be  of 
this  particular  character,  is,  however,  no  further  necessary,  than  inas- 
much as  no  others  could  enable  us  to  deduce  conclusions  which,  with 
due  corrections,  would  be  true  of  real  objects  :  and  in  fact,  when  our 
aim  is  only  to  illusti'ate  truths  and  not  to  investigate  them,  we  are  not 
under  any  such  restriction.  We  might  suppose  an  imaginary  animal, 
and  work  out  by  deduction,  from  the  known  laws  of  physiology,  its 
natural  history;  or  an  imaginary  commonwenlth,  and  from  the  elements 
composing  it,  might  argue  what  would  be  its  fate.  And  the  conclu- 
sions which  we  might  thus  draw  from  purely  arbitrary  hypotheses, 
might  form  a  highly  useful  intellectual  exercise  :  but  as  they  could  only 
teach  us  what  would  be  the  properties  of  objects  which  do  not  really 
exist,  they  would  not  constitute  any  addition  to  our  knowledge  :  while 
on  the  contrary,  if  the  hypothesis  merely  divests  a  real  object  of  some 
portion  of  its  properties,  \Vithout  clothing  it  in  false  ones,  the  conclu- 
sions will  always  express,  under  known  liability  to  correction,  actual 
truth. 

§  3.  But  although  Mr.  Wliewell  has  not  shaken  Stewart's  doctrine 
as  to  the  hypothetical  chai'acter  of  that  portion  of  the  first  principles  of 
geometry  which  are  involved  in  the  so-called  definitions,  he  has,  I  con- 
ceive, gi'esLtly  the  advantage  of  Stewart  on  another  important  point 
in  the  theory  of  geometrical  reasoning;  the  necessity  of  admitting, 
among  those  first  jn-inciples,  axioms  as  well  as  definitions.  Some  of 
the  axioms  of  Euclid  might,  no  doubt,  be  exhibited  in  the  form  of  defi- 
nitions, or  might  be  deduced,  by  reasoning,  fi-om  propositions  similar  to 
ivhat  9,re  so  called.  Thus,  if  instead  of  the  axiom.  Magnitudes  which 
can  be  made  to  coincide  are  equal,  we  introduce  a  definition,  "  Equal 
magnitudes  arc  those  which  may  be  -so  applied  to  one  another  as  to 
coincide  ;"  the  three  axioms  which  follow,  (Magnitudes  which  are  equal 
to  the  same  are  equal  to  one  another — If  equals  are  added  to  equals 
the  sums  are  equal — ^If  equals  are  taken  from  equals  the  remainders 
are  equal,)  may  be  proved  by,  an  imaginai'y  superposition,  resembling 
that  by  which  the  fourth  proposition  of  the  first  book  of  Euclid  is  de- 
monstrated. But  although  these  and  several  others  may  be  struck  out 
of  the  list  of  first  princi])les,  because,  though  not  requiring  demon- 
stration, they  are  susceptible  of  it ;  there  will  be  found  in  the  list  of 
axioms  two  or  three  fundamental  trutJis,  not  capable  of  being  demon- 
strated :  among  which  I  agree  with  Mr.  WTiewell  in  placing  the  prop- 


152  REASONING. 

osition  that  two  straight  lines  cannot  inclose  a  space,  (or  its  equivalent, 
Straight  lines  which  coincide  in  two  points  coincide  altogether,)  and 
some  property  of  parallel  lines,  other  than  that  which  constitutes  their 
definition  :  the  most  suitable,  perhaps,  being  that  selected  by  Professor 
Playfair  :  "  Two  straight  lines  which  intersect  each  other  cannot  both 
of  them  be  parallel  to  a  third  straight  line."* 

The  axioms,  as  well  those  which  are  indemonstrable  as  those  which 
admit  of  being  demonstrated,  differ  from  that  other  class  of  funda- 
mental principles  which  are  involved  in  the  definitions,  in  this,  that 
they  are  true  without  any  mixture  of  hypothesis.  That  things  which 
are  equal  to  the  same  thing  are  equal  to  one  another,  is  as  true  of  the 
lines  and  figures  in  nature,  as  it  would  be  of  the  imaginary  ones 
assumed  in  the  definitions.  In  this  respect,  however,  mathematics 
is  only  on  a  par  with  most  other  sciences.  In  almost  all  sciences 
there  are  some  general  propositions  which  are  exactly  true,  while  the 
greater  part  are  only  more  or  less  distant  approximations  to  the  truth. 
Thus  in  mechanics,  the  first  law  of  motion,  (the  continuance  of  a  move- 
ment once  impressed,  until  stopped  or  slackened  by  some  resisting  force,) 
is  true  without  a  particle  of  qualification  or  error ;  it  is  not  affected  by 
the  frictions,  rigidities,  and  miscellaneous  disturbing  causes,  which 
qualify,  for  example,  the  theories  of  the  lever  and  of  the  pulley.  The 
rotation  of  the  earth  in  twenty-four  hours,  of  the  same  length  as  in  our 
time,  has  gone  on  since  the  first  accurate  observations,  without  the 
increase  or  diminution  of  one  second  in  all  that  period.  These  are 
inductions  which  require  no  fiction  to  make  them  be  received  as  accu- 
rately true  :  but  along  with  them  there  are  others,  as  for  instance  the 
propositions  respecting  the  figure  of  the  earth,  which  are  but  approxi- 
mations to  the  truth  ;  and  in  order  to  use  them  for  the  further  advance- 
ment of  our  knowledge,  we  must  feign  that  ihey  are  exactly  true, 
although  they  really  want  something  of  being  so. 

§  4.  It  remains  to  inquire,  what  is  the  ground  of  our  belief  in  axioms 
— what  is  the  evidence  on  which  they  rest  1  I  answer,  they  are  ex- 
perimental truths ;  generalizations  from  observation.  The  proposition, 
Two  straight  lines  cannot  inclose  a  space — or  in  other  words.  Two 
sti'aight  lines  which  have  once  met,  do  not  meet  again,  but  continue  to 
diverge — is  an  induction  from  the  evidence  of  our  senses. 

This  opinion  runs  counter  to  a  philosophic  prejudice  of  long  stand- 
ing and  great  strength,  and  there  is  probably  no  one  proposition  enun- 
ciated in  this  work  for  which  a  more  unfavorable  reception  is  to  be  ex- 
pected. It  is,  however,  no  new  opinion  ;  and  even  if  it  were  so,  would 
be  entitled  to  be  judged,  not  by  its  novelty,  but  by  the  strength  of  the 
arguments  by  which  it  can  be  supported.  I  consider  it  very  fortunate 
that  so  eminent  a  champion  of  the  contrary  opinion  as  Mr.  Whewcll, 
has  recently  found  occasion  for  a  most  elaborate  treatment  of  the  whole 
theory  of  axioms,  in  attempting  to  construct  the  philosophy  of  the 

*  We  might,  it  is  true,  insert  this  property  into  the  definition  of  parallel  lines,  framing-  the 
definition  so  as  to  require,  bo/h  that  when  produced  indefinitely  they  shall  never  meet,  and 
also  that  any  straight  line  which  intersects  one  of  them  shall,  if  prolonged,  meet  the  other. 
But  by  doing  this  we  by  no  means  get  rid  of  the  assumption  ;  we  are  still  obliged  to  take 
for  granted  the  geometrical  truth,  that  all  straight  lines  in  the  same  plane,  which  have  the 
former  of  these  properties,  have  also  the  latter.  P'or  if  it  were  possible  that  they  should 
not,  that  is,  if  any  straight  lines  other  than  those  which  are  parallel  according  fo  the  defini- 
tion, had  the  property  of  never  meeting  although  indefinitely  produced,  the  demonstrationa 
of  the  subsequent  portions  of  the  theory  of  parallels  could  not  be  nijdntained. 


DEMONSTRATION,    AND    NECESSARY    TRUTHS.  153 

mathematical  ami  physical  sciences  on  the  basis  of  the  doctrine  against 
which  I  now  coiUcnil.  Wlioever  is  anxious  that  a  discussion  should  go 
to  the  bottom  ot'the  subject,  must  rejoice  to  see  the  opposite  side  of 
the  question  worthily  represented.  If  what  is  said  by  such  a  man  as 
Mr.  Whewell,  in  support  of  an  opinion  which  he  has  made  the  founda- 
tion of  a  systematic  work,  can  be  shown  not  to  be  conclusive,  enough 
will  have  been  done  without  going  further  to  seek  stronger  arguments 
and  a  more  powerful  adversary. 

It  is  not  necessary  to  show  that  the  truths  which  we  call  axioms  are 
originally  suggested  by  observation,  and  that  we  should  never  have 
known  that  two  straight  lines  cannot  inclose  a  space  if  we  had  never 
seen  a  straight  line  :  thus  much  being  admitted  by  Mr.  Whewell,  and 
by  all,  in  recent  times,  who  have  adopted  his  view  of  the  subject.  But 
they  contend,  that  it  is  not  experience  which  proves  the  axiom  ;  but  that 
its  truth  is  perceived  a  priori,  by  the  constitution  of  the  miaid  itself, 
from  the  first  moment  when  the  meaning  of  the  proposition  is  appre- 
hended ;  and  without  any  necessity  for  verifying  it  by  repeated  trials, 
as  is  requisite  in  the  case  of  ti-uths  really  ascertained  by  observa- 
tion. 

They  cannot,  however,  but  allow  that  the  truth  of  the  axiom,  Two 
straight  lines  cannot  inclose  a  space,  even  if  evident  independently  of 
experience,  is  also  evident  from  experience.  Wliether  the  axiom  needs 
confirmation  or  not,  it  receives  confirmation  in  almost  every  instant  of 
our  lives  ;  since  we  cannot  look  at  any  two  straight  lines  which  inter- 
sect one  another,  without  seeing  that  fi-om  that  point  they  continue  to 
diverge  more  and  more.  Experimental  proof  crowds  in  upon  us  in 
such  endless  profusion,  and  without  one  instance  in  which  there  can  be 
even  a  suspicion  of  an  exception  to  the  rule,  that  we  should  soon  have 
a  stronger  ground  for  believing  the  axiom,  even  as  an  experimental 
truth,  than  we  have  for  almost  any  of  the  general  truths  which  we  con- 
fessedly learn  from  the  evidence  of  our  senses.  Independently  of  a 
priori  evidence,  we  should  certainly  believe  it  with  an  intensity  of  con- 
viction far  greater  than  we  accord  to  any  ordinary  physical  truth  ;  and 
this  too  at  a  time  of  life  much  earlier  than  that  from  which  we  date  al- 
most any  part  of  our  acquired  knowledge,  and  much  too  early  to  admit 
of  our  retaining  any  recollection  of  the  history  of  our  intellectual  ope- 
rations at  that  period.  Where  then  is  the  necessity  for  assuming  that 
our  recognition  of  these  truths  has  a  different  origin  from  the  rest  of  our 
knowledge,  when  its  existence  is  perfectly  accounted  for  by  supposing 
its  origin  to  be  the  same  ?  when  the  causes  which  produce  belief  in  all 
other  instances,  exist  in  this  instance,  and  in  a  degree  of  strength  as 
much  superior  to  what  exists  in  other  cases,  as  the  intensity  of  the  be- 
lief itself  is  superior  1  The  burden  of  proof  lies  upon  the  advocates  of 
the  contrary  opinion  :  it  is  for  them  to  point  out  some  fact,  inconsistent 
with  the  supposition  that  this  part  of  our  knowledge  of  nature  is  derived 
from  the  same  sources  as  every  other  part. 

This,  for  instance,  they  would  be  able  to  do,  if  they  could  prove 
chronologically  that  we  have  the  conviction  (at  least  practically)  so 
early  in  infancy  as  to  be  anterior  to  those  impressions  on  the  senses, 
upon  which,  on  the  other  theory,  the  conviction  is  founded.  This, 
however,  cannot  be  proved ;  the  point  being  too  far  back  to  be  wnthin 
the  reach  of  memory,  and  too  obscure  for  external  observation.  The 
advocates  of  the  a  priori  theory  are  obliged  to  have  recourse  to  other 


154  REASONING. 

arguments.     These  are  reducible  to  two,  which  I  shali  endeavor  to 
state  as  clearly  and  a^  forcibly, as  possible. 

§  5.  In  the  first  place  it  is  said,  that  if  ovir  assent  to  the  proposition 
that  two  straight  lines  cannot  inclose  a  space,  were  derived  from  the 
senses,  we  could  only  be  convinced  of  its  truth  by  actual  trial,  that  is, 
by  seeing  or  feeling  the  straight  liijes  ;  whereas  in  fact  it  is  seen  to  be 
ti-ue  by. merely  thinking  of  them.  That  a  stone  thrown  into  water 
goes  to  the  bottom,'may  be  perceived  by  our  senses,  but  mere  think- 
ing of  a  stone  thrown  into  the  water  will  never  lead  us  to  that  conclu- 
sion :  not  so,  however,  with  the  axioms  relating  to  sti'aight  lines  :  if  I 
could  be  made  to  conceive  what  a  straight  line  is,  without  having  seen 
one,  I  should  at  once  recognize  that  two  such  lines  cannot  inclose  a 
space.  Intuition  is  "imaginary  looking;"*  but  experience  must  be 
real  looking  :  if  we  see  a  property  of  straight  lines  to  be  true  by  merely 
fancying  ourselves  to  be  looking  at  them,  the  ground  of  our  belief  can- 
not be  the  senses,  or  experience  ;  it  must  be  something  mental. 

To  this  argument  it  might  be  added  in  the  case  of  this  particular 
axiom  (for  the  assertion  would  not  be  true  of  all  axioms),  that  the  evi- 
dence of  it  from  actual  ocular  inspection,  is  not  only  unnecessary,  but 
unattainable.  What  says  the  axiom  1  That  two  straight  lines  cannot 
inclose  a  space ;  that  after  having  once  intersected,  if  they  are  pro- 
longed to  infinity  they  do  not  meet,  but  continue  to  diverge  fi-om  one 
another.  How  can  this,  in  any  single  case,  be  proved  by  actual 
observation  1  We  may  follow  the  lines  to  any  distance  we  please  ;  but 
we  cannot  follow  them  to  infinity:  for  aught  our  senses  can  testify, 
they  may,  immediately  beyond  the  furthest  point  to  which  we  have 
traced  them,  begin  to  approach,  and  at  last  meet.  Unless,  therefore, 
we  had  some  other  proof  of  the  impossibility  than  observation  affords 
us,  we  should  have  no  ground  for  believing  the  axiom  at  all. 

To  these  arguments,  which  I  trust  I  cannot  be  accused  of  under- 
stating, a  satisfactory  answer  will,  I  conceive,  be  found,  if  we  advert 
to  one  of  the  characteristic  properties  of  geometrical  forms — their 
capacity  of  being  painted  in  the  imagination  with  a  distinctness  equal 
to  reality  :  in  other  wordsi,  the  exact  resemblance  of  our  ideas  of  form 
to  the  sensations  which  suggest  them.  This,  in  the  first  place,  enables 
us  to  make  (at  least  with  a  little  practice)  mental  pictures  of  all  possible 
combinations  of  lines  and  angles,  which  resemble  the  realities  quite  as 
well  as  any  which  we  could  make  upon  paper;  and  in  the  next  place, 
makes  those  pictures  just  as  fit  subjects  of  geometrical  experimentation 
as  the  realities  themselves;  inasmuch  as  pictures,  if  sufficiently  accu- 
rate, exhibit  of  course  all  the  properties  which  would  be  manifested 
by  the  realities  at  one  given  instant,  and  on  simple  inspection  :  and  in 
geometry  we  are  concerned  only  with  such  properties,  and  not  with 
that  which  pictures  could  not  exhibit,  the  mutual  action  of  bodies  one 
upon  another.  The  foundations  of  geometry  would  therefore  be  laid 
in  direct  experience,  even  if  the  experiments  (which  in  this  case  consist 
merely  in  attentive  contemplation)  were  practised  solely  upon  what  we 
call  our  ideas,  that  is,  upon  the  diagrams  in  our  minds,  and  not  upon 
outward  objects.  For  in  all  systems  of  experimentation  we  talvO  some 
objects  to  serve,  as  representatives  of  aU  whjich  resemble  them  ;  and  in 

*  Whewell's  Philosophy  of  the  Inductive  Sciences,  i.,  130. 


DEMONSTKATIOV,    AXD    NECCSSAUY    TRUTHS.  155 

the  present  case  the  conditions  which  qualify  a  real,  object  to  be  the 
representative  of  its  clas*,  arc  completely  fulfilled  by  an  object  existing 
only  in  our  fancy.  "Without  denying,  therefore,  the  possibility  ot 
satisfying  ourselves  that  two  sti-aight  lines  cantiot  inclose  a  s])ace,  by 
merely  thinking  of  straight  lines  without  actually  looking  at  them ;  I 
contend,  tluit  we  do  not  beUeve  this  truth  on  the  ground  of  the  imagi- 
nary intuition  simply,  but  because  we  know  that  the  imaginary  lines 
exactly  resemble  real  ones,  and  that  we  may  conclude  from  them  to 
real  ones  with  quite  as  much  certainty  as  we  could  conclude  from  one 
real  line  to  another.  The  conclusion,  therefore,  is  still  an  induction 
from  obsei-Vation.  And  we  should  not  be  authorized  to  substitute 
obsenation  of  the  image  in  our  mind,  for  obsei-vation  of  the  reality,  if 
we  had  not  learnt  by  long  continued  experience  that  all  the  properties 
of  the  reality  are  faithfully  represented  in  the  image ;  just  as  we 
should  be  scientifically  warranted,  in  describing  the  sliape  and  color  of 
an  animal  Nvhich  we  had  never  seen,  fi-om  a  plaotogenic  picture  made 
of  it  with  a  daguerreotype  ;•  but  not  until  we  had  leanit  by  ample 
exj>erience,  that  observation  of  such  a  picture  is  precisely  equivalent 
to  observation  of  the  original. 

These  considerations  also  remove  the  objection  aiising  from  the 
impossibity  of  ocularly  following  the  lines  in.  their  prolongation  to 
infinity.  For  though,  in  order  actually  to  see  that  two  given  lines 
never  meet,  it  would  be  necessary  to  follow  them  to  infinity  :  yet 
A\'ithout  doing  so  we  may  know  that  if  they  ever  do  meet,  or  indeed  if, 
after  diverging  fi-om  one  another,  they  begin  again  to  approach,  this 
must  take  place  not  at  an  infinite,  but  at  a  finite  distance.  Supposing, 
therefore,  such  to  be  the  case,  we  can  transport  ourselves  thither  in 
imagination,  and  can  frame  a  mental  image  of  the  appearance  which 
one  or  both  of  the  lines  must  present  at  that  point,  which  we  may  rely 
upon  as  being  precisely  similar  to  the  reality.  Now,  -^vhether  we  fix 
our  contemplation  upon  this  imaginary  picture,  or  call  to  mind  the 
generalizations  we  have  had  occasion  to  make  fi'om  fonner  ocular 
obser\-atic»n,  we  shall  either  way  be  equally  satisfied,  that  a  line  which, 
after  diverging  fi-om  another  straight  line,  begins  to  approach  to  it, 
produces  the  impression  on  our  senses  which  we  describe  by  the 
expression,  "  a  bent  line,"  not  by  the  expression,  "  a  straight  line." 

§  6.  The  first  of  the  two  great  arguments  in  support  of  the  theory 
that  axioms  are  a  priori  truths,  having,  I  tliink,  been  sufficiently  an- 
swered ;  I  proceed..to  the  second,  on  which  most  stress  is  usually  laid, 
and  which  is  chiefly  insisted  upon  by  Mr.  ^Vliewell.  Axioms  (it  is 
asserted)  are  conceived  by  iis  not  only  as  tnie,  but  as  universally  and 
necessarily  true.  Now,  experience  cannot  possibly  give  to  any  propo- 
sition this  character.  I  may  have  seen  snow  a  hundred  times,  and 
may  have  seen  that  it  was  white,  but  this  cannot  give  me  entire  assur- 
ance even  that  all  snow  is  white  ;  much  less  that  snow  must  be  white. 
"However  many  instances  we  may  have  observed  of  the  truth  of  a 
proposition,  there  is  nothing  to  assure  us  that  the  next  case  shall  not  be 
an  exception  to  the  rule.  If  it  be  strictly  true  that  every  ruminant 
animal  yet  known  has  cloven  hoofs,  we  still  cannot  be  sure  that  some 
creature  will  not  hereafter  be  discovered  which  has  the  first  of  these 

attributes,  without  having  the  other Experience  must  always  consist 

of  a  limited  number  of  observations :  and,  however  numerous  these 


156  REASOXING. 

may  be,  they  can  show  nothing  with  regard  to  the  infinite  number  of 
cases  in  which  the  experiment  has  not  been  made."  Moreover,  axioms 
are  not  only  universal,  they  are  also  necessary.  Now  "  experience 
cannot  offer  the  smallest  ground  for  the  necessity  of  a  proposition. 
She  can  obseiTO  and  record  what  has  happened  ;  but  she  cannot  find, 
in  any  case,  or  in  any  accumulation  of  cases,  any  reason  for  what  must 
happen.  She  may  see  objects  side  by  side ;  but  she  cannot  see  a  rea- 
son why  they  must  ever  be  side  by  side.  She  finds  certain  events  to 
occur  in  succession  ;  but  the  succession  supplies,  in  its  occurrence,  no 
reason  for  its  recurrence.  She  contemplates  external  objects  ;  but  she 
cannot  detect  any  internal  bond,  which  indissolubly  connects  the  future 
with  the  past,  the  possible  with  the  real.  To  learn  a  proposition  by  ex- 
perience, and  to  see  it  to  be  necessarily  true,  are  two  altogether  different 
processes  of  thought."*  And  Mr.  Whewell  adds,  "  If  any  one  does 
not  clearly  comprehend  this  distinction  of  necessary  and  contingent 
truths,  he  will  not  be  able  to  go  along  with  us  in  our  researches  into 
the  foundations  of  human  knowledge ;  nor  indeed,  to  pursue  with 
success  any  speculation  on  the  subject."t 

In  order  to  leani  what  the  distinction  is,  the  non-recognition  of  which 
incurs  this  denunciation,  let  us  refer  again  to  Mr.  Whewell.  "  Neces- 
sary truths  are  those  in  which  we  not  only  learn  that  the  proposition 
is  true,  but  see  that  it  7nust  be  true ;  in  which  the  negation  of  the 
truth  is  not  only  false,  but  impossible;  in  which  we  cannot,  even  by 
an  effort  of  imagination,  or  in  a  supposition,  conceive  the  reverse  of 
that  which  is  asserted.  That  there  are  such  truths  cannot  be  doubted. 
We  may  take,  for  example,  all  relations  of  number.  Three  and  Two, 
added  together,  make  Five.  We  cannot  conceive  it  to  be  otherwise. 
We  cannot,  by  any  freak  of  thought,  imagine  Three  and  Two  to  make 
Seven."* 

Although  Mr.  W^hewell  has  naturally  and  properly  employed  a 
variety  of  phrases  to  bring  his  meaning  more  forcibly  home,  he  will,  I 
presume,  allow  that  they  are  all  equivalent ;  and  that  what  he  means  by 
a  necessaiy  truth,  would  be  sufficiently  defined,  a  proposition  the 
negation  of  which  is  not  only  false  but  inconceivable.  I  am  unable  to 
find  in  any  of  INIr.  ^Vhewell's  expressions,  turn  them  what  way  you 
will,  a  meaning  beyond  this,  and  I  do  not  believe  he  would  contend 
that  they  mean  anything  more. 

This,  therefore,  is  the  principle  asserted :  that  propositions,  the 
negation  of  which  is  inconceivable,  or  in  other  woi-ds,  which  we  can- 
not figure  to  ourselves  as  being  false,  must  rest  upon  evidence  of  a 
higher  and  more  cogent  description  than  any  which  expeiience  can 
afford.  And  we  have  next  to  consider  whether  there  is  any  ground 
for  this  assertion. 

Now  I  cannot  but  wonder  that  so  much  stress  should  be  laid  upon  the 
circumstance  of  inconceivableness,  when  there  is  such  ample  experience 
to  show  that  our  capacity  or  incapacity  of  conceiving  a  thing  has  very 
little  to  do  with  the  possibility  of  the  thing  in  itself;  but  is  in  truth  very 
much  an  affair  of  accident,  and  depends  upon  the  past  history  and 
habits  of  our  own  minds.  There  is  no  more  generally  acknowledtred 
fact  in  human  nature,  than  the  extreme  difficulty  at  first  felt  in  con- 
ceiving anything  as  possible,  which  is  in  contradiction  to  long  estab- 

*  Whewell's  Philosophy  of  the  Inductive  Sciences,  i.,  5&— 61. 
t  njid-,  57.  t  Ibid.,  i.,  54,  55. 


DEMONSTRATION,    AND    NECESSARY    TRUTHS.  157 

lisbed  and  familiar  experience  ;  or  even  to  old  and  familiar  habits  of 
thought.  And  this  difficulty  is  a  necessary  result  of  the  fundamental 
laws  of  the  human  mind.  When  we  have  often  seen  and  thought  of 
two  things  together,  and  have  never  in  any  one  instance  either  seen 
or  thought  of  them  separately,  there  is  by  the  primary  laws  of  asso- 
ciation an  increasing  difficulty,  which  in  the  end  becomes  insuperable, 
of  conceiving  the  two  things  apart.  This  is  most  of  all  conspicuous  in 
uneducated  persons,  who  are  in  general  utterly  unable  to  separate  any 
two  ideas  which  have  once  become  firmly  associated  in  their  minds ; 
and  if  persons  of  cultivated  intellect  have  any  advantage  on  the  point, 
it  is  only  because,  having  seen  and  heard  and  read  more,  and  being 
more  accustomed  to  exercise  their  imagination,  they  have  experienced 
their  sensations  and  thoughts  in  more  varied  combinations,  and  have 
been  prevented  from  forming  many  of  these  inseparable  associations. 
But  this  advantage  has  necessarily  its  limits.  The  man  of  the  most 
practised  intellect  is  not  exempt  from  the  universal  laws  of  our  concep- 
tive  faculty.  If  daily  habit  presents  to  him  for  a  long  period  two  facts  in 
combination,  and  if  he  is  not  led  during  that  period  either  by  accident 
or  intention  to  think  of  them  apart,  he  will  in  time  become  incapable 
of  doing  so  even  by  the  strongest  effiart ;  and  the  supposition  that  the 
two  facts  can  be  separated  in  nature,  will  at  last  present  itself  to  his 
mind  with  all  the  characters  of  an  inconceivable  phenomenon.  There 
are  remarkable  instances  of  this  in  the  history  of  science  :  instances,  in 
which  the  wisest  men  rejected  as  impossible,  because  inconceivable, 
things  which  their  posterity,  by  earlier  practice  and  longer  perseve- 
rance in  the  attempt,  found  it  quite  easy  to  conceive,  and  which  every- 
body now  knows  to  be  true.  There  was  a  time  when  men  of  the  most 
cultivated  intellects,  and  the  most  emancipated  from  the  dominion  of 
early  prejudice,  could  not  credit  the  existence  of  antipodes ;  were 
unable  to  conceive,  in  opposition  to  old  association,  the  force  of  gravity 
acting  upwards  instead  of  downwards.  The  Cartesians  long  rejected 
the  Newtonian  doctrine  of  the  gravitation  of  all  bodies  towards  one 
another,  on  the  faith  of  a  general  proposition,  the  reverse  of  which 
seemed  to  them  to  be  inconceivable — the  proposition  that  a  body  can- 
not act  where  it  is  not.  All  the  cumbrous  machinery  of  imaginary 
vortices,  assumed  without  the  smallest  particle  of  evidence,  appeared 
to  these  philosophers  a  more  rational  mode  of  explaining  the  heavenly 
motions,  than  one  which  involved  what  seemed  to  them  so  great  an 
absurdity.*  And  they  no  doubt  found  it  as  impossible  to  conceive 
that  a  body  should  act  upon  the  earth,  at  the  distance  of  the  sun  or 
moon,  as  we  find  it  to  conceive  an  end  to  space  or  time,  or  two  straight 
lines  inclosing  a  space.  Newton  himself  had  not  been  able  to  realize 
the  conception,  or  we  should  not  have  had  his  hypothesis  of  a  subtle 

*  It  would  be  difficult  to  name  a  man  more  remarkable  at  once  for  the  greatness  and  the 
universality  of  his  intellectual  powers,  than  Leibnitz.  Yet  this  great  man  gave  as  a  reaspn 
for  rejecting  Newton's  scheme  of  the  solar  system,  that  God  could  not  make  a  body  revolve 
rouiid  a  distant  centre,  unless  either  by  some  impelling  mechanism,  or  by  miracle : — "  Tout- 
ce  qui  n'est  pas  explicable,"  says  he  in  a  letter  to  the  Abbe  Conti,  "par  la  nature  des  crea- 
tures, est  miraculeux.  II  no  suffit  pas  de  dire:  Dieu  a  fait  une  telle  loi  de  nature :  done 
la  chose  est  naturelle.  II  faut  que  la  loi  soit  executable  par  les  natures  des  creatures.  Si 
Dieu  donnait  cette  loi,  par  exemple,  a  un  corps  libre,  de  toumer  a  I'entour  d'un  certain 
centre,  il  faudrait  ou  qu'il  y  joignil  d'aulres  corps  q-ui  par  Icur  impulsion  Vobligeasscnt  de  rcster 
toujours  dans  son  orbite  circidaire,  ou  qu'il  nut  un  ange  a  ses  trousses,  ou  enfm  il  faudrait  qu'il  y 
concourut  extraordinairement ;  car  naturellement  il  s'ecartera  par  la  tangente." — Worlui  iff 
Leibnitz,  ed.  Dutens,  iii.,  4-lC. 


158  REASONING. 

ether;  the  occult  cause  of  gravitation  ;  and  his  writings  prove,  that 
although  he  deemed  the  particular  nature  of  the  inteiTnediate  agency 
a  matter  of  conjecture,  the  necessity  of  some  such  agency  appeared  to 
him  indubitable.  It  would  seem  that  even  now  the  majority  of  scien- 
tific men  have  not  completely  got  over  this  very  difficulty ;  for  though 
they  have  at  last  learnt  to  conceive  the  sun  attracting  the  eaith  with- 
out any  intervening  fluid,  they  cannot  yet  conceive  the  sun  illuminating 
the  earth  without  some  such  medium.  - 

If,  then,  it  be  so  natural  to  the  human  mind,  even  in  its  highest 
state  of  culture,  to  be  incapable  of  conceiving,  and  on  that  ground  to 
believe  impossible,  what  is  afterwards  not  only  found  to  be  conceivable 
but  proved  to  be  true ;  what  wonder  if  in  cases  where  the  association 
is  still  older,  more  confiraied,  and  more  familiar,  and  in  which  nothing 
ever  occurs  to  shake  our  conviction,  or  even  suggest  to  us  any  concep- 
tion at  variance  with  the  association,  the  acquired  incapacity  should 
continue,  and  be  mistaken  for  a  natural  incapacity  1  It  is  true  our  ex- 
perience of  the  varieties  in  nature  enables  us,  within  certain  limits,  to 
conceive  other  varieties  analogous  to  them.  We  can  conceive  the  sun 
or  moon  falling;  for  although  we  never  saw  them  fall,  nor  ever  perhaps 
ima<Tined  them  falUng,  we  have  seen  so  many  other  things  fall,  that 
we  have  innumerable  familiar  analogies  to  assist  the  conception; 
which,  after  all,  we  should  probably  have  some  difficulty  in  fi-aming, 
were  we  not  well  accustomed  to  see  the  sun  and  moon  move  (or 
appear  to  move),  so  that  we  are  only  called  upon  to  conceive  a  slight 
change  in  the  direction  of  motion,  a  circumstance  familiar  to  our  ex- 
perience. But  when  experience  affijrds  no  model  on  which  to  shape 
the  new  conception,  how  is  it  possible  for  us  to  form  it  ?  How,  for 
example,  can  we  imagine  an  end  to  space  or  timel  We  neyer  saw 
any  object  without  something  beyond  it,  nor  experienced-  any  feeling 
without  something  following  it.  When,  therefore,  we  attempt  to 
conceive  the  last  point  of  space,  we  have  the  idea  in-esistibly  raised 
of  other  points  beyond  it.  When  we  try  to  imagine  the  last  instant 
of  time,  we  cannot  help  conceiving  another  instant  after  it.  Nor  is 
there  any  necessity  to  assume,  as  is  done  by  the  school  to  which  Mr. 
Whewell  belongs,  a  peculiar  fundamental  law  of  the  mind  to  account 
for  the  feeling  of  infinity  inherent  in  our  conceptions  of  space  and 
time;  that  apparent  infinity  is  sufficiently  accounted  for  by  sim23ler 
and  universally  acknowledged  laws. 

Now,  in  the  case  of  a  geometrical  axiom,  such,  for  example,  as  that 
two  straight  lines  cannot  inclose  a  space — a  truth  w^ich  is  testified  to 
us  by  our  veiy  earliest  impressions  of  the  external  world — how  is  it 
possible  (whether  those  external  impressions  be  or  be  not  the  gi-ound 
of  our  belief)  that  the  reverse  of  the  proposition  can  be  otherwise 
than  inconceivable'  to  us  ?  What  analogy  have  we,  what  similar  order 
of  facts  in  any  other  branch  of  our  experience,  to  facilitate  to  us  the 
conception  of  two  straight  lines  inclosing  a  space?  Nor  is  even  this 
all.  I  have  already  called  attention  to  the  peculiar  property  of  our 
impressions  of  form,  that  the  ideas  or  mental  images  exactly  resemble 
their  prototypes,  and  adequately  represent  them  for  the  purposes  of 
scientific  observation.  From  this^  and  fi-om  the  intuitive  character  of 
the  obsei-\^ation,  which  in  this  case  reduces  itself  to  simple  inspection, 
we  cannot  so  m.uch  as  call  up  in  our  imagination  two  straight  lines,  in 
order  to  attempt  to  conceive  them  inclosing  a  space,  without  by  that 


DEMONSTRATION,    AND    NECESSARY    TRUTHS.  159 

very  act  repeating  the  philosophical  experiment  whicli  establishes  the 
contraiy.  Will  it  really  be  contended  thSt  t>he  inconceivableness  of 
the  tliiuff,  under  such  circumstances,  proves  anything  against  the  ex- 
perimental origin  of  the  conviction  I  Is  it  not  clear  that  in  whichever 
mode  our  beUef  in  the  pi'oposition  may  have  originated,  the  impossi- 
bility of  our  conceiving  the  negative  of  it  must,  under  either  hypothesis, 
be  tJic  same  ?  As,  tlien,  Mr.  Whewell  oxliorts  those  who  have  any 
difficulty  in  recognizing  the  distinction  held  by  him  between  necessary 
and  contingent  ti'uths,  to  study  geometry — a  condition  which  I  can 
assure  him  I  have  conscientiously  fulfilled — I,  in  return,  with  equal 
confidence,  exhort  those  who  agree  with  Mr.  Whewell,  to  study  the 
elementary  laws  of  association  ;  being  convinced  that  nothing  more  is 
requisite  than  a  moderate  familiarity  with  those  laws,  to  dispel  the 
illusion  which  ascribes  a  peculiar  necessity  to  our  earliest  inductioHS 
fi'om  experience,  and  measures  the  possibility  of  things  in  themselvea, 
by  the  human  capacity  of  conceiving  them. 

I  hope  to  be  pardoned  for  adding,  that  Mr.  "Wliewell  himself  has 
both  confirmed  by  his  testimony  the  effect  of  habitual  association  in 
giving  to  an  experimental  truth  the  appearance  6f  a  necessary' one,  and 
attbrded  a  striking  instance  of  that  remarkable  law  in  his  own  person. 
In  h\s  Philosajjhy  of  the  Inductive  Sciences  he  continually  asserts, 'that 
propositions  which  not  only  are  not  self-evident,  but  whicli  we  know  to 
have  been  discovered  gradually,  and  by  gieat  efforts  of  genius  and  pa- 
tience, have,  when  Once  established,  appeared  so  self-evident  that,  but 
for  historical  evidence,  it  would  have  been  impossible  to  conceive  that 
they  had  not  been  recognized  from  the  first  by  all  pereons  in  a  sound 
state  of  tlieir  faculties.  "  We  now  despise  those  who,  in  the  Coperni- 
can  controversy,  could  not  conceive  the  appai'ent  motion  of  the  sun  on 
the  heliocenti'ic  hypothesis;  or  those  who,  in  opposition  to  Galileo, 
thought  that  a  uniform  force  might  be  tliat  which  generated  a  velocity 
proportional  to  the  space ;  or  those  who  held  there  was  something  ab- 
surd in  N'ewtoii's  doctrine  of  the  different  refrangibility  of  differently 
colored  rays ;  or  those  who  imagined  that  when  elements  combine,  their 
sensible  qualities  must  be  manifest  in  the  compound;  or  those  who  were 
reluctant  to  give  up  the  distinction  of  vegetables  into  herbs,  shrubs,  and 
trees.  We  cannot  help  thinking  that  men  must  have  been  singularly 
dull  of  comprehension  to  fii|d  a  difficulty  in  admitting  what  is  to  us  so 
plain  and  simple.  We  have  a  latent  perstiasion  that  we  in  their  place 
should  have  been  Aviser  and  moro  clear-sighted ;  that  we  should  have 
taken  the  right  side,. and  given  our  assent  at  once  to  the  truth.  Yet  in 
reality  such  a  persuasipn  is  a  mere  delusion.  The  persons  who,  in  such 
instances  as  the  above,  were  on  the  losing  side,  were  very  far  in  most 
cases  from  beiYig  persons  more  prejudiced,  or  ,stupid,  or  naiTow-minded, 
than  the  greater  part  of  rpankind  now  are ;  and  the  cause  for  which 
they  fought  was  far  from  being  a  manifestly  bad  one,  till  it  had  been  so 
decided  by  the  result  of  the  war. ...  So  complete  has  been  the  victory 
of  truth  in  most  of  these  instances,  that  at  present  we  can  hardly  ima- 
gine die  struggle  to  have  been  necessary.  The  very  essence  of  these  tri- 
umphs is,  that  they  lead  us  to  regard  tltc  views  we  reject  as  not  only  false, 
hut  inconceivahle.^'* 

This  last  proposition  is  precisely  what  I  contend  for  ;  and  I  ask  no 

*  Philosophy  of  the  Indwtive  Sckivce^,  vol.  ij.,  p.  174. 


160  REASONING. 

more,  m  order  to  overthrow  the  whole  theory  of  Mr.  Whewell  on  the 
nature  of  the  evidence  of  axioms.  For  what  is  that  theory  ?  That  the 
truth  of  axioms  cannot  have  been  learnt  from  experience,  because  their 
falsity  is  inconceivable.  But  Mr.  Whewell  himself  says,  that  we  are 
continually  led  by  the  natural  progress  of  thought,  to  regard  as  incon- 
ceivable what  our  forefathers  not  only  conceived  but  believed,  nay, 
even  (he  might  have  added)  were  unable  to  conceive  the  contrarv  of. 
Mr.  Whewell  cannot  intend  to  justify  this  mode  of  thought ;  he  cannot 
mean  to  say,  that  we  can  be  right  in  regarding  as  inconceivable  what 
others  have  conceived,  and  as  self-evident  what  to  others  did  not  appear 
e\"ident  at  all.  After  so  complete  an  admission  that  inconceivablenesa 
is  an  accidental  thing,  not  inherent  in  the  phenomenon  itself,  but  de- 
pendent on  the  mental  history  of  the  person  who  tries  to  conceive  it, 
how  can  he  ever  call  upon  us  to  reject  a  proposition  as  impossible  on 
no  other  gi'ound  than  its  inconceivableness  ?  Yet  he  not  only  does  so, 
but  has  unintentionally  afforded  some  of  the  most  remarkable  exam- 
ples which  can  be  cited  of  the  very  illusion  which  he  has  himself  so 
clearly  pointed  out.  W^e  select  as  specimens,  his  remarks  on  the  evi- 
dence of  the  three  laws  of  motion,  and  of  the  atomic  theory. 

With  respect  to  the  laws  of  motion,  Mr.  Whewell  says :  "  No  one 
can  doubt  that,  in  historical  fact,  these  laws  were  collected  from  expe- 
rience. That  such  is  the  case  is  no  matter  of  conjecture.  We  know 
the  time,  the  persons,  the  circumstances,  belonging  to  each  step  of  each 
discovery."*  After  such  a  testimony,  to  adduce  evidence  of  the  fact 
would  be  supei-fluous.  And  not  only  were  these  laws  by  no  means 
intuitively  evident,  but  some  of  them  were  originally  paradoxes.  The 
first  law  was  especially  so.  That  a  body,  once  in  motion,  would  con- 
tinue for  ever  to  move  in  the  same  direction  with  undiminished  velo- 
city unless  acted  upon  by  some  new  force,  was  a  proposition  which 
mankind  found  for  a  long  time  the  gi'eatest  difficulty  in  crediting.  It 
stood  opposed  to  apparent  experience  of  the  most  familiar  kind,  which 
taught  that  it  was  the  nature  of  motion  to  abate  gradually,  and  at  last 
terminate  of  itself  Yet  when  once  the  contrary  doctrine  was  firmly 
established,  mathematicians,  as  Mr.  Whewell  observes,  speedily  began 
to  believe  that  laws,  thus  conti-adictory  to  first  appearances,  and  which, 
even  after  full  proof  had  been  obtained,  it  had  required  generations  to 
render  familiar  to  the  minds  of  the  scientific  world,  were  under  "  a 
demonsti'able  necessity,  compelling  them  to  be  such  as  they  are  and 
no  other  ;"  and  ]Mr.  Wliewell,  though  he  has  "  not  ventured  absolutely 
to  pronounce"  that  all  these  laws  "  can  be  rigorously  traced  to  an  ab- 
solute necessity  in  the  nature  of  things, "t  does  actually  think  in  that 
manner  of  the  law  just  mentioned  ;  of  which  he  says  :  "  Though  the 
discovery  of  the  first  law  of  motion  was  made,  historically  speaking,  by 
means  of  experiment,  we  have  now  attained  a  point  of  view  in  which 
we  see  that  it  might  have  been  certainly  kno\\Ti  to  be  true,  independ- 
ently of  experience."!  Can  there  be  a  more  striking  exemplification 
than  is  here  afforded,  of  the  effect  of  association  which  we  have  de- 
scribed \  Philosophers,  for  generations,  have  the  most  exta-aordinary 
difficulty  in  putting  certain  ideas  together ;  they  at  last  succeed  in  doing 
so;  and  after  a  sufficient  repetition  of  the  process,  they  first  fancy  a 
natural  bond  between  the  ideas,  then  experience  a  growing  difficulty 

*  Philosophy  of  the  Liduxtiue  Sciaices,  i.,  238.         t  Ibid.,  237.         t  Ibid,  213. 


DEMONSTRATION,    AND   NECESSARY   TRUTHS.  161 

which  at  last,  by  the  coutlnuation  of  tlie  same  progress,  becomes  an  im- 
possibility, of  severing  them  from  one  another.  If  such  be  the  pro- 
gress of  an  experimental  conviction  of  which  the  date  is  of  yesterday, 
and  which  is  in  opposition  to  first  appearances,  how  must  it  fare  with 
those  which  are  conformable  to  appearances  femiliar  from  the  first 
dawn  of  intelligence,  and  of  the  coijclusiveness  of  which,  from  the 
earliest  records  of  human  thought,  no  skeptic  has  suggested  even  a  mo- 
mentary doubt  1 

The  other  instance  which  we  shall  quote  is  a  truly  astonishing  one. 
and  may  be  called  the  reductio  ad  ahsurdum  of  the  theory  of  inconceiv- 
ableness.  Speaking  of  the  laws  of  chemical  composition,  Mr.  Wlie- 
well  says  :*  "  That  they  could  never  have  been  clearly  understood,  and 
therefore  never  firmly  established,  without  laborious  and  exact  exper- 
iments, is  certain  ;  but  yet  we  may  venture  to  say,  that  being  once 
kno\\'n,  they  possess  an  evidence  beyond  that  of  mere  experiment. 
For  Jtoic,  in  fact,  can  tve  conceive  combinations,  othenvise  than  as  defi- 
nite in  kind  and  qicantity  1  If  we  were  to  suppose  each  element  ready 
to  combine  with  any  other  indifferently,  and  indifferently  in  any  quan- 
tity, we  should  have  a  world  in  which  all  would  be  confusion  and  in- 
definiteness.  There  would  be  no  fixed  kinds  of  bodies ;  salts,  and 
stones,  and  ores,  would  approach  to  and  graduate  into  each  other  by 
insensible  degrees.  Instead  of  this,  we  know  that  the  world  consists 
of  bodies  distinguishable  from  each  other  by  definite  differences,  capa- 
ble of  being  classified  and  named,  and  of  having  general  propositions 
asserted  concerning  them.  And  as  xoe  cannot  conceive  a  world  in  which 
this  should  not  he  the  case,  it  would  appear  that  we  cannot  conceive  a 
state  of  things  in  which  the  laws  of  the  combination  of  elements  should 
not  be  of  that  definite  and  measured  kind  which  we  have  above  asserted." 

That  a  philosopher  of  Mr.  Whewell's  eminence  should  gravely  as- 
sert that  we  cannnot  conceive  a  world  in  which  the  simple  elements 
would  combine  in  other  than  definite  proportions  ;  that  by  dint  of  med- 
itating on  a  scientific  truth,  the  original  discoverer  of  which  is  still  living, 
he  should  have  rendered  the  association  in  his  own  mind  between  the 
idea  of  combination  and  that  of  constant  proportions  so  familiar  and  in- 
timate as  to  be  unable  to  conceive  the  one  fact  without  the  other ;  is  so 
signal  an  instance  of  the  law  of  human  nature  for  which  I  am  contend- 
ing, that  one  word  more  in  illustration  must  be  quite  superfluous.  I 
shall,  only,  therefore,  express  my  satisfaction  that  so  long  as  the  pro- 
gi'ess  of  scientific  instmction  has  not  rendered  this  association  as  indis- 
soluble in  the  minds  of  most  people  as  Mr.  Whewell  finds  it,  the 
majority  of  mankind  will  be  fairly  able  to  judge,  from  this  example,  of 
the  value  of  the  evidence  which  he  deems  sufficient  to  prove  that  a 
scientific  proposition  might  be  known  to  be  true  independently  of 
experience.! 

*  Philosophy  of  the  Indtictive  Sciences,  i.,  384,  385. 

+  The  Quarterly  Review  for  June,  1841,  contains  an  article,  of  great  ability,  on  Mr. 
Whewell's  two  great  works,  the  writer  of  which  maintains,  on  the  subject  of  axioms,  the 
doctrine  advanced  in  the  text,  that  they  are  generalizations  from  experience,  and  supports 
that  opinion  by  a  line  of  argument  strikingly  coinciding  with  mine.  When  I  state  that  the 
whole  of  the  present  chapter  was  written  before  I  had  seen  the  article  (the  greater  part, 
indeed,  before  it  was  published),  it  is  not  my  object  to  occupy  the  reader's  attention  with  a 
matter  so  unimportant  as  the  degree  of  oripinahty  which  may  or  may  not  belong  to  any 
portion  of  my  own  speculations,  but  to  obtain  for  an  opinion  which  is  opiiosed  to  reigning 
doctrines,  the  recommendation  derived  from  a  striking  concurrence  of  sentiment  between 
two  inquirers  entirely  independent  of  one  another.  1  have  much  pleasure  in  citing  from  a 
writer  of  the  extensive  acquirements  in  physical  and  metaphysical  knowledge  and  the  ca- 


162  REASONING. 


CHAPTER  VL 

THE    SAME    SUBJECT   CONTINUED. 

§  1.  In  the  examination  which  formed  the  subject  of  the  last  chapter, 
into  the  nature  of  the  evidence  of  those  deductive  sciences  which  are 
commonly  represented  to  be  systems  of  necessary  truth,  we  have  been 
led  to  the  following  conclusions.  The  results  of  those  sciences  are 
indeed  necessary,  in  the  sense  of  necessarily  following  from  certain  first 
principles,  commonly  called  axioms  and  definitions;  of  being  certainly 
true  if  those  axioms  and  definitions  are  so.     But  their  claim  to  the 

pacity  of  systematic  thought  which  the  article  evinces,  passages  so  remarkably  in  unison 
with  my  own  views  as  the  following  : — 

"  The  truths  of  geometry  are  summed  up  and  embodied  in  its  definitions  and  axioms.  .  . 
Let  us  turn  to  the  axioms,  and  what  do  we  find  ?  A  string  of  propositions  concerning 
magnitude  in  the  abstract,  which  are  equally  true  of  space,  time,  force,  number,  and  every 
other  magnitude  susceptible  of  aggregation  and  subdivision.  Such  propositions,  where  they 
are  not  mere  definitions,  as  some  of  them  are,  carry  their  inductive  origin  on  the  face  of 
their  enunciation.  .  .  .  Those  which  declare  that  two  straight  lines  cannot  inclose  a  space, 
and  that  two  straight  lines  which  cut  one  another  cannot  both  be  parallel  to  a  third,  are  in 
reality  the  only  ones  which  express  characteristic  properties  of  space,  and  these  it  will  be 
worth  while  to  consider  more  nearly.  Now  the  only  clear  notion  we  can  form  of  straight- 
ness  is  uniformity  of  direction,  for  space  in  its  ultimate  analysis  is  nothing  but  an  assem- 
blage of  distances  and  directions.  And  (not  to  dwell  on  the  notion  of  continued  contem- 
plation,  i.  e.,  mental  experience,  as  included  in  the  very  idea  of  uniformity  ;  nor  on  that  of 
transfer  of  the  contemplating  being  from  point  to  point,  and  of  experience,  during  such 
transfer,  of  the  homogeneity  of  the  interval  passed  over)  we  cannot  even  propose  the  propo- 
sition in  an  intelligible  form,  to  any  one  whose  experience  ever  since  he  was  born  has  not 
assured  him  of  the  fact.  The  unity  of  direction,  or  that  we  cannot  march  from  a  given 
point  by  more  than  one  path  direct  to  the  same  object,  is  matter  of  practical  experience 
long  before  it  can  by  possibility  become  matter  of  abstract  thought.  We  cannot  attempt 
mentally  to  exemplify  the  conditions  of  the  assertion  in  an  imaginary  case  opposed  to  it,  ivithout  vi- 
olating our  habitual  recollection  of  this  experience,  and  defacing  our  mental  picture  of  space  as 
grounded  on  it.  What  but  experience,  we  may  ask,  can  possibly  assure  us  of  the  homo- 
geneity of  the  parts  of  distance,  time,  force,  and  measurable  aggregates  in  general,  on 
which  the  truth  of  the  other  axioms  depends  ?  As  regards  the  latter  axiom,  after  what  has 
been  said  it  must  be  clear  that  the  very  same  course  of  remarks  equally  applies  to  its  case, 
and  that  its  truth  is  quite  as  much  forced  on  the  mind  as  that  of  the  former  by  daily  and 
hourly  experience,  .  .  .  including  always,  be  it  observed,  in  our  notion  of  experience,  that  which  is 
gained  by  contemplation  of  the  inward  picture  which  the  mind  forms  to  itself  in  any  proposed  case, 
or  which  it  arbitrarily  selects  as  an  example — such  picture,  i/i  virtue  of  the  extreme  simplicity  of  these 
primary  relations,  being  called  up  by  the  imagination  with  as  7nuch  vividness  and  clearness  as  could 
be  done  by  any  external  impression,  which  is  the  only  meaning  we  can  attach  to  the  word  intuition, 
as  applied  to  such  relations." 

And  again,  of  the  axioms  of  mechanics  :^"  As  we  admit  no  such  propositions,  other  than 
as  truths  inductively  collected  from  observation,  even  in  geometry  itself,  it  can  hardly  be 
expected  that,  in  a  science  of  obviously  contingent  relations,  we  should  acquiesce  in  acon- 
trary  view.  Let  us  take  one  of  these  axioms  and  examine  its  evidence  :  for  instance,  that 
equal  forces  perpendicularly  applied  at  the  opposite  ends  of  equal  arms  of  a  straight  lever 
will  balance  each  other.  What  but  experience,  we  may  ask,  in  the  first  place,  can  possibly 
inform  us  that  a  force  so  applied  will  have  any  tendency  to  turn  the  lever  on  its  centre  at 
all?  or  that  force  can  be  so  transmitted  along  a  rigid  line  perpendicular  to  its  direction,  as 
to  act  elsewhere  in  space  than  along  its  own  line  of  action  ?  Surely  this  is  so  far  from  be- 
ing self-evident  that  it  has  even  a  paradoxical  appearance,  which  is  only  to  be  removed  by 
giving  our  lever  thickness,  material  composition, -and  molecular  powers.  Again  we  con- 
clude, that  the  two  forces,  being  equal  and  applied  under  precisely  similar  circumstances, 
must,  if  they  exert  any  effort  at  all  to  turn  the  lever,  exert  equal  and  opposite  efforts :  but 
what  ^  priori  reasoning  can  possibly  assure  us  that  they  do  act  under  precisely  similar  cir- 
cumstances? that  points  which  differ  in  place,  are  similarly  circumstanced  as  regards  the 
exertion  of  force  ?  that  universal  space  may  not  have  relations  to  universal  force — or,  at  all 
events,  that  the  organization  of  the  material  universe  may  not  be  such  as  to  place  that  por- 
tion of  space  occupied  by  it  in  such  relations  to  the  forces  exerted  in  it,  as  may  invalidate 
the  absolute  similarity  of  circumstances  assumed  ?  Or  we  may  argue,  what  have  we  to  do 
with  the  notion  of  angular  movement  in  the  lever  at  all  ?  The  case  is  one  of  rest,  and  of 
quiescent  destruction  of  force  by  force.    Now  how  is  this  destruction  effected  ?    Assuredly 


DEMONSTRATIOV,  AND    NECESSARY    TRUTHS.  163 

character  of  necessity  in  any  sense  beyond  this,  as  implying  an  evidence 
independent  of  and  snporior  to  observation  and  experience,  must  depend 
upon  the  previous  estabHshment  of  such  a  claim  in  favor  of  the  defini- 
tions and  axioms  themselves.  With  regard  to  axioms,  we  found  that, 
considered  as  experimental  truths,  they  I'est  upon  superabundant  and 
obvious  evidence.  We  inquired,  whether,  since  this  is  the  case,  it  be 
necessaiy  to  suppose  any  other  evidence  of  those  truths  than  experi- 
mental evidence,  any  other  origin  for  our  belief  of  them  than  an  experi- 
mental origin.  We  decided,  that  the  burden  of  proof  lies  with  those 
who  maintain  the  affirmative,  and  we  examined,  at  considerable  length, 
such  arguments  as  they  have  produced.  The  examination  having  led 
to  the  rejection  of  those  arguments,  we  have  thought  ourselves  war- 
ranted in  concluding  that  axioms  are  but  a  class,  the  highest  class,  of 

by  the  counterpressure  which  supports  the  fulcrum.  But  would  not  this  destruction 
equally  arise,  and  by  the  same  amount  of  counteracting  force,  if  each  force  simply  pressed 
its  own  half  of  the  lever  against  the  fulcrum  ?  And  what  can  assure  us  that  it  is  not  so, 
except  removal  of  one  or  other  force,  and  consequent  tilting  of  the  lever  ?  The  other  fun- 
damental axiom  of  statics,  that  the  pressure  on  the  point  of  support  is  the  sum  of  the 
weights  ...  is  merely  a  scientific  transformation  and  more  refined  mode  of  stating  a  coarse 
and  obvious  result  of  universal  experience,  viz.,  that  tire  weight  of  a  rigid  body  is  the  same, 
handle  it  or  suspend  it  in  what  position  or  by  what  point  we  will,  and  that  whatever  sus- 
tains it  sustains  its  total  weight.  Assuredly,  as  Mr.  Whewell  justly  remarks,  '  No  one 
probably  ever  made  a  trial  for  the  purpose  of  showing  that  the  pressure  on  the  support  is 
equal  to  the  sum  of  the  weights.' .  .  .  But  it  is  precisely  because  in  every  action  of  his  life 
from  earliest  infancy  he  has  been  continually  making  the  trial,  and  seeing  it  made  by  every 
other  living  being  about  him,  that  he  never  dreams  of  staking  its  result  on  one  additional 
attempt  made  with  scientific  accuracy.  This  would  be  as  if  a  man  should  resolve  to  de- 
cide by  experiment  whether  his  eyes  were  useful  for  the  purpose  of  seeing,  by  hermetically 
sealing  himself  up  for  half  an  hour  in  a  metal  case." 

On  the  "  paradox  of  universal  propositions  obtained  by  experience,"  the  same  writer 
says :  "  If  there  be  necessary  and  universal  truths  expressible  in  propositions  of  axiomatic 
simplicity  and  obviousness,  and  having  for  their  subject-matter  the  elements  of  all  our  ex- 
perience and  all  our  knowledge,  surely  these  are  the  truths  which,  if  experience  suggests  to 
us  any  truths  at  all,  it  ought  to  suggest  most  readily,  clearly,  and  unceasingly.  If  it  were 
a  truth,  universal  and  necessary,  that  a  net  is  spread  over  the  whole  surface  of  every  plan- 
etary globe,  we  should  not  travel  far  on  our  own  without  getting  entangled  in  its  meshes, 
and  making  the  necessity  of  some  means  of  extrication  an  axiom  of  locomotion.  .  .  .There 
is,  therefore,  nothing  paradoxical,  but  the  reverse,  in  our  being  led  by  observation  to  a  re- 
cognition of  such  truths,  as  general  propositions,  coextensive  at  least  with  all  human  expe- 
rience. That  they  pervade  all  the  objects  of  experience,  must  ensure  their  continual  sug- 
gestion by  experience  ;  that  they  are  true,  must  ensure  that  consistency  of  suggestion,  that 
iteration  of  uncontradicted  assertion,  which  commands  implicit  assent,  and  removes  all  oc- 
casion of  exception  ;  that  they  are  simple,  and  admit  of  no  misunderstanding,  must  secure 
their  admission  by  every  mind." 

"  A  truth,  necessary  and  universal,  relative  to  any  object  of  our  knowledge,  must  verify 
itself  in  every  instance  where  that  object  is  before  our  contemplation,  and  if  at  the  same 
time  it  be  simple  and  intelligible,  its  verification  must  be  obvious.  The  setitiment  of  such  a 
truth  cannot,  therefore,  but  be  present  to  our  minds  whenever  that  object  is  contemplated,  and  must 
therefore  make  a  part  of  the  menial  picture  or  idea  of  that  object  which  we  may  on  any  occasion  stimmon 
before  our  imagination.  .  .  .  All  propositions,  therefore,  become  not  only  untrue  but  inconceivable,  if 
.  .  .  axioms  be  violated  in  therr  enunciation." 

Another  high  authority  (if  indeed  it  be  another  authority)  may  be  cited  in  favor  of  the 
doctrine  that  axioms  rest  upon  the  evidence  of  induction.  "  The  axioms  of  geometry  them- 
selves may  be  regarded  as  in  some  sort  an  appeal  to  experience,  not  corporeal,  but  mental. 
When  we  say,  the  whole  is  greater  than  its  part,  we  announce  a  general  fact,  which  rests, 
it  is  true,  on  our  ideas  of  whole  and  part ;  but,  in  abstracting  these  notions,  we  begin  by 
considering  them  as  subsisting  in  space,  and  tune,  and  body,  and  again,  in  linear,  and  su- 
perficial, and  solid  space.  Again,  when  we  say,  the  equals  of  equals  are  equal,  we  men- 
tally make  comparisons,  in  equal  spaces,  equal  times,  &c.,  so  that  these  axioms,  however  self- 
evident,  are  still  general  propositions  so  far  of  the  inductive  kind,  that,  independently  of  ex- 
perience, they  would  not  present  themselves  to  the  mind.  The  only  diilerence  between 
these  and  axioms  obtained  from  extensive  induction  is  this,  that,  in  raising  the  axioms  of 
geometry,  the  instances  oifer  themselves  spontaneously,  and  without  the  trouble  of  search, 
and  are  few  and  simple  ;  in  raismg  those  of  nature,  they  are  infinitely  numerous,  compli- 
cated, and  remote,  so  that  the  most  diligent  research  and  the  utmost  acuteness  are  required 
to  unravel  their  web  and  place  their  meaning  in  evidence."— Sir  J.  Herschel's  Discourse 
on  the  Htudy  of  Natural  Philosophy,  pp.  95,  96. 


164  BEASONIVG. 

inductions  from  experience  :  the  simplest  and  easiest  cases  of  generali- 
zation from  the  facts  furnished  to  us  by  our  senses  or  by  our  internal 
consciousness. 

While  the  axioms  of  demonstrative  sciences  thus  appeared  to  be 
experimental  truths,  the  definitions,  as  they  are  incorrectly  called,  qf 
those  sciences,  were  found  by  us  to  be  generalizations  from  experience 
which  are  not  even,  accurately  speaking,  truths ;  being  propositions  in 
which,  while  we  assert  of  some  kind  of  object,  some  j^roperty  or  prop- 
erties which  observation  shows  to  belong  to  it,  we  at  the  same  time 
deny  that  it  possesses  any  other  properties,  although  in  truth  other 
properties  do  in  every  individual  instance  accompany,  and  in  most  or 
even  in  all  instances,  modify  the  property  thus  exclusively  predicated. 
The  denial,  therefore,  is  a  mere  fiction,  or  'supposition,  made  for  the 
purpose  of  excluding  the  consideration  of  those  modifying  circum- 
stances, when  their  influence  is  of  too  trifling  amount  to  be  worth  con- 
sidering, or  adjourning  it,  when  important,  to  a  more  convenient 
moment. 

From  these  considerations  it  would  appear  that  Deductive  or  De- 
monstrative Sciences  are  all,  without  exception.  Inductive  Sciences : 
that  their  evidence  is  that  of  experience,  but  that  they  are  also,  in  virtue 
of  the  peculiar  character  of  one  indispensable  portion  of  the  general 
formulae  according  to  which  their  inductions  are  made.  Hypothetical 
Sciences.  Their  conclusions  are  only  true  upon  certain  suppositions, 
which  are,  or  ought  to  be,  approximations  to  the  truth,  but  are  seldom, 
if  ever,  exactly  true  ;  and  to  this  hypothetical  character  is  to  be  ascribed 
the  peculiar  certainty,  which  is  supposed  to  be  inherent  in  demon- 
stration. 

What  we  have  now  asserted,  however,  cannot  be  received  as  univer- 
sally true  of  Deductive  or  Demonstrative  Sciences  vmtil  verified  by 
being  applied  to  the  most  remarkable  of  all  those  sciences,  that  of  Num- 
bers ;  the  theory  of  the  Calculus  ;  Arithmetic  and  Algebra.  It  is  harder 
to  believe  of  the  doctrines  of  this  science  than  of  any  other,  either  that 
they  are  not  truths  d  priori,  but  experimental  truths,  or  that  their  pe- 
cuHm-  certainty  is  o\\nng  to  their  being  not  absolute  but  only  conditional 
truths.  This,  therefore,  is  a  case  which  mei'its  examination  apart;  and 
the  more  so,  because  on  this  subject  we  have  a  double  set  of  doctrines 
to  contend  with;  that  of  Mr.  Whewell  and  the  d  priori  philosophers  on 
one  side ;  and  on  the  other,  a  philosophical  theory  the  most  opposite 
to  theirs,  which  was  at  one  time  very  generally  received,  and  is  still 
far  fi-om  being  altogether  exploded  among  metaphysicians. 

§  2.  This  theory  "attempts  to  solve  the  difficulty  apparently  inherent 
in  the  case,  by  representing  the  propositions  of  the  science  of  numbers 
as  merely  verbal,  and  its  processes  as  simple  transformations  of  lan- 
guage, substitutions  of  one  expression  for  another.  The  proposition, 
Two  and  one  are  equal  to  three,  according  to  these  philosophers,  is  not 
a  truth,  is  not  the  assertion  of  a  really  existing  fact,  but  a  definition  of 
the  word  three  ;  a  statement  that  mankind  have  agi-eed  to  use  the  name 
three  as  a  sign  exactly  equivalent  to  two  and  one;  to  call  by  the  former 
name  whatever  is  called  by  the  other  more  clumsy  phrase.  According 
to  this  doctrine,  the  longest  process  in  algebra  is  but  a  succession  of 
changes  in  terminology,  by  which  equivalent  expressions  are  substi- 
tuted one  for  another ;  a  series  of  translations  of  the  same  fact,  fi-om 


DEMONSTRATION,   AND    NECESSARY    TRUTHS.  1G5 

one  into  another  language  :  though  how,  after  such  a  series  of  transla- 
tions, the  fact  itself  comes  out  changed,  (as  when  we  demonstrate  a  new 
geometrical  theorem  by  algebra,)  they  have  not  explained ;  and  it  is  a 
difficulty  which  is  fatal  to  their  theory. 

It  must  be  acknowledged  that  there  arc  peculiarities  in  the  processes 
of  arithmetic  and  algebra  which  render  tho  abine  theory  very  plausi- 
ble, and  have  not  unnaturally  made  those  sciences  the  stronghold  of 
Nominalism.  The  doctrine  that  we  can  discover  facts,  detect  the 
hidden  processes  of  nature,  by  an  artful  manipulation  of  language,  is 
so  contrary  to  common  sense,  that  a  person  must  have  made  some 
advances  in  philosophy  to  believe  it ;  men  fly  to  so  paradoxical  a  belief 
to  avoid,  as  they  think,  some  even  greater  difficulty,  which  the  vulgar 
do  not  see.  What  has  led  many  to  believe  that  reasoning  is  a  mere 
verbal  process,  is,  that  no  other  theory  seemed  reconcilable  with  the 
nature  of  the  Science  of  Numbers.  For  we  do  not  carry  any  ideas 
along  with  us  when  we  use  the  symbols  of  arithmetic  or  of  algebra. 
In  a  geometrical  demonstration  we  have  a  mental  diagram,  if  not  one 
upon  paper;  AB,  AC,  are  present  to  our  imagination  as  lines,  inter- 
secting other  lines,  forming  an  angle  with  one  another,  and  the  like ; 
but  not  so  a  and  h.  These  may  represent  lines  or  any  other  mao-ni- 
tudes,  but  those  magnitudes  are  never  thought  of;  nothing  is  realized 
in  our  imagination  but  a  and  h.  The  ideas  which,  on  the  particular 
occasion,  they  happen  to  represent,  are  banished  from  the  mind  during 
every  intermediate  part  of  the  process  between  the  beginning,  when 
the  premisses  are  translated  from  things  into  signs,  and  the  end,  when 
the  conclusion  is  translated  back  from  signs  into  things.  Nothing, 
then,  being  in  the  reasoner's  mind  but  the  symbols,  what  can  seem 
more  inadmissible  than  to  pretend  that  the  reasoning  process  has  to  do 
with  anything  more  ]  We  seem  to  have  come  to  one  of  Bacon's  Pre- 
rogative Instances  ;  an  experimcntuvi  crucis  on  the  nature  of  reasoning 
itself 

Nevertheless  it  will  appear  on  consideration,  that  this  apparently  so 
decisive  instance  is  no  instance  at  all ;  that  there  is  in  every  step  of 
an  arithmetical  or  algebraical  calculation  a  real  induction,  a  real  infer- 
ence of  facts  from  facts ;  and  that  what  disguises  the  induction 
is  simply  its  comprehensive  nature,  and  the  consequent  extreme 
generality  of  the  language.  All  numbers  must  be  numbers  of  some- 
thing :  there  are  no  such  things  as  numbers  in  the  abstract.  Ten  must 
mean  ten  bodies,  or  ten  sounds,  or  ten  beatings  of  the  pulse.  But 
though  numbers  must  be  numbers  of  something,  they  may  be  numbers 
<if  anything.  Propositions,  therefore,  concerning  numbers,  have  the 
remarkable  peculiarity  that  they  are  propositions  concerning  all  things 
whatever ;  all  objects,  all  existences  of  every  kind,  known  to  our 
experience.  All  things  possess  quantity ;  consist  of  parts  which  can 
be  numbered ;  and  in  that  character  possess  all  the  properties  which 
are  called  properties  of  numbers.  That  half  of  four  is  two  must  be 
ti-ue  whatever  the  word  four  represents,  whether  four  men,  four  miles, 
or  four  pounds  weight.  We  need  only  conceive  a  thing  divided  into 
four  equal  pai'ts,  (and  all  things  may  be  conceived  as  so  divided,)  to  be 
able  to  predicate  of  it  every  property  of  the  immber  four,  tliat  is, 
every  arithmetical  proposition  in  wliich  the  number  four  stands  on  one 
side  of  the  equation.  Algebra  extends  the  generalization  still  further: 
every  number  represents  that  particular  number  of  all  things  without 


166  REASONING. 

distinction,  but  every  algebraical  symbol  does  more,  it  represents  ail 
numbers  without  distinction.  As  soon  as  we  conceive  a  thing  divided 
into  equal  parts,  without  knowing  into  what  numbers  of  parts,  we  may 
call  it  a  or  x,  and  apply  to  it,  without  danger  of  eiTor,  every  alge- 
braical formula  in  the  books.  The  proposition,  2(«  -\-b)  =  2a-^  2b, 
is  a  ti-uth  coextensive  with  the  creation.  Since  then  algebraical 
truths  are  true  of  all  things  whatever,  and  not,  like  those  of  geometry, 
true  of  Hues  only  or  angles  only,  it  is  no  wonder  that  the  symbols 
should  not  excite  in  our  minds  ideas  of  any  things  in  particular. 
When  we  demonstrate  the  forty-seventh  proposition  of  Euclid,  it  is 
not  necessary  that  the  words  should  raise  in  us  an  image  of  all  right- 
angled  triangles,  but  only  of  some  one  right-angled  triangle :  so  in 
algebra  we  need  not,  under  the  symbol  a,  pictiire  to  ourselves  all 
things  whatever,  but  only  some  one  thing ;  why  not,  then,  the  letter 
itself]  The  mere  written  characters,  a,  b,  x,  ?/,  z,  serve  as  well  for 
representatives  of  Things  in  general,  as  any  more  complex  and 
apparently  more  concrete  conception.  That  we  are  conscious  of 
them  however  in  their  character  of  things,  and  not  of  mere  signs,  is 
evident  from  tlie  fact  that  our  whole  process  of  reasoning  is  carried  on 
by  predicating  of  them  the  properties  of  things.  In  resolving  an 
alo-ebraic  equation,  by  what  rules  do  we  proceed  ]  By  applying  at 
each  step  to  a,  b,  and  x,  the  proposition  that  equals  added  to  equals 
make  equals ;  that  equals  taken  from  equals  leave  equals ;  'and  other 
propositions  founded  upon  these  two.  These  are  not  properties  of 
language,  or  of  signs  as  such,  but  of  magnitudes,  which  is  as  much  as 
to  say,  of  all  things.  The  inferences,  therefore,  which  are  successively 
drawn,  are  inferences  conceniing  Things,  not  symbols ;  although  as 
any  Things  whatever  will  serve  the  turn,  there  is  no  necessity  for 
keeping  the  idea  of  the  Thing  at  all  distinct,  and  consequently  the 
process  of  thought  may,  in  this  case,  be  allowed  without  danger  to  do 
what  all  processes  of  thought,  when  they  have  been  performed  often, 
will  do  if  permitted,  namely,  to  become  entirely  mechanical.  Hence 
the  general  language  of  algebra  comes  to  be  used  familiarly  without 
exciting  ideas,  as  all  other  general  language  is  prone  to  do  from  mere 
habit,  though  in  no  other  case  than  this  can  it  be  done  with  complete 
safety.  But  when  we  look  back  to  see  from  whence  the  probative 
force  of  die  process  is  derived,  we  find  that  at  every  single  step, 
unless  we  suppose  ourselves  to  be  thinking  and  talking  of  the  things, 
and  not  the  mere  symbols,  the  evidence  fails. 

There  is  another  circumstance,  which,  still  more  than  that  which  we 
have  now  mentioned,  gives  plausibility  to  the  notion  that  the  proposi- 
tions of  arithmetic  and  algebra  are  merely  verbal.  This  is,  that  when 
considered  as  propositions  respecting  Things,  tliey  all  have  the  appear- 
ance of  being  identical  propositions.  The  assertion.  Two  and  one 
are  equal  to  three,  considered  as  an  assertion  respecting  objects,  as 
for  instance  "  Two  pebbles  and  one  pebble  are  equal  to  three  peb- 
bles," does  not  affirm  equality  between  two  collections  of  pebbles,  but 
absolute  identity.  It  affirms  that  if  we  put  one  pebble  to  two  pebbles, 
those  very  pebbles  are  three.  The  objects,  therefore,  being  the  very 
same,  and  the  mere  assertion  that  "  objects  are  themselves"  being  in- 
significant, it  seems  but  natural  to  consider  the  proposition,  Two  and 
one  are  equal  to  three,  as  asserting  mere  identity  of  signification  be- 
tvi'een  the  two  names. 


DEMONSTRATION,    AND    NECESSARY    TRUTHS.  167 

This,  however,  though  it  looks  so  plausible,  will  not  stand  examin- 
ation. The  expression,  "  two  pebbles  and  one  pebble,"  and  the  ex- 
pression, "  tlirce  pebbles,"  stand  indeed  for  the  same  aggregation  of 
objects,  but  they  by  no  means  stand  for  the  same  physical  fact.  They 
are  names  of  the  same  objects,  but  of  those  objects  in  two  diflerent 
stales :  though  they  <^('note  the  same  things,  their  fo«notation  is  differ- 
ent. Three  pebbles  in  two  separate  parcels,  and  three  pebbles  in 
one  parcel,  do  not  make  thu  same  impression  on  our  senses ;  and  the  as- 
sertion that  tlie  very  same  pebbles  may  by  an  alteration  of  place  and  by 
arrangement  be  made  to  pr<)duce  either  the  one  set  of  sensations  or  the 
other,  though  it  is  a  very  familiar  proposition,  is  not  an  identical  one. 
It  is  a  truth  kuo\\ni  to  us  by  early  and  constant  experience :  an  induc- 
tive trutli :  and  such  truths  are  the  foundation  of  the  science  of  Num- 
ber. The  fundamental  truths  of  that  science  all  rest  upon  the  evidence 
of  sense ;  they  are  proved  by  showing  to  our  eyes  and  our  fingers  that 
any  given  number  of  objects,  ten  balls  for  example,  may  by  separation 
and  rearrangement  exhibit  to  our  senses  all  the  different  sets  of  num- 
bers riie  sum  of  which  is  equal  to  ten.  All  the  improved  methods  of 
teaching  arithmetic  to  children  proceed  upon  a  knowledge  of  this  fact. 
All  who  wish  to  cany  the  child's  mind  along  with  tliem  in  learning 
arithmetic;  all  who  (as  Dr.  Biber  in  his  remarkable  Lectures  on  Edu- 
cation, expresses  it)  wish  to  teach  numbers,  and  not  mere  ciphers — now 
teach  it  through  the  evidence  of  the  senses,  in  the  manner  we  have 
described.* 

We  may,  if  we  please,  call  the  proposition  "  Three  is  two  and  one," 
a  definition  of  the  number  three,  and  assert  that  arithmetic,  as  it  has 
been  asserted  that  geometiy,  is  a  science  founded  upon  definitions.  But 
they  are  definitions  in  the  geometrical  sense,  not  the  logical ;  asseiting 
not  the  meaning  of  a  term  only,  but  along  with  it  an  observed  matter 
of  fact.  The  proposition,  "  A  circle  is  a  figure  bounded  by  aline  which 
has  all  its  points  equally  distant  from  a  point  within  it,"  is  called  the 
definition  of  a  circle;  but  the  proposition  from  which  so  many  conse- 
quences follow,  and  which  is  really  a  first  principle  of  geometry,  is, 
that  figures  answering  to  this  description  exist.  And  thus  we  may 
call,  "  Three  is  two  and  one,"  a  definition  of  three  ;  but  the  calcula- 
tions which  depend  upon  that  proposition  do  not  follow  fi-om  the  defi- 
nition itself,  but  from  an  arithmetical  theorem  presupposed  in  it,  namely, 
that  collections  of  objects  exist,  which  while  they  impress  the  senses 
thus,  ",",  may  be  separated  into  two  parts,  thus,  o  o  o.  This  propo- 
sition being  granted,  we  term  all  such  parcels  Threes,  after  which  the 
enunciation  of  the  above-mentioned  physical  fact  will  serve  also  for  a 
definition  of  the  word  Three. 

The  Science  of  Number  is  thus  no  exception  to  the  conclusion  we 
previously  annved  at,  that  the  ju'ocesses  even  of  deductive  sciences  are 
altogether  inductive,  and  that  their  first  principles  are  generalizations 

*  See,  for  illustrations  of  various  sorts,  Professor  Leslie's  Philosophy  of  Arithmetic ;  and 
see  also  two  of  the  most  efficient  books  ever  written  for  training  the  infant  intellect, 
Mr.  Horace  Grant's  Arithmetic  for  Young  Children,  and  his  Secotid  Utage  of  Arithmetic, 
both  published  by  the  Society  for  the  Diffusion  of  Useful  Knowledge. 

"Number,"  says  the  reviewer  of  Mr.  Whevvell,  already  cited,  "  we  cannot  help  regarding 
as  an  abstraction,  and  consequently  its  general  properties  or  its  axioms  to  be  of  necessity 
inductively  concluded  from  the  consideration  of  particular  cases.  And  surely  this  is  the 
way  in  which  children  do  acquire  their  knowledge  of  number,  and  in  which  they  learn  its 
axioms.  The  apples  and  the  marbles  are  put  in  requisition,  and  through  the  multitude  of 
gingerbread  nuts  their  ideas  acquire  clearness,  precision,  and  generality." 


168  REASONING, 

from  experience.  It  remains  to  be  examined  whether  this  science 
resembles  geometry  in  the  further  circumstance,  that  some  of  its  induc- 
tions are  not  exactly  true ;  and  that  the  peculiar  certainty  ascribed  to 
it,  on  account  of  which  its  propositions  are  called  Necessary  Truths,  is 
fictitious  and  hypothetical,  being  true  in  no  other  sense  than  that  those 
propositions  necessarily  follow  from  the  hypothesis  of  the  truth  of  prem- 
isses which  are  avowedly  mere  approximations  to  truth. 

§  3.  The  inductions  of  arithmetic  are  of  two  sorts  :  first,  those  which 
we  have  just  expounded,  such  as  One  and  one  are  two,  Two  and  one 
are  three,  &c.,  which  may  be  called  the  definitions  of  the  various 
numbers,  in  the  improper  or  geometrical  sense  of  the  word  Definition ; 
and  secondly,  the  two  following  axioms :  The  sums  of  equals  are  equal, 
The  differences  of  equals  are  equal.  These  two  are  sufficient ;  for  the 
corresponding  propositions  respecting  unequals  may  be  proved  from 
these,  by  the  process  well  known  to  mathematicians  under  the  name  of 
reductio  ad  ahsurdum. 

These  axioms,  and  likewise  the  so-called  definitions,  are,  as  already 
shown,  results  of  induction ;  true  of  all  objects  whatever,  and,  as  it  may 
seem,  exactly  true,  without  any  hypothetical  assumption  of  unqualified 
truth  where  an  approximation  to  it  is  all  that  exists.  The  conclusions, 
therefore,  it  will  naturally  be  inferred,  are  exactly  true,  and  the  science 
of  number  is  an  exception  to  other  demonstrative  sciences  in  this,  that 
the  absolute  certainty  which  is  predicable  of  its  demonstrations  is  inde- 
pendent of  all  hypothesis. 

On  more  accurate  investigation,  however,  it  will  be  found  that,  even 
in  this  case,  there  is  one  hypothetical  element  in  the  ratiocination.  In 
all  propositions  concerning  numbers,  a  condition  is  implied,  without 
which  none  of  them  would  be  true ;  and  that  condition  is  an  assump- 
tion which  maybe  false.  The  condition  is,  that  1  =  1;  that  all  the 
numbers  are  numbers  of  the  same  or  of  equal  units.  liet  this  be  doubt- 
ful, and  not  one  of  the  propositions  of  arithmetic  will  hold  true.  How 
can  we  know  that  one  pound  and  one  pound  make  two  pounds,  if  one 
of  the  pounds  may  be  troy,  and  the  other  avoirdupois  ]  They  may  not 
make  two  pounds  of  either,  or  of  any  weight.  How  can  we  know  that 
a  forty-horse  power  is  always  equal  to  itself,  unless  we  assume  that  all 
horses  are  of  equal  strength  %  It  is  certain  that  1  is  always  equal  in 
number  to  1 ;  and  where  the  inere  number  of  objects,  or  of  the  parts 
of  an  object,  without  supposing  them  to  be  equivalent  in  any  other 
respect,  is  all  that  is  material,  the  conclusions  of  aiithmetic,  so  far  as 
they  go  to  that  alone,  are  true  without  mixture  of  hypothesis.  There 
are  a  few  such  cases ;  as,  for  instance,  an  inquiry  into  the  amount  of 
population  of  any  country.  It  is  indifferent  to  that  inquiry  whether 
they  are  grown  people  or  children,  strong  or  weak,  tall  or  short ;  the 
only  thing  we  want  to  ascertain  is  their  number.  Bvit  whenever,  from 
equality  or  inequality  of  number,  equality  or  inequality  in  any  other 
respect  is  to  be  infen-ed,  arithmetic  carried  into  such  inquiries  becomes 
as  hypothetical  a  science  as  geometry.  All  units  must  be  assumed  to 
be  equal  in  that  other  respect ;  and  this  is  never  precisely  time,  for 
one  pound  weight  is  not  exactly  equal  to  another,  nor  one  mile's  length 
to  another;  a  nicer  balance,  or  more  accurate  measuring  instruments, 
would  always  detect  some  diflference. 

What  is  commonly  called  mathematical  certainty,  therefore,  which 


DEMONSTRATION,    AND   NECESSARY    TRUTHS.  1G9 

comprises  the  two-fold  conception  of  unconditional  truth  and  perfect 
accuracy,  is  not  an  attribute  of  all  mathematical  truths,  but  of  those 
only  which  relate  to  pure  Number,  as  distinguished  from  Quantity, 
in  the  more  enlarged  sense ;  and  only  so  long  as  we  abstain  fi-om  sup- 
posing that  the  numbers  are  a  precise  index  to  actual  quantities.  The 
certainty  usually  ascribed  to  the  conclusions  of  geometiy,  and  even  to 
those  of  mechanics,  is  nothing  whatever  but  certainty  -of  inference. 
We  can  have  full  assurance  of  particular  results  under  particular  sup- 
positions, but  we  cannot  have  the  same  assurance  that  these  suppositions 
are  accurately  true,  nor  that  they  include  all  the  data  which  may  exer- 
cise an  influence  over  the  result  in  any  given  instance. 

§  4.  It  appears,  therefore,  that  the  method  of  all  Deductive  Sciences 
is  hypothetical.  They  proceed  by  tracing  the  consequences  of  certain 
assumptions ;  leaving  for  separate  consideration  whether  the  assump- 
tions are  true  or  not,  and  if  not  pxactly  true,  whether  they  are  a  suffi- 
ciently near  approximation  to  the  ti-uth.  The  reason  is  obvious.  Since 
it  is  only  in  questions  of  pure  number  that  the  assumptions  are  exactly 
ti-ue,  and  even  there,  only  so  long  as  no  conclusions  except  purely  nu- 
merical ones  are  to  be  founded  upon  them  ;  it  must,  in  all  other  cases 
of  deductive  investigation,  form  a  part  of  the  inquiry,  to  detennine  how 
much  the  assumptions  want  of  being  exactly  true  in  the  case  in  hand. 
This  is  generally  a  matter  of  observation,  to  be  repeated  in  every  fresh 
case ;  or  if  it  has  to  be  settled  by  argument  instead  of  obsei-vation,  may  re- 
quii-e,  in  every  difterent  case,  different  evidence,  and  present  every  de- 
gi-ee  of  difficulty  from  the  lowest  to  the  highest.  But  the  other  part  of  the 
process — viz.,  to  determine  what  else  may  be  concluded  if  we  find,  and 
in  proportion  as  we  find,  the  assumptions  to  be  true — may  be  performed 
once  for  all,  and  the  results  held  ready  to  be  employed  as  the  occasions 
turn  up  for  use.  We  thus  do  all  beforehand  that  can  be  so  done,  and 
leave  the  least  possible  work  to  be  performed  when  cases  arise  and  press 
for  a  decision.  This  inquiry  into  the  inferences  which  can  be  dravni 
fi-om  assumptions,  is  what  properly  constitutes  Demonstrative  Science. 

It  is  of  course  quite  as  practicable  to  aiTive  at  new  conclusions  from 
facts  assumed,  as  from  facts  observed ;  from  fictitious,  as  from  real,  in- 
ductions. Deduction,  as  we  have  seen,  consists  of  a  series  of  inferences 
in  this  form  :  a  is  a  mark  of  h,  b  of  c,  c  of  d,  therefore  a  is  a  mark  of  d, 
which  last  may  be  a  truth  inaccessible  to  direct  observation.  In  like 
manner  it  is  allowable  to  say,  Suppose  tliat  a  were  a  mark  of  i,  h  of  c, 
and  cofd,a  would  be  a  mark  of  ^Z,  which  last  conclusion  was  not  thought 
of  by  those  who  laid  down  the  premisses.  A  system  of  propositions  as 
complicated  as  geometry  might  be  deduced  fi-om  assumptions  which  are 
false  ;  as  was  done  by  Ptolemy,  Des,cartes,  and  others,  in  their  attempts 
to  explain  synthetically  the  phenomena  of  the  solar  system,  on  the  sup- 
position that  the  apparent  motions  of  the  heavenly  bodies  were  the  real 
motions,  or  were  produced  in  some  way  more  or  less  different  fi-om  the 
true  one.  Sometimes  the  same  thing  is  knowingly  done,  for  the  pur- 
pose of  showing  the  falsity  of  the  assumption  ;  which  is  called  a  reduc- 
tio  ad  absurdum.  In  such  cases,  the  reasoning  is  as  follows :  a  is  a 
mark  ofb,  and  b  of  c  ;  now  if  c  were  also  a  mark  of  J,  a  would  be  a  mark 
of  d ;  but  d  is  known  to  be  a  mark  of  the  absence  of  a  ;  conso(iuently  a 
would  be  a  mark  of  its  own  absence,  which  is  a  contradiction ;  there- 
fore c  is  not  a  mark  of  d. 
Y 


170  REASONING. 

§  5.  It  has  even  been  held  by  some  philosophers,  that  all  ratiocina- 
tion rests  in  the  last  resort  upon  a  reductio  ad  abstirdum ;  since  the 
way  to  enforce  assent  to  it,  in  case  of  obscurity,  would  be  to  show  that 
if  the  conclusion  be  denied  we  must  deny  some  one  at  least  of  the 
premisses,  which,  as  they  are  all  supposed  true,  would  be  a  contradic- 
tion. And,  in  accordance  with  this,  many  have  thought  that  the  pecu- 
liar nature  of  the  e\adence  of  ratiocination  consisted  in  the  impossibility 
of  admitting  the  premisses  and  rejecting  the  conclusion  without  a  con- 
tradiction in  tei-ms.  This  theory,  however,  is  quite  inadmissible  as  an 
explanation  of  the  gi-ounds  on  which  ratiocination  itself  rests.  If  any 
one  denies  the  conclusion  notwithstanding  his  admission  of  the  prem- 
isses, he  is  not  involved  in  any  direct  and  express  contradiction  until  he 
is  compelled  to  deny  some  premiss ;  and  he  can  only  be  forced  to  do 
this  by  a  rcditctm  ad  ahsurdum,  that  is,  by  another  ratiocination  :  now, 
if  he  denies  the  validity  of  the  reasoning  process  itself,  he  can  no  more 
be  forced  to  assent  to  the  second  syllogism  than  to  the  first.  In  truth, 
therefore,  no  one  is  ever  forced  to  a  contradiction  in  terms  :  he  can 
only  be  forced  to  a  contradiction  (or  rather  an  infringement)  of  the 
fundamental  maxim  of  ratiocination,  namely,  that  whatever  has  a  mark, 
has  what  it  is  a  mark  of;  or  (in  the  case  of  universal  propositions), 
that  whatever  is  a  mark  of  a  thing,  is  a  mark  of  whatever  else  that 
thing  is  a  mark  of  For  in  the  case  of  every  con-ect  argument,  as  soon 
as  thrown  into  the  syllogistic  foiTn,  it  is  evident  without  the  aid  of  any 
other  syllogism,  that  he  who,  admitting  the  premisses,  fails  to  draw 
the  conclusion,  does  not  conform  to  the  above  axiom. 

Without  attaching  exaggerated  importance  to  the  distinction  now 
drawTi,  I  think  it  enables  us  to  characterize  in  a  more  accurate  manner 
than  is  usually  done,  the  nature  of  demonstrative  evidence  and  of  logi- 
cal necessity.  That  is  necessary,  fi-om  which  to  withhold  our  assent 
would  be  to  \'iolate  the  above  axiom.  And  since  the  axiom  can  only 
be  violated  by  assenting  to  premisses  and  rejecting  a  legitimate  con- 
clusion from  them,  nothing  is  necessary  except  the  connexion  between 
a  conclusion  and  premisses ;  of  which  doctrine,  the  whole  of  this  and 
the  preceding  chapter  are  submitted  as  the  proof. 

We  have  now  proceeded  as  far  in  the  theory  of  Deduction  as  we 
can  advance  in  the  present  stage  of  our  inquiry.  Any  further  insight 
into  the  subject  requires  that  the  foundation  shall  have  been  laid  of 
the  philosophic  theory  of  Induction  itself;  in  which  theory  that  of 
deduction,  as  a  mode  of  induction,  which  we  have  now  shown  it  to  be, 
■will  assume  spontaneously  the  place  which  belongs  to  it,  and  will  re- 
ceive its  share  of  whatever  light  may  be  thrown  upon  the  great  intel- 
lectual operation  of  which  it  forms  so  important  a  part. 

We  here,  therefore,  close  the  Second  Book.  The  theory  of  Induc- 
tion, in  the  most  comprehensive  sense  of  the  term,  will  form  the  sub- 
ject of  the  Third. 


BOOK  III. 

OF  INDUCTION. 


"  According  to  the  doctrine  now  stated,  the  highest,  or  rather  the  only  proper  object  of 
physics,  is  to  ascertain  those  estabhshed  conjunctions  of  successive  events,  which  consti- 
tute the  order  of  the  universe;  to  record  the  phenomena  which  it  exhibits  to  our  observa- 
tions, or  which  it  discloses  to  our  experiments ;  and  to  refer  these  phenomena  to  their  gen- 
eral laws."— D.  Stewart,  Elements  of  the  Philosophy  of  the  Human  Mind,  vol.  ii.,  chap.  iv. 
sect.  1. 

"  In  such  cases  the  inductive  and  deductive  methods  of  inquiry  may  be  said  to  go  hand 
in  hand,  the  one  verifying  the  conclusions  deduced  by  the  other;  and  the  combination  of 
experiment  and  theory,  which  may  thus  be  brought  to  bear  in  such  cases,  forms  an  engine 
of  discovery  infinitely  more  powerful  than  either  taken  separately.  This  state  of  any  de- 
partment of  science  is  perhaps  of  all  others  the  most  interesting,  and  that  which  promises 
the  most  to  research." — Sir  J.  Herschel,  Discourse  on  the  Study  of  Natural  Philosophy. 


CHAPTER  I. 

PRELIMINARY  OBSERVATIONS    ON    INDUCTION   IN    GENERAL. 

§  1.  The  portion  of  the  present  inquiry  upon  which  we  are  now 
about  to  enter,  may  be  considered  as  the  principal,  both  from  its  sur- 
passing in  intricacy  all  the  other  branches,  and  because  it  relates  to  a  pro- 
cess which  has  been  shown  in  the  preceding  Book  to  be  that  in  which 
the  Investigation  of  Nature  essentially  consists.  We  have  found  that 
all  Inference,  consequently  all  Proof,  and  all  discovery  of  truths  not 
self-evident,  consists  of  inductions,  and  the  interpretation  of  inductions  : 
that  all  our  knowledge,  not  intuitive,  comes  to  us  exclusively  from 
that  source.  What  Induction  is,  therefore,  and  what  conditions  render 
it  legitimate,  cannot  but  be  deemed  the  main  question  of  the  science  of 
logic — the  question  which  includes  all  others.  It  is,  however,  one 
which  professed  writers  on  logic  have  almost  entirely  passed  over. 
The  generalities  of  the  subject  have  not  been  altogether  neglected  by 
metaphysicians ;  but,  for  want  of  sufficient  acquaintance  with  the  pro- 
cesses by  which  science  has  actually  succeeded  in  establishing  general 
truths,  their  analysis  of  the  inductive  operation,  even  when  unexcep- 
tionable as  to  coiTectness,  has  not  been  specific  enough  to  be  made 
the  foundation  of  practical  rules,  which  might  be  for  induction  itself 
what  the  rules  of  the  syllogism  are  for  the  interpretation  of  induction : 
while  those  by  whom  physical  science  has  been  carried  to  its  present 
high  state  of  improvement — and  who,  to  arrive  at  a  complete  theory  of 
the  process,  needed  only  to  generalize,  and  adapt  to  all  varieties  of 
problems,  the  methods  which  they  themselves  employed  in  their  ha- 
bitual pursuits — never  until  very  lately  made  any  serious  attempt  to 
philosophize  on  the  subject,  nor  regarded  the  mode  in  which  they  ar- 
rived at  their  conclusions  as  deserving  of  study,  independently  of  the 
conclusions  themselves. 


172  INDUCTION. 

Although,  for  these  reasons,  there  is  not  yet  extant  a  body  of  Induc- 
tive Logic,  scientifically  constructed ;  the  materials  for  its  construction 
exist,  widely  scattered,  but  abundant :  and  the  selection  and  arrange- 
ment of  those  materials  is  a  task  with  which  intellects  of  the  highest 
order,  possessed  of  the  necessary  acqviirements,  have  at  length  consent- 
ed to  occupy  themselves.  Within  a  few  years  three  wa'iters,  profoundly 
versed  in  every  branch  of  physical  science,  and  not  unaccustomed  to 
carry  their  speculations  into  still  higher  regions  of  knowledge,  have 
made  attempts,  of  unequal  but  all  of  very  great  merit,  towards  the 
creation  of  a  Philosophy  of  Induction  :  Sir  John  Herschel,  in  his  Dis- 
course OH  the  Study  of  Natural  Philosophy  ;  Mr.  Whewell,  in  his  His- 
tory and  Philosophy  of  the  Inductive  Sciences;  and,  greatest  of  all, 
M.  Auguste  Comte,  in  his  Cours  de  Philosophic  Positive,  a  work  which 
only  requires  to  be  better  known,  to  place  its  author  in  the  very  high- 
est class  of  European  thinkers.  That  the  present  writer  does  not 
consider  any  of  these  philosophers,  or  even  all  of  them  together,  to  have 
entirely  accoinplished  this  important  work,  is  implied  in  his  attempting 
to  contribute  something  further  towards  its  achievement ;  but  with  his 
comparatively  imperfect  knowledge  of  the  various  physical  sciences, 
the  attempt  would  have  been  desperate  unless  the  materials  had 
been  brought  together,  and  had  undergone  a  partial  elaboration,  by 
their  more  competent  hands  ;  even  if  he  could  have  dispensed  with 
the  many  important  logical  ideas  and  principles,  for  the  first  sugges- 
tion of  which  he  has  been  indebted  to  one  or  other  of  those  writers. 

§  2.  For  the  pui-poses  of  the  present  inquiry.  Induction  may  be  de- 
fined, the  operation  of  discovering  and  proving  general  propositions. 
It  is  true  that  (as  already  shown)  the  process  of  indirectly  ascertaining  in- 
dividual facts,  is  as  truly  inductive  as  that  by  which  we  establish  general 
truths.  But  it  is  not  a  different  kind  of  induction ;  it  is  another  form  of  the 
very  same  process :  since,  on  the  one  hand,  generals  are  but  collec- 
tions of  particulars,  definite  in  kind  but  indefinite  in  number;  and  on  the 
other  hand,  whenever  the  evidence  which  we  derive  fi-om  observation 
of  known  cases  justifies  us  in  drawing  an  inference  respecting  even  one 
unknown  case,  we  should  on  the  same  evidence  be  justified  in  drawing 
a  similar  inference  with  respect  to  a  whole  class  of  cases.  The  infer- 
ence either  does  not  hold  at  all,  or  it  holds  in  all  cases  of  a  certain  de- 
scription ;  in  all  cases  which,  in  certain  definable  respects,  resemble 
those  we  have  observed. 

If  these  remarks  are  just ;  if  the  principles  and  rules  of  inference  are 
the  same  whether  we  infer  general  propositions  or  individual  facts ;  it 
follows  that  a  complete  logic  of  the  sciences  would  be  also  a  complete 
logic  of  practical  business  and  common  life.  Since  there  is  no  case  of 
legitimate  inference  from  experience,  in  which  the  conclusion  may  not 
legitimately  be  a  general  proposition  ;  an  analysis  of  the  process  by 
which  general  truths  are  arrived  at,  is  virtually  an  analysis  of  all  induc- 
tion whatever.  Whether  we  are  inquiring  into  a  scientific  principle  or 
into  an  individual  fact,  and  whether  we  proceed  by  experiment  or  by  ra- 
tiocination, every  step  in  the  train  of  inferences  is  essentially  inductive, 
and  the  legitimacy  of  the  induction  depends  in  both  cases  upon  the  same 
conditions. 

True  it  is  that  in  the  case  of  the  practical  inquirer,  who  is  endeavor- 
ing to  ascertain  facts  not  for  the  purposes  of  science  but  for  those  of 


INDUCTION  IN  GENERAL.  173 

business,  such  for  instance  as  the  advocate  or  the  judge,  the  chief  diffi- 
culty is  one  in  which  the  principles  of  induction  will  aUbrd  him  no  as- 
sistance. It  lies  not  in  mahing  his  inductions  but  in  the  selection  of 
them ;  in  choosing  from  among  all  general  propositions  ascertained  to 
be  true,  those  which  furnish  him  with  marks  by  which  he  may  trace 
whether  the  given  subject  possesses  or  not  the  predicate  in  question. 
In  arguing  a  doubtful  question  of  fact  before  a  jury,  the  general  prop- 
ositions or  principles  to  which  the  advocate  appeals  are  mostly,  in  them- 
selves, sufficiently  ti-ite,  and  assented  to  as  soon  as  stated  :  his  skill  lies 
in  bringing  his  case  under  those  propositions  or  princij)les  ;  in  calling 
to  mind  such  of  the  known  or  recognized  maxims  of  probability  as  ad- 
mit of  application  to  the  case  in  hand,  and  selecting  from  among  them 
those  best  adapted  to  his  object.  Success  is  here  dependent  upon  nat- 
ural or  acquired  sagacity,  aided  by  knowledge  of  the  particular  subject, 
and  of  subjects  allied  with  it.  Invention,  though  it  can  be  cultivated, 
cannot  be  reduced  to  rule  ;  there  is  no  science  which  will  enable  a  man 
to  bethink  himself  of  that  which  will  suit  his  purpose. 

But  when  he  has  thought  of  something,  science  can  tell  him  whether 
that  which  he  has  thought  of  will  suit  his  purpose  or  not.  The  inquirer 
or  arguer  must  be  guided  by  his  own  knowledge  and  sagacity  in  his 
choice  of  the  inductions  out  of  which  he  will  construct  his  argument. 
But  the  validity  of  the  argument  when  constructed,  depends  upon 
principles  and  must  be  tried  by  tests  which  are  the  same  for  all  de- 
scriptions of  inquiries,  whether  the  result  be  to  give  A  an  estate,  or  to 
enrich  science  with  a  new  general  truth.  In  the  one  case  and  in  the 
other,  the  senses,  or  testimony,  must  decide  on  the  individual  facts ; 
the  rules  of  the  syllogism  will  determine  whether,  those  facts  being 
supposed  correct,  the  case  really  falls  within  the  formulas  of  the  differ- 
ent inductions  under  which  it  has  been  successively  brought ;  and  finally, 
the  legitimacy  of  the  inductions  themselves  must  be  decided  by  other 
rules,  and  these  it  is  now  our  purpose  to  investigate.  If  this  third  part 
of  the  operation  be,  in  many  of  the  questions  of  practical  life,  not  the 
most,  but  the  least  arduous  portion  of  it,  we  have  seen  that  this  is  also 
the  case  in  some  great  departTnents  of  the  field  of  science  ;  in  all  those 
which  are  principally  deductive,  and  most  of  all  in  mathematics  ;  where 
the  inductions  themselves  are  few  in  number,  and  so  obvious  and  ele- 
mentary, that  they  seem  to  stand  in  no  need  of  the  evidence  of  experi- 
ence, while  to  combine  them  so  as  to  prove  a  given  theorem  or  solve  a 
problem,  may  call  for  the  highest  powers  of  invention  and  contrivance 
with  which  our  species  is  gifted. 

If  the  identity  of  the  logical  processes  which  prove  particular  facts 
and  those  which  establish  general  scientific  ti'uths,  required  any  addi- 
tional confii-mation,  it  would  be  sufficient  to  consider,  that  in  many 
branches  of  science  single  facts  have  to  be  proved,  as  well  as  princi- 
ples ;  facts  as  completely  individual  as  any  that  are  debated  in  a  court 
of  justice ;  but  which  are  proved  in  the  same  manner  as  the  other 
truths  of  the  science,  and  without  disturbing  in  any  degree  the  homo- 
geneity of  its  method.  A  remarkable  examjile  of  this  is  afforded  by 
astronomy.  The  individual  facts  upon  which  that  science  gi'ounds 
its  most  important  deductions,  sUch  facts  as  the  magnitudes  of  the 
bodies  of  the  solar  system,  their  distances  fi'om  one  another,  the  figure 
of  the  earth,  and  its  rotation,  are  scarcely  any  of  them  accessible  to 
our  means  of  direct  observation :  they  are  proved  indirectly,  by  the 


174  IXDUCTIOX. 

aid  of  inductions  founded  on  other  facts  v.hicli  we  can  more  easily 
reach.  For  example,  the  distance  of  the  moon  from  the  earth  was 
determined  by  a  very  circuitous  process.  The  share  which  direct 
observation  had  in  the  work  consisted  in  ascertaining,  at  one  and  the 
same  instant,  the  zenith  distances  of  the  moon,  as  seen  from  two 
points  very  remote  from  one  another  on  the  earth's  surface.  The 
ascertainment  of  these  angular  distances  ascertained  their  supple- 
ments ;  and  since  the  angle  at  the  earth's  centre  subtended  by  the 
distance  between  the  two  places  of  observation  was  deducible  by 
spherical  trigonometry  from  the  latitude  and  longitude  of  those  places, 
the  angle  at  the  moon  subtended  by  the  same  line  became  the  fourth 
angle  of  a  quadrilateral  of  which  the  other  three  angles  were  known. 
The  four  angles  being  thus  ascertained,  and  two  sides  of  the  quadri- 
lateral being  radii  of  the  earth ;  the  two  remaining  sides  and  the  diag- 
onal, or  in  other  words,  the  moon's  distance  from  the  two  places  of 
observation  and  from  the  centre  of  the  eaith,  could  be  ascertained,  at 
least  in  terms  of  the  earth's  radius,  fi'om  elementary  theorems  of  geom- 
etry. At  each  step  in  this  demonsti'ation  we  take  in  a  new  induction, 
represented,  in  the  aggregate  of  its  results,  by  a  general  proposition. 

Not  only  is  the  process  by  which  an  individual  astronomical  fact 
was  thus  ascertained,  exactly  similar  to  those  by  which  the  same 
science  establishes  its  general  truths,  but  moreover  (as  we  have  shown 
to  be  the  case  in  all  legitimate  reasoning)  a  general  proposition  might 
have  been  concluded  instead  of  a  single  fact.  In  strictness,  indeed, 
the  result  of  the  reasoning  is  a  general  proposition ;  a  theorem  re- 
specting the  distance,  not  of  the  moon  in  particular,  but  of  ani/  inac- 
•cessible  object ;  showing  in  what  relation  that  distance  stands  to  certain 
other  quantities.  And  although  the  moon  is  almost  the  only  heavenly 
body  the  distance  of  which  from  the  earth  can  really  be  thus  ascer- 
tained, this  is  merely  owing  to  the  accidental  circumstances  of  the 
other  heavenly  bodies,  which  render  them  incapable  of  affording  such 
data  as  the  application  of  the  theorem  requires ;  for  the  theorem  itself 
is  as  true  of  them  as  it  is  of  the  moon. 

We  shall  fall  into  no  error,  then,  if  in  treating  of  Induction,  we  limit 
our  attention  to  the  establishment  of  general  propositions.  The  prin- 
ciples and  rules  of  Induction,  as  directed  to  this  end,  are  the  principles 
and  rules  of  all  Induction;  and  the  logic  of  Science  is  the  universal 
Logic,  applicable  to  all  inquiries  in  which  man  can  engage,  and  the 
test  of  all  the  conclusions  at  which  he  can  anive  by  inference. 


CHAPTER  II. 

OF   INDUCTIONS  I>tPROPERLY  SO   CALLED. 

§  1.  Induction,  then,  is  that  operation  of  the  mind,  by  which  v^e  in- 
fer that  what  we  know  to  be  true  in  a  particular  case  or  cases,  ^\all  be 
?,rue  in  all  cases  which  resemble  the  former  in  certain  assignable 
respects.  In  other  words.  Induction  is  the  process  by  which  we  con- 
dude  that  what  is  tiiie  of  certain  individuals  of  a  class  is  tnie  of  the 


INDUCTIONS    IMPROPEULY    SO    CALLED.  175 

whole  class,  or  that  what  is  true  at  certain  times  will  be  true  under 
similar  circumstances  at  all  times. 

This  definition  excludes  from  the  meaning  of  the  term  Induction, 
various  logical  operations,  to  which  it  is  not  unusual  to  apply  that 
name. 

Induction,  as  above  defined,  is  a  process  of  inference ;  it  px'oceeds 
from  the  known  to  the  unknown  ;  and  any  operation  involving  no  in- 
ference, any  process  in  which  what  seems  the  conclusion  is  no  wider 
than  the  premisses  from  which  it  is  drawn,  does  not  fall  within  the 
meaning  of  the  term.  Yet  in  the  common  books  of  Logic  we  find 
this  laid  down  as  the  most  perfect,  indeed  the  only  quite  perfect,  form 
of  induction.  In  those  books,  every  process  which  sets  out  from  a 
less  general  and  terminates  in  a  more  general  expression — which  ad- 
mits of  being  stated  in  the  form,  "  This  and  that  A  are  B,  therefore 
every  A  is  B" — is  called  an  induction,  whether  anything  be  really 
concluded  or  not ;  and  the  induction  is  asserted  to  be  not  perfect,  un- 
less every  single  individual  of  the  class  A  is  included  in  the  antecedent, 
or  premiss  :  that  is,  unless  what  we  affirm  of  the  class,  has  already 
been  ascertained  to  be  true  of  every  individual  in  it,  so  that  the 
nominal  conclusion  is  not  really  a  conclusion,  but  a  mere  reassertion 
of  the  premisses.  If  we  were  to  say.  All  the  planets  shine  by  the 
sun's  light,  from  observation  of  each  separate  planet,  or  All  the 
Apostles  were  Jews,  .because  this  is  ti'ue  of  Peter,  Paul,  John,  and 
eveiy  other  apostle — these,  and  such  as  these,  would,  in  the  phrase- 
ology in  question,  be  called  pez-fect,  and  the  only  perfect,  Inductions. 
This,  however,  is  a  totally  different  kind  of  induction  from  ours ;  it  is 
no  inference  from  facts  known  to  facts  unknown,  but  a  mere  short- 
hand registration  of  facts  known.  The  two  simulated  arguments, 
wlilch  we  have  quoted,  are  not  generalizations ;  the  propositions  pur- 
porting to  be  conclusions  from  them,  are  not  really  general  proposi- 
tions. A  general  proposition  is  one  in  which  the  predicate  is  affirmed 
or  denied  of  an  unlimited  number  of  individuals  ;  namely,  all,  whether 
few  or  many,  existing  or  capable  of  existing,  which  possess  the  prop- 
erties connoted  by  the  subject  of  tlie  proposition.  "AH  men  are  mor- 
tal" does  not  mean  all  now  living,  but  all  men  past,  present,  and  to 
come.  ^Vhen  the  signification  of  the  term  is  limited  so  as  to  render  it 
a  name  not  for  any  and  every  individual  falling  under  a  certain  gen- 
eral description,  but  only  for  each  of  a  number  of  individuals  desig- 
nated as  such,  and  as  it  were  counted  off  individually,  the  proposition, 
though  it  may  be  general  in  its  language,  is  no  general  proposition, 
but  merely  that  number  of  singular  propositions,  written  in  an 
abridged  character.  The  operation  may  be  very  useful,  as  most 
forms  of  abridged  notation  are  ;  but  it  is  no  pait  of  the  investigation 
of  ti-uth,  though  often  bearing  an  important  part  in  the  preparation  of 
the  materials  for  that  investigation. 

§  2.  A  second  process  which  requires  to  be  distinguished  from 
Induction,  is  one  to  which  matliematicians  sometimes  give  that  name : 
and  which  so  far  resembles  Induction  properly  so  called,  that  the 
propositions  it  leads  to  are  really  general  propositions.  For  example, 
when  we  have  proved,  with  respect  to  the  circle,  that  a  straight  line 
caimot  meet  it  in  more  than  two  points,  and  when  the  same  tiling  has 
been  successively  proved  of  the  ellipse,  the  parabola,  and  the  hyj>cr- 


176  INDUCTION. 

bola,  it  may  be  laid  down. as  an  universal  property  of  the  sections  of 
the  cone.  In  this  example  there  is  no  induction,  because  there  is  no 
inference :  the  conclusion  is  a  mere  summing  up  of  what  was  asserted 
in  the  various  propositions  from  which  it  is  drawn.  A  case  somewhat, 
thouo-h  not  altogether,  similar,  is  the  proof  of  a  geometrical  theorem 
by  means  of  a  diagram.  Whether  the  diagram  be  on  paper  or  only 
in  the  imagination,  the  demonstration  (as  we  formerly  observed*)  does 
not  prove  directly  the  general  theorem ;  it  proves  only  that  the  con- 
clusion, which  the  theorem  asserts  generally,  is  true  of  the  particular 
ti-iangle  or  circle  exhibited  in  the  diagram  :  but  since  we  perceive  that 
in  the  same  way  in  which  we  have  proved  it  of  that  circle,  it  might 
also  be  proved  of  any  other  circle,  we  gather  up  into  one  general 
expression  all  the  singular  propositions  susceptible  of  being  thus 
proved,  and  embody  them  in  an  universal  jjrojDosition.  Having  shown 
that  the  three  angles  of  the  triangle  ABC  are  together  equal  to  two 
right  angles,  we  conclude  that  this  is  true  of  every  other  triangle,  not 
because  it  is  true  of  A  B  C,  but  for  the  same  reason  which  proved  it 
to  be  true  of  A  B  C.  If  this  were  to  be  called  Induction,  an  appro- 
priate name  for  it  would  be,  Induction  by  parity  of  reasoning.  But 
the  term  cannot  properly  belong  to  it ;  the  characteristic  quality  of 
Induction  is  wanting,  since  the  truth  obtained,  though  really  general, 
is  not  believed  on  the  evidence  of  particular  instances.  We  do  not 
conclude  that  all  triangles  have  the  property  because  some  triangles 
have,  but  from  the  ulterior  demonstrative  evidence  which  was  the 
gi'ound  of  our  conviction  in  the  particular  instances. 

There  are  nevertheless,  in  mathematics,  some  examples  of  so-called 
induction,  in  which  the  conclusion  does  bear  the  appearance  of  a 
generalization  grounded  upon  some  of  the  particular  cases  included 
in  it.  A  mathematician,  when  he  has  calculated  a  sufficient  number 
of  the  terms  of  an  algebraical  or  arithmetical  series  to  have  ascer- 
tained what  is  called  the  Icnv  of  the  series,  does  not  hesitate  to  fill  up 
any  number  of  the  succeeding  terms  without  repeating  the  calculations. 
But  I  apprehend  he  only  does  so  when  it  is  apparent  fi-om  a  priori 
considerations  (which  might  be  exhibited  in  the  form  of  demonstration) 
that  the  mode  of  formation  of  the  subsequent  terms,  each  from  that 
which  preceded  it,  must  be  similar  to  the  fonnation  of  the  terms  which 
have  been  already  calculated.  And  when  the  attempt  has  been 
hazarded  without  the  sanction  of  such  general  considerations,  there 
are  instances  upon  record  in  which  it  has  led  to  false  results. 

It  is  said  that  Newton  discovered  the  binomial  theorem  by  induc- 
tion ;  by  raising  a  binomial  successively  to  a  certain  number  of  powers, 
and  comparing  those  powers  with  one  another  until  he  detected  the 
relation  in  which  the  algebraic  foi-mula  of  each  power  stands  to  the 
exponent  of  that  power,  and  to  the  two  terms  of  the  binomial.  The 
fact  is  not  improbable  :  but  a  mind  like  Newton's,  which  seemed  to 
aiTive  per  saltuvi  at  principles  and  conclusions  that  ordinary  mathe- 
maticians only  reached  by  a  succession  of  steps,  certainly  could  not 
have  performed  the  comparison  in  question  without  being  led  by  it  to 
the  a  priori  ground  of  the  law ;  since  any  one  who  understands  suf- 
ficiently the  nature  of  multiplication  to  venture  upon  multiplying 
several  lines  of  figures  or  symbols  at  one  operation,  cannot  but  perceive 

*  Supra,  p.  127,  128. 


INDUCTIONS    IMl'KOrERLY    SO    CALLED.  177 

that  in  ra,isina-  a  binomial  to  a  jiower,  the  co^fficieiits  must  dcpciul 
upon  the  laws  of  permutation  and  lombination :  and  as  soon  as  this  is 
recognized,  the  theorem  is  demonstrated.  Indeed,  wheii  once  it  was 
seen  that  the  law  j)revailed  in  a  few  of  the  low^  powers,  its  identity 
with  the  law  of  permutation  would  at  once  suggest  the  considerations 
which  prove  it  to  olrtain  universally.  Even,  therefore,  such  cases  as 
these,  are  but  examples  of  what  I  have  called  induc-tion  by  parity  of 
reasoning,  that  is,  not  really  induction,  because  iu)t  involving  any  infer- 
ence of  a  general  proposition  from  particular  instances.* 

§  3.  There  remains  a  third  improper  use  of  the  term  Induction, 
which  it  is  of  real  importance  to  clear  up,  because  the  theory  of 
induction  has  been,  to  no  ordinai-y  degree,  confused  by  it,  and  because 
the  confusion  is  exemplified  in,  the  most  recent  and  most  elaborate 
treatise  on  the  inductive  philosophy  which  exists  in  our  language. 
The  error  in  question  is  that  of  confounding  a  mere  description  of  a 
set  of  observed  phenomena,  with  an  induction  from  them. 

Suppose  that  a  phenomenon  consists  of  parts,  and  that  these  parts 
are  only  capable  of  being  obser\"«d  separately,  aiul  as  it  were  piece- 
meal. Wlien  the  observations  have  been  inade,  there  is  a  convenience 
.  (amounting  for  many  purposes  to  a  necessity)  in  obtaining  a  represen- 
tation of  the  phenomenon  as  a  whole,  by  combining,  or,  as  we  may 
say,  piecing  these  detached  fragments  together.  A  navigator  sailing 
in  the  midst  of  the  ocean  discovers  land  :  he  cannot  at  first,  or  by  any 
one  observation,  determine  whether  it  is  a  continent  or  an  island  ;  but 
he  coasts  along  it,  and  after  a  few  days,  finds  himself  to  have  sailed 
completely  round  it :  he  then  pronounces  it  an  island.  Now  there 
was  no  particular  time  or  place  of  observation  at  which  he  could  per- 
ceive that  this  land  was  entirely  suiTounded  by  water :  he  ascertained 
the  fact  by  a  succession  of  partial  observations,  and  then  selected  a 
general  expression  which  summed  up  in  two  or  three  words  the  whole 
of  what  he  so  observed.  But  is  there  anything  of  the  nature  of  an 
induction  in  this  process  ?  Did  he  infer  anything  that  had  not  been 
observed,  from  something  else  which  had  I  Certainly  not.  That  the 
land  in  question  is  an  island,  is  not  an  inference  fi-om  the  partial  facts 
which  the  navigator  saw  in  the  course  of  his  circumnavigation ;  it  is 
the  facts  themselves  ;  it  is  a  summary  of  those  facts  ;  the  description  of 
a  complex  fact,  to  which  those  simpler  ones  are  as  the  parts  of  a  whole. 

Now  there  is  no  difference  in  kind  between  this  simple  operation, 
and  that  by  which  Kepler  ascertained  the  nature  of  the  planetary 
orbits  :  and  Kepler's  operation,  all  at  least  that  was  characteristic  in 
it,  was  not  more  an  inductive  act  than  that  (jf  our  supposed  navigator. 

The  object  of  Kepler  was  to  determine  the  real  path  described  by 
each  of  the  planets,  or  let  us  say  the  planet  Mars  (for  it  was  of  that 
body  that  he  first  established  two  of  the  three  gi-eat  astronomical 
truths  which  bear  his  name).  To  do  this  there  was  no  other  mode 
than  that  of  direct  obsei-v'atron :  and  all  which  observation  could  do 
was  to  ascertain  a  great  number  of  the  successive  places  of  the  planet ; 
or  rather,  of  its  apparent  places.  That  the  planet  occupied  success- 
ively all  these  positions,  or  at  all  events,  positions  which  produced  the 

*  I  am  happy  to  be  able  to  refer,  in  confirmation  of  this  view  of  what  is  called  induction 
in  mathematics,  to  the  highest  English  authority  on  the  philosophy  of  algebra,  Mr.  Pea- 
cock.    See  pp.  107-8  of  liis  profound  Treatise  on  Algebra. 

z 


278  INDUCTION. 


same 


impressions  on  riie  eye,  and  that  it  passed  from  one  of  these  to 
another  insensibly,  and  without  any  apparent  breach  of  continuity  ; 
thus  much  the  senses,  with  the  aid  of  the  proper  instruments,  could 
ascertain.  What  Kepler  did  more  than  this,  was  to  find  what  sort  of 
a  curve  these  different  points  would  make,  supposing  them  to  be  all 
ioined  together.  He  expressed  the  whole  series  of  the  observed 
places  of  Mars  by  what  Mr.  Whewell  calls  the  general  conception  of 
an  ellipse.  This  operation  was  far  fi-om  being  as  easy  as  that  of  the 
navio-ator  who  expressed  the  series  of  his  observations  on  successive 
points  of  the  coast  by  the  general  conception  of  an  island.  But  it  is 
the  very  same  sort  of  operation  ;  and  if  the  one  is  not  an  induction  but 
a  description,  this  must  also  be  true  of  the  other. 

To  avoid  misapprehension,  we  must  remark  that  Kepler,  in  one 
respect,  performed  a  real  act  of  induction;  namely,  in  concluding  that 
because  the  observed  places  of  Mars  were  correctly  represented  by 
points  in  an  imaginary  ellipse,  therefore  Mars  would  continue^  to  re- 
volve in  that  same  ellipse  ;  and  even  in  concluding  that  the  position  of 
the  planet  during  the  time  which  intervened  between  two  observa- 
tions, must  have  coincided  with  the  intermediate  points  of  the  curve. 
But  this  really  inductive  operation  requires  to  be  carefully  distin- 
guished from  the  mere  act  of  bringing  the  facts  actually  observed 
under  a  o-eneral  description.  So  distinct  are  these  two  operations, 
that  the  one  might  have  been  performed  without  the  other.  Men 
mio-ht  and  did  make  correct  indvictions  concerning  the  heavenly  mo- 
tions, before  they  had  obtained  correct  general  descriptions  of  them. 
It  was  known  that  the  planets  always  moved  in  the  same  paths,  long 
before  it  had  been  ascertained  that  those  paths  were  ellipses.  Men 
early  remarked  that  the  same  set  of  apparent  positions  returned  pe- 
riodically. When  they  obtained  a  new  description  of  the  phenomenon, 
they  did  not  necessarily  make  any  further  induction,  nor  (which  is  the 
true  test  of  a  new  general  ti'Uth)  add  anything  to  the  power  of  predic- 
tion which  they  already 


§  4.  The  descriptive  operation  which  enables  a  number  of  details  to 
be  summed  up  in  a  single  proposition,  Mr.  "Whewell,  by  an  aptly- 
chosen  expression,  has  termed  the  Colligation  of  Facts.*  In  most  of 
his  observations  concerning  that  mental  process  I  fully  agree,  and 
would  gladly  transfer  all  that  portion  of  his  book  into  my  own  pages, 
I  only  think  him  mistaken  in  setting  up  this  kind  of  operation,  which 
according  to  the  old  and  received  meaning  of  the  term  is  not  induction 
at  all,  as  the  type  of  induction  generally;  a,nd  laying  down,  throughout 
his  work,  as  principles  of  induction,  the  principles  of  mere  colligation. 

Mr.  Whewell  maintains  that  the  general  proposition  which  binds 
to"-ether  the  particular  facts  and  makes  them,  as  it  were,  one  fact,  is 
not  the  mere  sum  of  those  facts,  but  something  more,  since  there  is 
introduced  a  conception  of  the  mind,  which  did  not  exist  in  the  facts 
themselves.  "  The  particular  facts,"  says  he,t  "  are  not  merely  brought 
to"-ether,  but  there  is  a  new  element  added  to  the  combination  by  the 
ve!ry  act  of  thought  by  which  they  are  combined.  . .  .When  the  Greelvs, 
after  long  observing  the  motions  of  the  planets,  saw  that  these  motions 
might  be  rightly  considered  as  produced  by  the  motion  of  one  wheel 

•  Philosophy  of  the  Inductive  Sciences,  ii.,  213,  214.  t  Ibid. 


IXDUCTIONS    IMPROrERLY    SO   CALLED.  179 

revolving  in  tlio  inside  of  anollier  wheel,  these  wheels  were  creations 
of  their  minds,  added  to  the  facts  which  tliey  perceived  by  sense. 
And  even  if  the  wheels  were  no  longer  supposed  to  be  material,  but 
were  reduced  to  mere  geometrical  spheres  or  circles,  they  were  not 
the  less  products  of  the  mind  alone — something  additional  to  the  facts 
observed.  The  same  is  the  case  in  all  other  discoveries.  The  facts 
are  known,  but  they  are  insulated  and  unconnected,  till  the  discoverer 
supplies  from  his  own  store  a  principle  of  connexion.  The  pearls  are 
there,  but  they  will  not  hang  together  till  some  one  provides  the  string." 

That  a  conception  of  the  mind  is  introduced  is  indeed  most  certain, 
and  Mr.  Whewell  has  rightly  stated  elsewhere,  that  to  hit  upon  the 
right  conception  is  often  a  far  more  difficult,  and  more  meritorious 
achievement,  than  to  prove  its  applicability  when  obtained.  But  a 
conception  implies,  and  coiTesponds  to,  something  conceived ;  and 
although  the  conception  itself  is  not  in  the  facts,  but  in  our  mind,  it 
must  be  a  conception  of  something  which  really  is  in  the  facts,  some 
property  which  they  actually  possess,  and  which  they  would  manifest 
to  oar  senses,  if  our  senses  were  able  to  take  cognizance  of  them.  If, 
for  instance,  the  planet  left  behind  it  in  space  a  visible  track,  and  if  the 
observer  were  in  a  fixed  position  at  such  a  distance  above  the  plane  of 
the  orbit  as  would  enable  him  to  see  the  whole  of  it  at  once,  he  would 
see  it  to  be  an  ellipse  ;  and  if  gifted  with  appropriate,  instruments,  and 
powers  of  locomotion,  he  could  prove  it  to  be  such  by  measuring  its 
different  dimensions.  These  things  are  indeed  impossible  to  us,  but 
not  impossible  in  themselves  j  if  they  were  so,  Kepler's  law  could  not 
be  true. 

Subject  to  the  indispensable  condition  which  has  just  been  stated,  I 
cannot  perceive  that  the  part  which  conceptions  have  in  the  operation 
of  studying  facts,  has  ever  been  overlooked  or  undefvalued  as  Mr.  Whe- 
well supposes  it  has.  No  one  ever  disputed  that  in  order  to  reason 
about  anything  we  must  have  a  conception  of  it;  or  that  when  we 
include  a  multitude  of  things  under  a  general  expression,  there  is 
implied  in  the  expression  a  conception  of  something  common  to  those 
things.  But  it  by  no  means  follows  that  the  conception  is  necessarily 
pre-existent,  or  constructed  by  the  mind  out  of  its  own  materials.  If 
the  facts  are  rightly  classed  under  the  conception,  it  is  because  there 
is  in  the  facts  themselves  something  of  which  the  conception  is  itself  a 
copy ;  and  which  if  we  cannot  directly  perceive,  it  is  because  of  the 
litnitcd  power  of  our  organs,  and  not  because  the  thing  itself  is  not 
there.  The  conception  itself  is  often  obtained  by  abstraction  from  the 
very  facts  which,  in  Mr.  Whewell's  language,  it  is  afterwards  called  in 
to  coimect.  This,  Mr.  Whewell  himself  admits,  when  he  observes, 
(which  he  does  on  several  occasions,)  how  great  a  service  would  be  ren- 
dered to  the  science  of  physiology  by  the  philosopher  "  who  should 
establish  a  2:)recise,  tenable,  and  consistent  conception  of  life."*  Such 
a  conception  can  only  be  abstracted  from  the  phenomena  of  life  itself; 
from  the  very  facts  which  it  is  put  in  requisition  to  connect.  In  other 
cases  (no  doubt)  instead  of  collecting  the  ctjnception  from  the  very 
phenomena  which  we  are  attempting  to  colligate,  we  selec't  it  from 
among  those  which  have  been,  jireviously  collected  by  abstraction  fiom 
other  facts.     In  the  instance  of  Kepler's  laws,  the  latter  was  the  case. 

*  Philosophi/  of  the  Inductive  Sciences,  vol  ii.,  p.  173. 


180  INDUCTION. 

The  facts  being  out  of  the  reach  of  being  observed,  in  any  such  man- 
ner as  would  have  enabled  the  senses  to  identify  directly  the  path  of 
the  planet,  the  conception  requisite  for  framing  a  general  description 
of  that  path  could  not  be  collected  by  abstraction  from  the  observations 
themselves ;  the  mind  had  to  supply  hypothetically,  from  among  the 
conceptions  it  had  obtained  from  other  portions  of  its  experience,  some 
one  which  would  correctly  represent  the  series  of  the  observed  facts. 
It  had  to  frame  a  supposition  respecting  the  general  course  of  the  phe- 
nomenon, and  ask  itself.  If  this  be  the  general  description,  what  will 
the  details  be'?  and  then  compare  these  with  the  details  actually 
observed.  If  they  agreed,  the  hypothesis  would  serve  for  a  descrip- 
tion of  the  phenomenon :  if  not,  it  was  necessarily  abandoned,  and 
another  tried.  It  is  such  a  case  as  this  which  gives  color  to  the  doc- 
trine that  the  mind,  in  framing  the  descriptions,  adds  something  of  its 
own  which  it  does  not  find  in  the  facts. 

Yet  it  is  a  fact,  surely,  that  the  planet  does  describe  an  ellipse ;  and 
a  fact  which  we  could  see,  if  we  had  adequate  visual  organs  and  a 
suitable  position.  Not  having  these  advantages,  but  possessing  the 
concejjtion  of  an  ellipse,  or  (to  express  the  meaning  in  less  technical 
language)  knowing  what  an  ellipse  was,  Kepler  tried  whether  the  ob- 
served places  of  the  planet  were  consistent  with  such  a  path.  He 
found  they  were  so ;  and  he,  consequently,  asserted  as  a  fact  that  the 
planet  moved  in  an  ellipse.  But  this  fact,  which  Kepler  did  not  add 
to,  but  found  in,  the  motions  of  the  planet,  namely,  that  it  occupied  in 
succession  the  various  points  in  the  circumference  of  a  given  ellipse, 
was  the  very  fact,  the  separate  parts  of  which  had  been  separately  ob- 
served ;  it  was  the  sum  of  the  different  observations.  It  superadded 
nothing  to  the  particular  facts  which  it  served  to  bind  together:  ex- 
cept, indeed,  the  knowledge  that  a  resemblance  existed  between  the 
planetary  oi'bit  and  other  ellipses  ;  an  accession  the  nature  and  amount 
of  which  will  be  fully  considered  hereafter.* 

Having  stated  this  fundamental  difference  between  my  views  and 
those  of  Mr.  Whewell,  I  must  add,  that  his  account  of  the  manner  in 
which  a  conception  is  selected,  suitable  to  express  the  facts,  appears 
to  me  perfectly- just.  The  experience  of  all  thinkers  will,  I  believe, 
testify  that  the  process  is  tentative ;  that  it  consists  of  a  succession  of 
guesses ;  many  being  rejected,  until  one  at  last  occurs  fit  to  be  chosen. 
We  know  from  Kepler  himself  that  before  hitting  upon  the  "  concep- 
tion" of  an  ellipse,  he  tried  nineteen  other  imaginaiy  paths,  which, 
finding  them  inconsistent  with  the  observations,  he  was  obliged  to  re- 
ject. But  as  Mr.  Whewell  truly  says,  the  successflil  hypothesis, 
although  a  guess,  ought  not  to  be  called  a  lucky,  but  a  skillful  guess. 
The  guesses  which  serve  to  give  mental  unity  and  wholeness  to  a 
chaos  of  scattered  particulars,  are  accidents  which  occur  to  no  minds 
but  those  abounding  in  knowledge  and  disciplined  in  scientific  combi- 
nations. 

How  far  this  tentative  method,  so  indipensable  as  a  means  to  the  col- 
ligation of  facts  for  pui^j^oses  of  description,  admits  of  application  to 
Induction  itself,  and  what  functions  belong  to  it  in  that  department, 
will  be  considered  in  the  chapter  of  the  present  Book  which  relates  to 
Hypotheses.     On  the  present  occasion  we  have  chiefly  tc  distinguish 

*  Vide  infra,  book  iv.,  ch.  I. 


INDUCTIONS  IMPROPERLY  SO  CALLED.  181 

this  process  of  colligation  from  Iridvulion  properly  so  called :  and  that 
the  distinction  may  be  made  clearer,  it  is  well  to  advert  to  a  curions 
and  interesting  remark  of  Mr.  Whewcll,  which  is  as  strikingly  true  of 
the  former  operation,  as  it  is  vineqviivocally  false  of  the  latter. 

In  different  stages  of  the  progress  of  knowledge,  philosophers  have 
employed,  for  the  colligation  of  the  same  order  of  facts,  difterent  con- 
ceptions. The  early  and  rude  observations  of  the  heavenly  bodies,  in 
which  minitte  precision  was  neither  attained  nor  sought,  presented  no- 
thing inconsistent  with  the  representation  of  the  path  of  a  planet  as  an 
exact  circle,  having  the  earth  for  its  centre.  As  observations  increased 
in  accuracy,  and  facts  were  disclosed  which  were  not  reconcilable 
with  this  simple  supposition,  fw  the  colligation  of  those  additional 
facts,  the  supposition  was  varied  ;  and  vaiied  again  and  again  as  facts 
became  more  numerous  and  precise.  The  earth  was  removed  fi-om 
the  centi'e  to  some  other  point  within  the  circle  ;  the  planet  was  sup- 
posed to  revolve  in  a  smaller  circle  called  an  epicycle,  round  an  im- 
aginary point  which  revolved  in  a  circle  round  the  earth  :  in  proportion 
as  observation  elicited  fresh  facts  contradictory  to  these  representations, 
other  epicycles  and  other  eccentrics  were  added,  producing  additional 
complication ;  until  at  last  Kepler  swept  all  these  circles  away,  and 
substituted  the  conception  of  an  exact  ellipse.  Even  this  is  found  not 
to  represent  with  complete  coiTectness  the  accurate  observations  of 
the  present  day,  which  disclose  many  slight  deviations  from  an  orbit 
exactly  elliptical.  Now  Mr.  Whewell  has  remarked  that  tliese  suc- 
cessive general  expressions,  though  apparently  so  conflicting,  were  all 
correct  :  they  all  answered  the  purpose  of  colligation  :  they  all  enabled 
the  mind  to  represent  to  itself  with  facility,  and  by  a  simultaneous 
glance,  the  whole  body  of  facts  at  that  time  ascertained ;  each  in  its 
tuni  served  as  a  correct  des.criptioYi  of  the  phenomena,  so  far  as  the 
senses  had  up  to  that  time  taken  cognizance  of  them.  If  a  necessity 
afterwards  arose  for  discarding  one  of  these  general  descriptions  of 
the  planet's  orbit,  and  fi-aming  a  different  imaginary  line,  by  which  to 
express  the  series  of  observed  positions,  it  was  because  a  number  of 
new  facts  had  now  been  added,  which  it  was  necessary  to  combine 
with  the  old  facts  into  one  general  description.  But  this  did  not  affect 
the  coiTectness  of  the  former  expression,  considered  as  a  general  state- 
ment of  the  only  facts  which  it  was  intended  to  represent.  And  so 
true  is  this,  that,  as  is  well  remarked  by  M.'Comte,  these  ancient  gen- 
eralizations, even  the  rudest  and  most  imperfect  of  them,  that  of  uni- 
fonn  movement  in  a  circle,  ai'e  so  far  from  being  entirely  false,  that 
they  are  even  now  habitually  employed  by  astronomers  when  oYily  a 
rough  approximation  to  correctness  is  required.  "  L'astronomie  mo- 
derne,  en  detruisant  sans  retour  Ics  hypotheses  primitives,  envisagees 
comme  lois  reelles  du  monde,  a  soigneusement  maintenu  leur  valeuiv 
positive  et  permanentc,  la  ]n-opriete  de  representer  commodement  les 
phenome'.nes  quand  il  s'agit  d'une  premiere  ebauche.  Nos  ressources 
a  cet  egard  sent  meme  bien  plus  etendues,  precisement  a  caiise  quie 
nous  ne  nous  faisons  ancune  illusion  sur  la  realite  des  hypotheses ;  ce 
qui  nous  permet  d'employer  sans  scrupule,  en  chaque  cas,  celle  que 
nous  jugeons  la  plus  avantageuso."* 

Mr.  Wliewell's  remark,  therefore,  is  as  just  as  it  is  interesting.    Suc- 

*■  CoMTE,  Cours  de  Philosophie  Positive,  vol,  ii.,  p.  202, 


182  INDUCTION. 

cessive  expressions  for  the  colligation  of  observed  facts,  or,  in  other 
words,  successive  descriptions  of  a  phenomenon  as  a  v^^hole,  w^hich  has 
been  observed  only  in  parts,  may,  though  conflicting,  be  all  correct  as 
far  as  they  go.  But  it  would  surely  be  absurd  to  assert  this  of  con- 
flicting inductions. 

The  jihilosojjhic  study  of  facts  may  be  undertaken  for  three  dif- 
ferent purposes :  the  simple  description  of  the  facts ;  their  explana- 
tion ;  or  their  prediction  :  meaning  by  prediction,  the  determination 
of  the  conditions  under  which  similar  facts  may  be  expected  again  to 
occur.  To  the  first  of  these  three  operations  the  name  of  Induction 
does  not  properly  belong :  to  the  other  •  two  it  does.  Now,  Mr. 
Whewell's  observation  is  true  of  the  first  alone.  Considered  as  a 
mere  description,  the  circular  theory  of  the  heavenly  motions  repre- 
sents perfectly  well  their  general  features ;  and  by  adding  epicycles 
without  limit,  those  inotions,  even  as  now  known  to  us,  might  be 
expressed  with  any  degree  of  accuracy  that  might  be  required.  The 
only  real  advantage  of  the  elliptical  theory,  as  a  mere  description, 
would  be  its  simplicity,  and  the  consequent  facility  of  conceiving  it 
and  reasoning  about  it :  for  it  would  not  really  be  more  true  than  the 
other.  Different  descriptions,  therefore,  may  be  all  true  :  but  not, 
surely,  different  explanations.  The  doctrine  that  the  heavenly  bodies 
moved  by  a  virtue  inherent  in  their  celestial  nature ;  the  doctrine  that 
they  were  moved  by  impact,  (which  led  to  the  hypothesis  of  vortices 
as  the  only  impelling  force  capable  of  whirling  bodies  in  circles,)  and 
the  Newtonian  doctrine,  that  they  are  moved  by  the  composition  of  a 
centripetal  with  an  original  projectile  force ;  all  these  are  explana- 
tions, collected  by  real  induction  from  supposed  parallel  cases ;  and 
they  were  all  successively  received  by  philosophers,  as  scientific 
truths  on  the  subject  of  the  heavenly  bodies.  Can  it  be  said  of 
these,  as  we  said  of  the  different  descriptions,  that  they  are  all  true 
as  far  as  they  gol  Is  it  not  clear  that  one  only  can  be  true  in  any 
degree,  and  the  other  two  must  be  altogether  false  1  So  much  for 
explanations :  let  us  now  compare  different  predictions :  the  first, 
that  eclipses  will  occur  whenever  one  planet  or  satellite  is  so  situated 
as  to  cast  its  shadow  upon  another ;  the  second,  that  they  will  occur 
whenever  some  great  calamity  is  impending  over  mankind.  Do 
these  two  doctrines  only  differ  in  the  degree  of  their  truth,  as  ex- 
pressing real  facts  with  unequal  degrees  of  accuracy]  Assuredly 
the  one  is  true,  and  the  other  absolutely  false. 

In  every  way,  therefore,  it  is  evident  that  when  Mr.  Whewell 
explains  induction  as  the  colligation  of  facts  by  means  of  appro- 
priate conceptions,  that  is,  conceptions  which  will  really  express 
them,  he  confounds  mere  description  of  the  observed  facts  with  in- 
ference from  those  facts,  and  ascribes  to  the  latter  what  is  a  char- 
acteristic property  of  the  former. 

There  is,  however,  between  Colligation  and  Induction,  a  real 
correlation,  which  it  is  important  to  conceive  coixectly.  Colligation 
is  not  always  induction;  but  induction  is  always  colligation.  The 
assertion  that  the  planets  move  in  ellipses,  was  but  a  mode  of  rep- 
resenting observed  facts  ;  it  was  but  a  colligation  ;  while  the  assertion 
that  .  they  are  drawn,  or  tend,  towards  the  sun,  was  the  statement 
of  a  new  fact,  inferred  by  induction.  But  the  induction,  once  made, 
accomplishes  the  purposes  of  colligation  likewise.     It  brings  the  saui© 


GROUND    OF    INDUCTION.  183 

facts,  whicb  Kepler  had  connected  by  his  conception  of  an  elhpse, 
under  the  additional  conception  of  bodies  acted  upon  by  a  central 
force,  and  serves  therefore  as  a  new  bond  of  connexion  for  those 
facts ;  a  new  principle  for  their  classification. 

Moreover,  that  general  description,  which  is  improperly  confounded 
with  induction,  is  nevertheless  a  necessary  preparation  for  induction ; 
no  less  necessary  than  correct  observation  of  the  facts  themselves. 
Without  the  previous  colligation  of  detached  observations  by  means 
of  one  general  conception,  we  could  never  have  obtained  any  basis  for 
an  induction,  excejit  in  the  case  of  phenomena  of  very  limited  compass. 
"VVe  should  not  be  able  to  affirm  any  predicates  at  all,  of  a  subject  in- 
capable of  being  observed  otherwise  than  piecemeal :  much  less  could 
we  extend  those  predicates  by  induction  to  other  similar  subjects. 
Induction,  therefore,  always  presupposes,  not  only  that  the  necessary 
observations  are  made  with  the  necessaiy  accuracy,  but  also  that  the 
results  of  these  obsen'ations  are,  so  far  as  practicable,  connected 
together  by  general  descriptions,  enabling  the  mind  to  represent  to 
itself  as  wholes  whatever  phenomena  are  capable  of  being  so  rep- 
resented. 

To  suppose,  however,  that  nothing  more  is  required  from  the  concep- 
tion than  that  it  shall  sei-\e  to  connect  the  obsei-vations,  would  be  to 
substitute  hypothesis  for  theory  and  imagination  for  proof  The 
connecting  link  must  be  some  character  which  really  exists  in  the  facts 
themselves,  and  which  would  manifest  itself  therein  if  the  conditions 
could  be  realized  which  our  organs  of  sense  require. 

What  more  may  be  usefully  said  on  the  subject  of  Colligation,  or  of 
the  correlative  expression  invented  by  Mr.  Wliewell,  the  Explication 
of  Conceptions,  and  generally  on  the  subject  of  ideas  and  mental 
representations  as  connected  with  the  study  of  facts,  will  find  a  more 
appropriate  place  in  the  Fourth  Book,  on  the  Operations  Subsidiary 
to  Induction:  to  which  the  reader  must  refer  for  the  removal  of  any 
difficulty  which  the  present  discussion  may  have  left. 


CHAPTER  III. 

OF  THE   GROUND   OF    INDUCTION. 


§  1.  Induction  properly  so  called,  as  distinguished  from  those  mental 
operations,  sometimes  though  improperly  designated  by  the  name, 
which  I  have  attempted  in  the  preceding  chapter  to  characterize,  may, 
then,  be  summarily  defined  as  Generalization  fi-om  Experience.  It 
consists  in  inferring  from  some  individual  instances  in  which  a  phe- 
nomenon is  obsei-ved  to  occur,  that  it  occurs  in  all  instances  of  a 
certain  class ;  namely,  in  all  which  resemble  the  former,  in  what  are 
regarded  as  the  material  circumstances. 

In  what  Way  the  material  circumstances  are  to  be  distinguished  fi-om 
those  which  are  immaterial,  or  why  some  of  the  circumstances  are 
material  and  others  not  so,  we  are  not  yet  ready  to  point  out.  We 
must  first  observe,  that  there  is  a  principle  implied  in  the  very  state- 
ment of  what  Induction  is ;  an  assumption  with  regard  to  the  course 


184  INDUCTION. 

of  nature  and  the  order  of  the  universe :  namely,  that  there  are  such 
things  in  natui'e  as  parallel  cases ;  that  what  happens  once,  \n\l,  under 
a  sufficient  degree  of  similaTity  of  circumstances^  happen  again,  and 
not  only  again,  but  always.  This,  I  say,  is  an  assumption,  involved  in 
every  case  of  induction.  And,  if  we  consult  the  actual  course  of 
nature,  we  find  that  the  assumption  is  waiTanted ;  the  fact  is  so.  The 
universe,  we  find,  is  so. constituted,  that  whatever  is  tine  in  any  one 
case,  is  true  in  all  cases  of  a  certain  description  ;  the  only  difficulty  is, 
to  find  u'//at  description. 

This  universal  fact,  which  is  our  waiTant  for  all  inference  from  expe- 
rience, has  been  described  by  diflerent  philosophers  in  different  forms 
of  language  :  that  the  course  of  nature  is  uniform  ;  that  the  universe  is 
governed  by  general  laws ;  and  the  like.  One  of  the  most  usual  of 
these  modes  of  expression,  but  also  one  of  the.  most  inadequate,  is  that 
which  has  been  brought  into  familiar  use  by  the  metaphysicians  of  the 
school  of  Reid  and  Stewart.  The  disposition  of  the  human  mind  to 
generalize  from  experience — a  propensity  considered  by  these  philo- 
sophers as  an  instinct  of  om-  nature — they  usually  describe  under  the 
name  of  "  our  intuitive  conviction  that  the  future  ^^:ill  resemble  the 
past."  Now  it  has  been  well  pointed  out  by  Mr.  Bailey,*  that  (whether 
the  tendency  be  qr  not  an  original  and  ultimate  element  of  our  nature), 
Time,  in  its  modifications  of  past,  present,  and  future,  has  no  concern 
either  with  the  belief  itself,  or  with  the  grounds  of  it.  We  believe 
that  fire  will  burn  to-morrow,  because  it  bunied  to-day  and  yesterday; 
but  we  believe,  on  precisely  tlie  same  gi-ounds,  that  it  burned  before 
we  were  born,  and  that  it  burns  this  very  day  in  Cochin-China.  It  is 
not  fi-om  the  past  to  the  future,  as  past  and  fiiture,  that  we  infer,  but 
from  the  known  to  the  unkno-wn ;  from  facts  observed  to  facts  unob- 
served ;  from  what  we  have  perceived,  or  been  directly  conscious  of, 
to  what  has  not  come  within  our  experience.  In  this  last  predicament 
is  the  whole  region  of  the  fliture ;  but  also  the  vastly  greater  portion 
of  the  present  and  of  the  past. 

Whatever  be  the  most  proper  mode  of  expressing  it,  the  proposition 
that  the  course  of  nature  is  uniform,  is  the  fundamental  principle,  or 
general  axiom,  of  Induction.  It  would  yet  be  a  great  error  to  offer 
this  large  generalization  as  any  explanation  of  the  inductive  proce&s. 
On  the  contrary,  I  hold  it  to  be  itself  an  instance  of  induction,  and 
induction  by  no  means  of  the  most  obvious  kind.  Far  from  being  the- 
first  induction  we  make,  it  is  one  of  the  last,  or  at  all  events  one  of 
those  which  are  latest  in  attaining  strict  philosophical  accuracy.  As 
a  general  maxim,  indeed,,it  has  scarcely  entered  into  the  minds  of  any 
but  philosophers ;  nor  even  by  them,  as  we  shall  have  many  opportu- 
nities of  remarking,  have  its  extent  and  limits  been  always  very  justly 
conceived.  Yet  this  principle,  though  so  far  from  being  our.  earliest 
induction,  must  be  considered  as  our  wan'ant  for  all  the  ojhers,  in  this 
sense,  that  unless  it  were  true,  all  other  inductions  would  be  fallacious. 
And  this,  as  we  have  ah'eady  seen,  is  the  sole  mode  in  which  the  gene- 
ral propositions  which  we  place  at  the  head  of  our  reasonings  when 
we  throw  them  into  syllogisms,  ever  really  contribute  to  their  validity. 
Archbishop  Wliately  has  well  remarked,  that  every  induction  is  a 
syUogism  with  the  major  premiss  suppressed ;  or  (as  I  prefer  express- 

*  Essays  on  the  Pursttit  of  TnitL 


GROUND    OF    INDUCTION.  185 

ing  it),  that  every  imluctioii  may  be  thrown  into  the  form  of  a  syllo- 
gism, by  supplying  a  major  premiiss.  If  this  be  actually  clone,  the 
principle  which  Ave  are  now  considering,  that  of  the  uniformity  of  the 
cour^^e  of  nature,  will  appear  as  the  ultimate  major  premiss  of  all  in- 
ductions ;  ami  will,  therefore,  stand  to  all  inductions  in  the  rplation  in 
which,  as  has  been  shown  at  so  much  length,  the  major  proposition  of 
a  syllogism  always  stands  to  the  conclusion;  not  contributing  at  all  to 
prove  it,  but  being  a  necessary  condition  of  it»  being  proved  ;  since  no 
conclusion  is.  proved  for  which  there  cannot  be  found  a  true  major 
j^remiss.* 

It  was  not  to  be  expected  that  in  the  case  of  this  axiom,  any  more 
than  of  other  axioms,  there  should  be  unanimity  among  philosophers 
with  respect  to  the  gi'ounds  upon  which  it  is  to  be  received  as  true. 
I  have  already  stated  that  I  regard  it  as  itself  a  generalization  from, 
experience.  Others  hold  it  to  be  a  principle  which,  antecedently  to 
any  verification  by  experience,  we  are  compelled  by  the  constitution 
of  our  thinking  faculty  to  assume  as  true.  Having  so  recently,  and  at 
so  much  length,  combated  a  similar  doctrine  as  applied  to  the  axioms 
of  mathematics,  by  arguments  which  are  in  a  great  measure  applicable 
to  the  present  case,  I  shall  defer  the  more  particular  discussion  of  this 

*  From  the  fact,  that  every  induction  maybe  expressed  in  the  form  of  a  syllogism. 
Archbishop  Whately  concludes  that  Induction  itself  is  but  a  peculiar  case  of  ratiocination, 
and  that  the  universal  type  of  all  Inference,  or  Reasoning,  is  the  Syllogism.  Our  own 
inquiries  have  led  us  to  a  directly  opposite  result.  Instead  of  resolving  Induction  into 
Ratiocination,  it  has  appeared  to  us  that  Ratiocination  is  itself  resolvable  into  Induction. 
The  Archbishop's  theory  may,  I  think,  be  shown  to  be  fallacious  by  following  out  his  ovvn 
train  of  thought.  The  induction,  "  Johi>«  Peter,  Thomas,  &c.,  are  mortal,  therefore  all 
mankind  are  mortal,"  may,  as  he  justly  says,  be  thrown  into  a  syllogism  by  preti.xing  as  a 
major  premiss  (what  is  at  any  rate  a  necessary  condition  of  the  validity  of  the  argument) 
namely,  that  whatever  is  true  of  John,  Peter,  Thomas,  &c,,  is  true  of  all  mankind.  So 
far  the  case  is  made  out ;  and  Archbishop  Whately  (who,  endowed  with  a  penetrating  and 
active  rather  than  a  patient  and  persevering  intellect,  seldom  fails  to  cast  his  sounding  line 
to  a  greater  depth  than  his  predecessors,  and  when  he  has  done  this,  scarcely  seem?  to 
care  whether  he  reaches  the  bottoui  or  not)  omitted  to  ask  himself  the  further  question, 
How  we  come  by  the  major  premiss '.  It  is  not  self-evident ;  nay, in  all  cases  of  unwarranted 
generalization,  it  is  not  true.  How,  then,  is  it  arrived  at?  Necessarily  either  by  induction 
or  ratiocination  ;  and  If  by  induction,  then,  on  the  Archbishop's  princi[)le&,  it  is  by  ratiocina- 
tion still,  that  is,  by  a  previous  syllogism.  This  previous  syllogism  it  is,  therefore,  necessary 
to  construct.  There  is,  in  the  long  run,  only  one  possible  construction  :  the  real  proof  that 
whatever  is  true  of  John,  Peter,  &c.,  is  true  of  all  mankind,  can  onf>'  be,  that  a  different 
supposition  would  be  inconsistent  with  the  uniformity  which  we' kndvv  to  exist  in,  the 
course  of  nature."  Whether  there  would  be  this  iuconsistcncy  or  nqt,  may  be  a  matter  of 
long  and  delicate  inquiry  ;  but  unless  there  would,  we  have  no  sufficient  ground  for  the 
major  of  the  inductive  syllogism.  It  hence  appears,  that  if  we  throw  the  whole  course  of 
any  inductive  argument  into  a  series  of  syllogisms,  we  shall  arrive  by  more  or  fewer  steps 
at  an  ultimate  syllogism,  which  will  have  for  its  major  premiss  the  principle,  or  axiom,  of 
the  uniformity  of  the  course  of  nature.  Having  reached  this  point,  wc  have  the  whole 
field  of  induction  laid  out  in  syllogisms,  and  every  instance  of  inference  from  experience 
exhibited  as  the  conclusion  of  ratiocination,  except  one  ;  but  that  one,  unhappily,  includes 
all  the  rest.  Whence  came  the  universal  major?  What  proves  to' us  that  nature  is 
governed  by  general  laws  ?  Where  are  the  premisses  of  the  syllogism  of  which  that  is  the 
conclusion?    Here,  at  least,  is  a  case  of  induction  which  cannot  be  resolved  into  syllogism. 

And  undoubtedly  it  would  be  the  ideal  perfection  of  Inductive  Philosophy  if  all  other 
general  truths  could  be  exhibited  as  conclusions  tjeduced  from  that  widest  generalization 
of  all.  But  such  a  mode  of  presenting  them,  however  useful  in  giving  coherence  and 
systematic  unity  to  our  thoughts,  would  be  an  inversion  of  the  real  order  of  proof.  This  great 
generalization  must  itself  have  been  founded  on  prior  generahzations :  the  obscurer  laws 
of  nature  were  discovered  by  means  of  it,  but  the  more  obvious  ones  must  have  been 
understood  and  assented  to  as  general  truths  before  it  was  ever  heard  of  We  should 
never  have  dared  to  affirm  that  all  phenomena  take  place  according  to  general  laws,  if  we  had 
not  first  arrived,  in  the  case  of  a  great  multitude  of  phenomena,  at  some  knowledge  of  the 
laws  themselves  ;  which  could  be  done  no  otherwise  than  by  induction.  .\rciii>ishop 
Whately's  theory,  therefore,  implying,  as  it  does,  the  consequence  that  we  never  could 
have  had  a  single  well-grounded  induction  unless  we  had  already  reached  that  highest 
generalization,  must,  I  conceive,  be  regarded  as  untenable. 
Aa 


186  INDUCTION. 

controverted  point  in  regard  to  the  fundamental  axiom  of  induction, 
until  a  more  advanced  period  of  our  inquiry*  At  present  it  is  of 
more  importance  to  understand  thoroughly  the  import  of  the  axiom 
itself  For  the  proposition,  that  the  course  of  nature  is  uniform,  pos- 
sesses rather  the  brevity  sviitable  to  popular,  than  the  precision  requi- 
site in  philosophical,  language  :  its  terms  require  to  be  explained,  and 
a  stricter  tlian  their  ordinary  signification  given  to  them,  before  the 
truth  of  the  assertion  can  be  admitted. 

§  2.  Every  person's  consciousness  assures  him  that  he  does  not  al- 
ways expect  uniforaiity  in  the  course  of  events;  he  does  riot  always 
believe  that  the  unknown  will  be  similar  to  the  known,  that  the  fu- 
ture will  resemble  the  past.  Nobody  believes  that  the  succession  of 
rain  and  fine  weather  will  be  the  same  in  every  future  year  as  in  the 
present.  Nobody  expects  to  have  the  same  dreams  repeated  every 
night.  On  the  contrary,  everybody  mentions  it  as  something  extraor- 
dinary, if  the  course  of  nature  is  constant,  and  resembles  itself,  in  these 
particulars.  To  look  for  constancy  where  constancy  is  not  to  be  ex- 
pected, as,  for  instance,  that  a  day  which  has  once  brought  good  for- 
tune'will  always  be  a  fortunate  day,  is  justly  accounted  superstition. 

The  course  of  nature,  in  truth,  is'  not  only  uniform,  it  is  also  infi- 
nitely various.  Some  phenomena  are  always  seen  to  recur  in  the  very 
same  combinations  in  which  we  met- with  them  at  first;  others  seem 
altogether  capricious ;  while  some,  which  we  had  been  accustomed  to 
regard  as  bound  down  exclusively  to  a  particular  set  of  combinations, 
we  unexpectedly  find  detached  from  some  of  the  elements  with  which 
we  had  hitherto  found  them  conjoined,  and  united  to  others  of  quite 
a  contrary  description.  To  an  inhabitant  of  Central  Africa,  fifty  years 
ago,  no  fact  probably  appeared  to  rest  upon  more  uniform  experience 
than  this,  that  all  human  beings  are  black.  To  Europeans,  not  many 
years  ago,  the  proposition,  All  swans  are  white,  appeared  an  equally 
unequivocal  instance  of  uniformity  in  the  course  of  nature.  Further 
experience 'has  proved  to  both  that  they  were  mistaken  ;  but  they  had 
to  wait  fifty  centuries  for  this  experience.  During  that  long  time, 
mankind  believed  in  an  uniformity  of  the  course  of  nature  where  no 
such  uniformity  really  existed. 

According  to  the  notion  which  the  ancients  entertained  of  induction, 
the  foregoing  were  cases  of  as  legitimate  inference  as  any  inductions 
whatever.  In  these  two  instances,  in  which,  the  conclusion  being 
false,  the  ground  of  inference  must  have  been  insufficient,  there  was, 
nevertheless,  as  much  ground  for  it  as  this  conception  of  induction  ad- 
mitted of  The  induction  of  the  ancients  has  been  well  described  by 
-Bacon,  under  the  name  of"Inductio  per  enumerationem  simplicem, 
ubi  non  reperitur  instantia  contradictoria."  It  consists  in  ascribing 
the  character  of  general  truths  to  all  propositions  which  are  true  in 
every  instance  that  we  happen  to  know  of  This  is  the  kind  of  induc- 
tion, if  it  deserves  the  name,  which  is  natural  to  the  mind  when  unac- 
customed to  ■  scientific  methods.  The  tendency,  which  some  call  an 
instinct,  and  which  others  account  for  by  association,  to  infer  the  fu- 
ture from  the  past,  the  known  from  the  unknown,  is  simply  a  habit  of 
expecting   that  what    has    been    found   true  once    or   several  times, 

*  Infra,  chap,  xxi. 


GROUND    OF    INDUCTION.  187 

and  never  yet  found  false,  will  be  found  true  again.  Wlietlicr  the 
instances  are  few  or  many,  conclusive  or  inconclusive,  does  not  much 
affect  the  matter :  these  are  considerations  which  occur  only  on  re- 
flection :  the  unprompted  tendency  of  the  mind  is  to  generalize  its  ex- 
perience, provided  this  points  all  in  one  direction ;  provided  no  other 
experience  of  a  conflicting  character  comes  unsought.  The  notion  of 
seeking  it,  of  experimenting  for  it,  of  interrogating  nature  (to  use 
Bacon's  expression),  is  of  much  later  growth.  The  observation  of  nature, 
by  uncultivated  intellects  is  purely  passive :  they  take  the  facts  which 
present  themselves,  without  taking  the  trouble  of  searching  for  more  : 
it  is  a  superior  mind  only  which  asks  itself  what  facts  ai-e  needed  to 
enable  it  to  come  to  a  sure  conclusion,  and  then  looks  out  for  these. 

But  although  we  have  always  a  propensity  to  generalize  from  un- 
varying experience,  we  are  not  always  warranted  in  doing  so.  Be- 
fore we  can  be  at  liberty  to  conclude  that  something  is  universally  true 
because  we  have  never  known  an  instance  to  the  contrary,  it  must  be 
proved  to  us  that  if  there  were  in  nature  any  instances  to  the  contrary, 
we  should  have  known  of  tliem.  This  assurance,  in  the  great  majority 
of  cases,  we  cannot  have,  or  can  have  only  in  a  very  moderate  degree. 
The  possibility  of  having  it,  is  the  foundation  on  which  we  shall  see 
hereafter  that  induction  by  simple  enumeration  may  in  some  remark- 
able cases  amount  to  full  proof.*  No  such  assurance,  however,  can 
be  had,  on  any  of  the  ordinary  subjects  of  scientific  inquiry.  Popular 
notions  are  usually  founded  upon  induction  by  simple  enumeration ; 
in  science  it  carries  us  but  a  little  way.  We  are  forced  to  begin  with 
it ;  we  must  often  rely  upon  it  provisionally,  in  the  absence  of  means 
of  more  searching  investigation.  But,  for  the  accurate  study  of  nature, 
we  require  a  surer  and  a  more  potent  instrument. 

It  was,  above  all,  by  pointing  out  the  insufficiency  of  this  rude  and 
loose  conception  of  Induction,  that  Bacon  merited  the  title  so  generally 
awarded  to  him,  of  Founder  of  the  Inductive  Philosophy.  The  value 
of  his  own  contributions  to  a  more  philosophical  theory  of  the  subject 
has  certainly  been  exaggerated.  Although  (along,  with  some  funda- 
mental errors)  his  wi'itings  contain,  more  or  less  fully  developed, 
several  of  the  most  important  principles  of  the  Inductive  Method, 
physical  investigation  has  now  far  outgrown  the  Baconian  conception 
of  Induction.  Moral  and  political  inquiry,  indeed,  are  as  yet  far 
behind  that  conception.  The  current  and  approved  modes  of  reason- 
ing on  these  subjects  are  still  of  the  same  vicious  description  against 
which  Bacon  protested  :  the  method  almost  exclusively  employed  by 
those  professing  to  treat  such  matters  inductively,  is  the  very  indicctio 
per  emuncrationcm  simplicem  which  he  condemns  ;  and  the  experience, 
which  we  hear  so  confidently  appeidcd  to  by  all  sects,  parties,  and  in- 
terests, is  still,  in  his  own  emphatic  words,  mera  palpatio. 

§  3.  In  order  to  a  better  understanding  of  the  problem  which  the 
logician  must  solve  if  he  would  establish  a  scientific  theory  of  Induc- 
tion, let  us  compare  a  few  cases  of  incorrect  inductions  with  others 
which  are  acknowledged  to  be  legitimate.  Some,  we  know,  which 
were  believed  for  centuries  to  be  correct,  were  nevertheless  incorrect. 
That  all  swans  are  white,  cannot  have  been  a  good  induction,  since 

*  Infra,  chap,  xxi,  xxii. 


188  INDUCTION. 

the  conclusion  has  turned  out  erroneous.  The  experience,  however, 
on  which  the  conclusion  rested  was  genuine.  From  the  earhest 
records,  the  testimony  of  all  the  inhabitants  of  the  known  world  was 
unanimous  on  the  point.  The  uniform  experience,  therefore,  of  the  in- 
habitants of  the  known  world,  agreeing  in  a  common  result,  without 
one  known  instance  of  deviation  from  that  result,  is  not  alwaysr  suffi- 
cient to  establish  a  general  conclusion. 

But  let  us  now  turn  to  an  instance  apparently  not  very  dissimilar  to 
this.  Mankind  were  wrong,  it  seems,  in  concluding  that  all  swans 
were  white  :  are  we  also  wrong,  when  vve  conclude  that  all  men's 
heads  grow  above  their  shoulders,  and  never  below,  in  spite  of  the 
conflicting  testimony  of  the  naturalist  Pliny  1  As  there  were  black 
swans,  although  civilized  men  had  existed  for  three  thousand  years  on 
the  earth  without  meeting  with  them,  may  there  not  also  be  "  men 
whose  heads  do  gi'ow  beneath  their  shoulders,"  notwithstanding  a 
father  less  perfect  unanimity  of  negative  testimony  from  all  observers  ? 
Most  persons  would  answer  No ;  it  was  more  credible  that  a  bird 
should  vary  in  its  color,  than  that  man  should  vary  in  the  relative  posi- 
tion of  his  principal  organs.  And  there  is  no  doubt  that  in  so  saying 
they  would  be  right :  but  to  say  why  they  are  right,  would  be  impos- 
sible, without  entering,  more  deeply  than  is  usually  done,  into  the  true 
theory  of  Induction. 

Again,  there  are  cases  in  which  we  reckon  with  the  most  unfailing 
confidence  upon  uniformity,  and  other  cases  in  which  we  do  not  count 
upon  it  at  all.  In  some,  we  feel  complete  assurance  that  the  future  will 
resemble  the  past,  the  unknown  be  precisely  similar  to  the  known.  In 
others,  however  invariable  may  be  the  result  obtained  fi-om  the  in- 
stances which  we  have  observed,  we  draw  from  them  no  more  than  a 
very  feeble  presumption  that  the  like  result  will  hold  in  all  other  cases. 
That  a  straight  line  is  the  shortest  distance  between  two  points,  we  do 
not  doubt  to  be  true  even  in  the  region  of  the  fixed  stars.  When  a  chem- 
ist announces  the  existence  and  properties  of  a  newly-discovered  sub- 
stance, if  we  confide  in  his  accuracy,  we  feel  assured  that  the  conclusions 
he  has  amved  at  will  hold  universally,  although  the  induction  be  founded 
but  on  a  single  instance.  We  do  not  withhold  our  assent,  waiting  for 
a  repetition  of  the  experiment ;  or  if  we  do,  it  is  fi"om  a  doubt  whether 
the  one  experiment  was  properly  made,  not  whether  if  properly  made 
it  would  be  conclusive.  Here  then,  is  a  general  law  of  nature,  in- 
feired  without  hesitation  fi-om  a  single  instance ;  an  universal  pi'opo- 
sition  from  a  singular  one.  Now  mark  another  case,  and  contrast  it 
with  this.  Not  all  the  instances  which  have  been  observed  since  the 
beginning  of  the  world,  in  support  of  the  general  proposition  that  all 
crows  are  black,  would  be  deemed  a  suffiijient  presumjjtion  of  the 
truth  of  the  proposition,  to  outweigh  the  testimony  of  one  unexcep- 
tionable witness  who  should  affirm  that  in  some  region  of  the  earth 
not  fully  explored,  he  had  caught  and  examined  a  crow,  and  had  found 
it  to  be  gray. 

Why  is  a  single  instance,  in  some  cases,  sufficient  for  a  complete  in- 
duction, while  in  others,  myriads  of  concurring  instances,  without  a 
single  exception  known  or  presumed,  go  such  a  very  little  way  towards 
establishing  an  universal  proposition  1  Whoever  can 'answer  this  ques- 
tion knows  more  of  the  philosophy  of  logic  than  the  wisest  of  the  an- 
cients, and  has  solved  the  great  problem  of  induction. 


LAWS    OF    NATURK.  189 

CHAPTER  IV. 

OF   LAWS  OF   NATURE. 

§  1.  In  the  contemplation  of  that  uniformity  in  the  course  of  nature, 
which  is  assumed  in  every  inference  from  exjierience,  one  of  the  iirst 
observations  that  present  themselves  is,  that  the  uniformity  in  question 
is  not  properly  uniformity,  but  uniformities.  The  general  regularity 
results  from  the  coexistence  of  partial  regularities.  The  course  of  na- 
ture in  general  is  constant,  because  the  course  of  each  of  the  various 
phenomena  that  compose  it  is  so.  A  certain  fact  invariably  occurs 
whenever  certain  circumstances  are  present,  and  does  not  occur  when 
they  are  absent ;  the  like  is  true  of  another  fact ;  and  so  on.  From 
these  separate  threads  of  connexion  between  parts  of  the  great  whole 
which  we  term  nature,  a  general  tissue  of  connexion  unavoidably 
weaves  itself,  by  which  the  whole  is  held  together.  If  A  is  gilways 
accompanied  by  D,  B  by  E,  and  C  by  F,  it  follows  that  AB  is  accom- 
panied by  D  E,  A  C  by  i)  F,  B  C  by  E  F,  and  finally,  A  B  C  by  D  E  F ; 
and  thus  the  general  character  of  regularity  is  produced,  which,  along 
with  and  in  the  midst  of  infinite  diversity,  pervades  all  nature. 

The  first  point,  therefore,  to  be  noted  in  regard  to  what  is  called  the 
uniformity  of  the  course  of  nature,  is,  that  it  is  itself  a  complex  fact, 
compounded  of  all  the  separate  uniformities  which  exist  in  respect  to 
single  phenomena.  These  various  uniformities,  when  ascertained  by 
what  is  regai'ded  as  a  sufficient  induction,  we  call  in  common  parlance, 
Laws  of  Nature.  Scientifically  speaking,  that  title  is  employed  in  a 
more  restricted  sense  to  designate  the  uniformities  when  reduced  to 
their  most  simple  expression.  Thus  in  the  illustration  already  em- 
ployed, there  were  seven  uniformities  ;  all  of  which,  if  considered  suf- 
ficiently certain,  would,  in  the  more  lax  application  of  the  term,  be 
called  laws  of  nature.  But  of  the  seven,  three  alone  are  properly  dis- 
tinct and  independent ;  these  being  presupposed,  the  others  follow  of 
course :  the  three  first,  therefore,  accoi'ding  to  the  stricter  acceptation, 
are  called  laws  of  nature,  the  remainder  not ;  because  they  are  in  truth 
mere  cases  of  the  three  first ;  virtually  included  in  them ;  said,  there- 
fore, to  result  from  them  :  whoever  affirras  those  three  has  abeady 
affiimed  all  the  rest. 

To  substitute  real  examples  for  symbolical  ones,  the  following  are 
three  uniformities,  or  call  them  laws  of  nature  :  the  law  that  air  has 
weight,  the  law  that  pressure  on  a  fluid  is  propagated  equally  in  all 
directions,  and  the  law  that  pressure  in  one  direction,  not  opposed  by 
an  equal  pressure  in  a  contrary  direction,  produces  motion,  which  does 
not  cease  imtil  equilibi'ium  is  restored.  From  these  three  uniformities 
we  should  be  able  to  predict  another  uniformity,  namely,  the  rise  of 
the  mercury  in  the  Torricellian  tube.  This,  in  the  stricter  use  of  the 
phra-se',  is  not  a  law  of  nature.  It  is  a  result  of  laws  of  nature.  It  is 
a  case  of  each  and  every  one  of  the  three  laws ;  and  is  the  only  occur- 
rence by  which  they  could  all  be  fulfilled.  If  the  mercury  were  not 
sustained  in  the  barometer,  and  sustained  at  such  a  height  that  the  col- 
umn of  mercury  were  equal  in  weight  to  a  column  of  the  atmosphere, 
of  the  same  diameter  j  here  would  be  a  case,  either  of  the  air  not 


190  INDUCTION. 

pressing  upon  the  surface  of  the  mercury  with  the  force  which  is  called 
its  weight,  or  of  the  downward  pressure  on  the  mercury  not  being 
propagated  equally  in  an  upward  direction,  or  of  a  body  pressed  in 
one  direction  and  not  in  the  direction  opposite,  either  not  moving  in 
the  direction  in  which  it  is  pressed,  or  stopping  before  it  had  attained 
equilibrium.  If  we  knew,  therefore,  the  three  simjile  laws,  but  had 
never  tried  the  Torricellian  experiment,  we  might  deduce  its  result 
from  those  laws.  The  known  weight  of  the  air,  combined  with  the 
position  of  the  apparatus,  would  bring  the  mercury  within  the  first  of 
the  three  inductions  ;  the  first  induction  would  bring  it  within  the  sec- 
ond, and  the  second  within  the  third,  in  the  manner  which  we  so  fully 
illustrated  in  treating  of  Ratiocination.  We  should  thus  come  to  know 
the  more  complex  uniformity,  independently  of  specific  experience, 
through  our  knowledge  of  the  simpler  ones  from  which  it  results  :  al- 
though, for  reasons  which  will  appear  hereafter,  verification  by  specific 
experience  would  still  be  desirable,  and  might  possibly  be  indis- 
pensable. \ 

Complex  uniformities  which,  like  this,  are  mere  cases  of  simpler 
ones,  and  have,  therefore,  been  virtually  inferred  in  affimiing  those, 
may  with  propriety  be  called  laws,  but  can  scarcely,  in  the  strictness 
of  scientific  speech,  be  termed  Laws  of  Nature.  It  is  the  custom  of 
philosophers,  wherever  they  can  trace  regularity  of  any  kind,  to  call 
the  general  proposition  which  expresses  the  nature  of  that  regularity, 
a  law  ;  as  when,  in  mathematics,  we  speak  of  the  law  of  decrease  of 
the  successive  terms  of  a  converging  series.  But  the  expression,  law 
of  nature,  is  generally  employed  by  scientific  men  with  a  sort  of  tacit 
reference  to  the  original  sense  of  the  word  latv,  namely,  the  expression 
of  the  will  of  a  superior ;  the  superior,  in  this  instance,  being  the  Ruler 
of  the  universe.  When,  therefore,  it  appeared  that  any  o^  the  uni- 
formities which  were  observed  in  nature,  would  result  spontaneously 
from  cei'tain  other  uniformities,  without  any  separate  act  of  creative 
will,  the  former  have  not  usually  been  spoken  of  as  laws  of  nature. 
According  to  another  mode  of  expression,  the  question.  What  are  the 
laws  of  nature  1  may  be  stated  thus  : — What  are  the  fewest  and  sim- 
plest assumptions,  which  being  granted,  the  whole  existing  order  of 
nature  would  result  1  Another  mode  of  stating  it  would  be  thus : 
What  are  the  fewest  general  propositions  from  which  all  the  uniformi- 
ties which  exist  in  the  universe  might  be  deductively  inferred  ? 

As  has  already  been  hinted  (and  will  be  more  fully  discussed  here- 
after) every  gi'eat  advance  which  marks  an  epoch  in  the  progress  of 
science,  has  consisted  in  a  step  made  towards  the  solution  of  this 
problem.  Even  a  simple  colligation  of  inductions  akeady  made,  with- 
out any  fresh  extension  of,  the  inductive  inference,  is  already  an  ad- 
vance in  that  direction.  When  Kepler  expressed  the  regularity  which 
exists  in  the  observed  motions'  of  the  heavenly  bodies,  by  the  three 
general  propositions  called  his  laws,  he,  in  so  doing,  pointed  out 
three  simple  volitions,  by  which,  instead  of  a  much  greater  number,  it 
appeared  that  the  whole  scheme  of  the  heavenly  motions,  so  far  as  yet 
observed,  might  be  conceived  to  have  been  produced.  A  similar,  and 
still  greater  step  was  made  when  these  laws,  which  at  first  did  not 
seem  to  be  included  in  any  more  general  truths,  were  discovered  to 
be  cases  of  the  three  laws  of  motion,  as  obtaining  among  bodies  which 
mutually  tend  towards  one  another  with  a  certain  force,  and  have  had 


LAW3    OF    NATURE.  191 

a  ceitain  instantaneous  impulse  originally  impressed  upon  tliem.  After 
this  great  discovery,  Kepler's  three  propositions,  though  still  called 
laws,  would  hai'dly,  by  any  person  accustomed  to  use  language  with 
precision,  be  temied  laws  ot'  nature  :  that  phrase  would  be  reserved 
for  the  simpler  laws  into  which  Newton,  as  the  expression  is,  resolved 
them. 

According  to  this  language,  every  well  grounded  inductive  generali- 
zation is  either  a  law  of  nature,  or  a  result  of  laws  of  nature,  capable, 
if  those  laws  are  knowai,  of  being  predicted  from  them.  And  the  prob- 
lem of  Inductive  Logic  may  be  summed  up  in  two  questions  :  How  to 
ascertain  the  laws  of  nature  ?  and.  How,  after  having  ascertained  them, 
to  follow  them  into  their  results  1  On  the  other  hand,  we  must  not 
suffer  ourselves  to  imagine  that  this  mode  of  statement  amounts  to  a 
real  analysis,  or  to  anything  but  a  mere  verbal  transformation  of  the 
problem ;  for  the  expi'ession,  Laws  of  Nature,  means  nothing  but  the 
uniformities  which  exist  among  natural  phenomena  (or,  in  other  words, 
the  results  of  induction),  when  reduced  to  their  simplest  expression. 
It  is,  however,  something  to  have  advanced  so  far,  as  to  see  that  the 
study  of  nature  is  the  study  of  laws,  not  a  law ;  of  uniformities,  in  the 
plural  number :  that  the  different  natural  phenomena  have  their  sepa- 
rate rules  or  modes  of  taking  place,  which,  though  much  intermixed 
and  entangled  with  one  another,  may,  to  a  certain  extent,  be  studied 
apart :  that  (to  resume  our  former  metaphor)  the  regularity  which 
exists  in  nature  is  a  web  composed  of  distinct  threads,  and  only  to  be 
understood  by  tracing  each  of  the  threads  separately  ;  for  which  pur- 
pose it  is  often  necessary  to  unravel  some  portion  of  the  web,  and  ex- 
hibit the  fibres  apart.  The  rules  of  experimental  inquiry  are  the  con- 
trivances for  um-aveling  the  web. 

§  2.  In  thus  attempting  to  ascertain  the  general  order  of  nature  by 
ascertaining  the  particular  order  of  the  occuiTence  of  each  one  of  the 
phenomena  of  nature,  the  most  scientific  proceeding  can  be  no  more- 
than  an  improved  form  of  that  which  was  primitively  pursued  by  the 
human  imderstanding,  as  yet  undirected  by  science.  When  men  first 
formed  the  idea  of  studying  phenomena  according  to  a  stricter  and 
surer  method  than  that  which  they  had  in  the  first  instance  spontane- 
ously adopted,  they  did  not,  conformably  to  the  well  meant  but  imprac- 
ticable precept  of  Descartes,  set  out  from  the  supposition  that  nothing 
had  been  already  ascertained.  Many  of  the  uniformities  existing 
among  phenomena  are  so  constant,  and  so  open  ta  observation,  as  to 
force  themselves  upon  men's  involuntary  recognition.  Some  facts  are 
so  perpetually  and  familiarly  accompanied  by  certain  others,  that  manr 
kind  learnt,  as  children  now  learn,  to  expect  the  one  where  they  found 
the  other,  long  before  they  knew  how  to  put  their  expectation  into 
words,  by  asserting,  in  a  proposition,  the  existence  of  a  connexion  be- 
tween those  phenomena.  No  science  was  needed  to  teach  men  that 
food  nourishes,  that  water  drowns,  or  quenches  thirst,  that  the  sun 
gives  light  and  heat,  that  bodies  fall  to  the  ground.  The  first  scien- 
tific inquirers  assumed  these  and  the  like  as  known  truths,  and  set  out 
from  them  to  discover  others  which  were  unknown  :  nor  were  they 
wrong  in  so  doing,  subject,  however,  as  they  afterwards  began  to  see, 
to  an  ulterior  revision  of  these  spontaneous  generalizations  themselves, 
when  the  progress  of  knowledge  pointed  out  limits  to  them,  or  showed 


192  INDUCTION. 

their  truth  to  be  conthigent  upon  some  other  circumstance  not  origi- 
nally attended  to.  It  will  appear,  I  think,  from  the  subsequent  part  of 
our  inquiry,  that  there  is  no  logical  fallacy  in  this  mode  of  proceeding  ; 
but  we  may  see  already  that  any  other  mode  is  rigorously  impractica- 
ble :  since  it  is  impossible  to  frame  any  scientific  method  of  induction, 
or  test  of  the  correctness  of  inductions,  vmless  ujjon  the  hypothesis  that 
some  inductions  of  unquestionable  certainty  have  been  already  made. 

Let  us  revert,  for  instance,  to  one  of  our  foraier  illustrations,  and 
consider  why  it  is  that,  with  exactly  the  same  amount  of  evidence, 
both  negative  and  positive,  we  did  not  reject  tlie  as.sertion  that  there 
are  black  swans,  while  we  should  refuse  credence  to  any  testimony 
which  assexted  that  there  were  men  weai'ing  their  heads  underneath 
their  shoulders.  The  first  assertion  was  more  ci'edible  than  the  latter. 
But  why  more  credible  ?  So  long  as  neither  phenomenon  had  been 
actually  witnessed,  what  reason  was  there  for  finding  the  one  harder 
to  be  believed  than  the  other  1  Apparently,  because  there  is  less  con- 
stancy in  the  colors  of  animals,  than  in  the  general  structure  of  their 
internal  anatomy.  But  how  do  we  know  this  ]  Doubtless,  fi-om 
experience.  It  appears,  then,  that  we  need  experience  to  inform  us, 
in  what  cases,  or  in  what  sorts  of  cases,  experience  is  to  be  relied 
upon.  Experience  must  be  consulted  in  order  to  learn  from  it  under 
what  circumstances  arguments  from  it  will  be  valid.  We  have  no 
ulterior  test  to  which  we  subject  expei'ience  in  general ;  but  we  make 
experience  its  own  test.  Experience  testifies,  that  among  the  uni- 
formities which  it  exhibits  or  seems  to  exhibit,  some  are  more  to  be 
relied  upon  than  others ;  and  uniformity,  therefore,  may  be  presumed, 
from  any  given  number  of  instances,  with  a  gi'eater  degree  of  assurance, 
in  proportion  as  the  case  belongs  to  a  class  in  which  the  nniformities 
have  hitherto  been  found  more  uniform. 

•This  mode  of  coixectihg  one  generalization  by  means  of  another, 
a  narrower  generalization  by  a  wider,  which  common  sense  suggests 
and  adopts  in  practice,  is  the  i-eal  type  of  scientific  Induction.  All 
that  art  can  do  is  but  to  give  accuracy  and  precision  to  this  process, 
and  adapt  it  to  all  varieties  of  cases,  without,  any  essential  alteration  in 
its  principle. 

There  are  of  course  no  means  of  ai:)plying  such  a  test  as  that  above 
described,  unless  we  already  possess  a  general  knowledge  of  tlie 
prevalent  character  of  the  uniformities  existing  throughout  natiu'e. 
The  indispensable  foundation,  therefore,  of  a  scientific  formula  of 
induction,  must  be  a  survey  of  the  inductions  to  which  mankind  have 
been  conducted  in  unscientific  practice ;  with  the  special  purpose  of 
ascertaining  -what  kinds  of  uniformities  have  been  found  perfectly 
invariable,  pei-vading  all  nature,  and  what  ai'e  those  which  have  been 
found  to  vary  with  difference  of  time,  place,  or  other  changeable 
circumstances. 

§  3.  The  necessity  of  such  a  survey  is  confirmed  by  the  considera- 
tion, that  the  stronger  inductions  are  the  touchstone  to  which  we 
always  endeavor  to  bring  the  weaker.  If  we  find  any  means  of 
deducing  one  of  the  less  strong  inductions  from  stronger  ones,  it 
acquires,  at  once,  all  the  strength  of  those  from  which  it  is  deduced ; 
and  even  adds  to  that  strength ;  since  the  independent  experience  on 
which  the  weaker  induction  previously  rested,  becomes  additional 


LAWS    OF    NATURE.  193 

evidence  of  the  truth  of  the  better  established  law  in  which  it  is  now 
found  to  be  included.  We  may  have  infeiTed,  from  historical  evidence, 
that  the  uncontrolled  government  of  a  monarchy,  of  au  aristocracy,  or 
of  the  majority,  will  commonly  be  a  tyranny  :  but  we  are  entitled  to 
rely  upon  this  generalization  with  much  gi-eater  assurance  when  it  is 
shown  to  be  a  corollary  from  still  better  established  truths ;  the 
infirmity  of  human  nature,  and  the  impossibility  of  maintaining  the 
predominance  of  reason  and  conscience  over  the  selfish  propensities 
by  any  means  except  such  as  the  supposition  of  absolute  power  neces- 
sarily excludes.  It  is  at  the  same  time  obvious  that  even  these  great 
facts  in  human  nature  derive  an  accession  of  evidence  from  the 
testimony  which  history  bears  to  the  effects  of  despotism.  The  strong 
induction  becomes  still  stronger  when  a  weaker  one  has  been  bound 
up  with  it. 

On  the  other  hand,  if  an  induction  conflicts  with  sti-onger  inductions, 
or  with  conclusions  capable  of  being  correctly  deduced  from  them,  then, 
unless  upon  reconsideration  it  should  appear  that  some  of  the  stronger 
inductions  have  been  sti'etched  too  far,  the  weaker  one  must  give  way. 
The  opinion  so  long  prevalent  that  a  comet,  or  any  other  unusual  ap- 
peaiance  in  the  heavenly  regions,  was  the  precursor  of  calamities  to 
mankind,  or  to  those  at  least  who  witnessed  it ;  the  belief  in  the  vera- 
city of  the  oracles  of  Delphi  or  Dodona ;  the  reliance  on  astrology,  or 
on  the  weather-prophecies  in  almanacs ;  were  doubtless  inductions  sup- 
posed to  be  grounded  on  exj)erience  :  and  faith  in  such  delusions  seems 
quite  capable  of  holding  out  against  a  gi-eat  multitude  of  failures,  pro- 
vided it  be  nourished  by  a  reasonable  number  of  casual  coincidences 
between  the  prediction  and  the  event.  What  has  really  put  an  end  to 
these  insufficient  inductions,  is  their  inconsistency  Avith  the  stronger  in- 
ductions subsequently  obtained  by  scientific  inquiry,  respecting  the 
causes  upon  which  terrestrial  events  really  depend ;  and  where  those 
scientific  truths  have  not  yet  peneti-ated,  the  same  or  similar  delusions 
still  prevail. 

It  may  be  affirmed  as  a  general  principle,  that  all  inductions,  whether 
strong  or  weak,  which  can  be  connected  together  by  a  ratiocination,  are 
confirmatory  of  one  another :  while  any  which  lead  deductively  to  con- 
sequences that  are  incompatible,  become  mutually  each  other's  test, 
showing  that  one  or  other  must  be  given  up,  or,  at  least,  more  guard- 
edly expressed.  In  the  case  of  inductions  which  confirm  each  other, 
the  one  which  becomes  a  conclusion  from  ratiocination  rises  to  at  least 
the  level  of  certainty  of  the  weakest  of  those  fi-om  which  it  is  deduced; 
while  in  general  all  are  more  or  less  increased  in  certainty.  Thus  the 
Torricellian  experiment,  though  a  mere  ease  of  three  more  general 
laws,  not  only  strengthened  gi'eatly  the  evidence  on  which  those  laws 
rested,  but  converted  one  of  them  (the  weight  of  the  atmosphere)  fi-om 
a  doubtful  generalization  into  one  of  the  best-established  doctrines  in 
the  range  of  physical  science. 

If,  then,  a  sui-vey  of  the  uniformities  which  have  been  ascertained  to 
exist  in  nature,  should  point  out  some  which,  as  far  as  any  human  pur- 
pose requires  ceitainty,  may  be  considered  as  absolutely  certain  and 
absolutely  universal ;  then  by  means  of  these  uniformities,  we  may  be 
able  to  raise  raultitudas  of  other  inductions  to  the  same  point  in  the 
scale.  For  if  we  can  show,  with  respect  to  any  induction,  that  either 
it  must  be  true,  or  one  of  these  certain  and  universal  inductions  must 
Bb 


194  INDUCTION. 

admit  of  an  exception  :  the  former  generalization  will  attain  the  same 
absolute  certainty  and  indefeasibleness  within  the  bounds  assigned  to 
it,  which  are  the  attributes  of  the  latter.  It  will  be  proved  to  be  a 
law ;  and  if  not  a  result  of  other  and  simpler  laws,  it  will  be  a  law  of 
nature. 

There  are  such  certain  and  universal^  inductions  ;  and  it  is  because 
there  are  such,  that  a  Logic  of  Induction  is  possible. 


CHAPTER  V. 

OF  THE   LAW  OF  UNIVERSAL   CAUSATION. 

§  1.  The  phenomena  of  nature  exist  in  two  distinct  relations  to  one 
another  ;  that  of  simultaneity,  and  that  of  succession.  Every  phenom- 
enon is  related,  in  an  uniform  manner,  to  some  phenomena  that  coexist 
with  it,  and  to  some  that  have  preceded  or  will  follow  it. 

Of  the  uniformities  which  exist  among  synchronous  phenomena,  the 
most  important,  on  every  account,  are  the  laws  of  number ;  and  next 
to  them  those  of  space,  or  in  other  words,  of  extension  and  figure.  The 
laws  of  number  are  common  to  synchronous  and  successive  phenome- 
na. That,  two  and  two  make  four,  is  equally, true  whether  the  second 
two  follow  the  first  two  or  accompany  them.  It  is  as  true  of  days  and 
years  as  of  feet  and  inches.  The  laws  of  extension  and  figure,  (in  other 
words,  the  theorems  of  geometry,  from  its  lowest  to  its  highest  branch- 
es,) are,  on  the  contrary,  laws  of  simultaneous  phenomena  only.  The 
various  parts  of  space,  and  of  the  objects  which  are  said  to  fill  space, 
coexist;  and  the  unvarying  laws  which  are  the  subject  of  the  science 
of  geometry,  are  an  expression  of  the  mode  of  their  coexistence. 

This  is  a  class  of  laws,  or  in  other  words,  of  uniformities,  for  the  com- 
prehension and  proof  of  which  it  is  not  necessary  to  suppose  any  lapse 
of  time,  any  variety  of  facts  or  events  succeeding  one  another.  If  all 
the  objects  in  the  universe  were  imchangeably  fixed,  and  had  remained 
in  that  condition  from  eternity,  the  propositions  of  geometry  would  still 
be  true  of  those  objects.  All  things  which  possess  extension,  or  in  other 
words,  which  fill  space,  are  subject  to  geometrical  laws.  Possessing 
extension,  they  possess  figure,  possessing  figure,  they  must  possess 
some  figure  in  particular,  and  have  all  the  properties  which  geometry 
assigns  to  that  figure.  If  one  body  be  a  sphere  and  the  other  a  cylin- 
der, of  equal  height  and  diameter,  the  one  will  be  exactly  two-thirds 
of  the  other,  let  the  nature  and  quality  of  the  material  be  what  it  will. 
Again,  each  body,  and  each  point  of  a  body,  must  occupy  some  place 
or  position  among  other  bodies ;  and  the  position  of  two  bodies  rela- 
tively to  each  other,  of  whatever  nature  the  bodies  be,  may  be  uner- 
ringly inferred  from  the  position  of  each  of  them  relatively  to  any  third 
body. 

In  the  laws  of  number,  then,  and  in  those  of  space,  we  recognize, 
in  the  most  unqualified  manner,  the  rigorous  universality  of  which  we 
are  in  quest.  Those  laws  have  been  in  all  ages  the  type  of  certainty, 
the  standard  of  comparison  for  all  inferior  degrees  of  evidence.  Their 
invariability  is  so  perfect,  that  we  are  unable  even  to  conceive  any 


LAW    OF    CAUSATION.  195 

exception  to  them;  and  philosophers  have  been  led,  although  (as  I 
have  endeavored  to  show)  erroneously,  to  consider  their  evidence  as 
lying  not  in  experience,  but  in  the  original  constitution  of  the  human 
intellect.  If,  therefore,  from  the  laws  of  space  and  number,  we  were 
able  to  deduce  unifermitics  of  any  other  description,  this  would  be 
conclusive  evidence  tu  us  that  those  other  unifonnities  possessed  the 
same  degi-ee  of  rigorous  certainty.  But  this  we  cannot  do.  From 
laws  of  space  and  number  alone,  nothing  can  be  deduced  but  laws  of 
space  and  number. 

Of  all  truths  relating  to  j)henomena,  the  most  valuable  to  us  are 
those  which  relate  to  the  order  of  their  succession.  On  a  knowledge 
of  these  is  founded  every  reasonable  anticipation  of  future  facts,  and 
whatever  power  we  possess  of  influencing  those  facts  to  our  advantage. 
Even  the  laws  of  geometry  are  chiefly  of  practical  importance  to  us  as 
being  a  portion  of  the  premisses  from  which  the  order  of  the  succession 
of  phenomena  may  be  inferred. 

Inasmuch  as  the  motion  of  bodies,  the  action  of  forces,  and  the 
propagation  of  influences  of  all  sorts,  take  place  in  certain  lines  and 
over  definite  spaces,  the  properties  of  those  lines  and  spaces  are  an 
important  part  of  the  laws  to  which  those  phenomena  are  themselves 
subject.  Moreover,  motions,  forces,  or  other  influences,  and  times,  arc 
numerable  quantities  ;  and  the  properties  of  number  are  applicable  to 
them  as  to  all  other  things.  But  although  the  laws  of  number  and 
space  are  important  elements  in  the  ascertainment  of  uniformities  of 
succession,  they  can  do  nothing  towards  it  when  taken  by  themselves. 
They  can  only  be  made  instrumental  to  that  purpose  when  we  combine 
with  them  additional  premisses,  expressive  of  uniformities  of  succession 
already  known.  By  taking,  for  instance,  as  premisses,  these  proposi- 
tions :  that  bodies  acted  upon  by  an  instantaneous  force  move  with 
uniform  velocity  in  straight  lines  ;  tliat  bodies  acted  upon  by  a  con- 
tinuous force  move  with  accelerated  velocity  in  straight  lines  ;  and 
that  bodies  acted  upon  by  two  forces  in  different  directions  move  in 
the  diagonal  of  a  parallelogram,  whose  sides  represent  the  direction 
and  quantity  of  those  forces  ;  we  may  by  combining  these  truths  with 
propositions  relating  to  the  properties  of  straight  lines  and  of  parallelo- 
grams, (as  that  a  tnangle  is  half  of  a  parallelogram  of  the  same  base 
and  altitude,)  deduce  another  important  uniformity  of  succession,  viz., 
that  a  body  moving  round  a  centre  of  force  describes  areas  propor- 
tional to  the  times.  But  unless  there  had  been  laws  of  succession  in 
our  premisses,  there  could  have  been  no  truths  of  succession  in  our 
conclusions.  A  similar  remark  might  be  extended  to  every  other  class 
of  phenomena  really  peculiar ;  and,  had  it  been  attended  to,  would 
have  prevented  many  chimerical  attempts  at  demonstrations  of  the 
indemonstrable,  and  explanations  of  what  cannot  be  explained. 

It  is  not,  therefore,  enough  for  us  that  the  laws  of  space,  which  are 
only  laws  of  simultaneous  phenomena,  and  the  laws  of  number,  which 
though  true  of  successive  phenomena  do  not  relate  to  their  succession, 
possess  that  rigorous  certainty  and  universality  of  which  we  are  in 
search.  "We  must  endeavor  to  find  some  law  of  succession  which  has 
those  same  attributes,  and  is  therefore  fit  to  be  made  the  foundation  of 
processes  for  discovering,  and  of  a  test  for  verifying,  all  other  uniformi- 
ties of  succession.  This  fundamental  law  must  resemble  the  truths  of 
geometry  in  their  most  remarkable  peculiarity,  that  of  never  being,  in 


196  INDUCTION. 

any  instance  whatever,  defeated  or  suspended  by  any  change  of  cir- 
cumstances. 

Now  among  all  those  uniformities  in  the  succession  of  phenomena, 
which  common  observation  is  sufficient  to  bring  to  light,  there  are  very 
few  which  have  any,  even  apparent,  pretension  to  this  rigorous  inde- 
feasibility  :  and  of  those  few,  one  only  has  been  found  capable  of  com- 
pletely sustaining  it.  In  that  one,  however,  we  recognize  a  law  which 
is  universal  also  in  another  sense ;  it  is  coextensive  with  the  entire 
field  of  successive  phenomena,  all  instances  whatever  of  succession 
being  examples  of  it.  This  law  is  the  Law  of  Causation.  It  is  an 
universal  truth  that  every  fact  which  has  a  beginning  has  a  cause. 

This  generalization  may  appear  to  some  minds  not  to  amount  to 
much,  since  after  all  it  asserts  only  this :  "  it  is  a  law,  that  every  event 
depends  upon  some  law."  We  must  not,  however,  conclude  that  the 
generality  of  the  principle  is  merely  verbal :  it  will  be  found  upon 
inspection  to  be  no  vague  or  unmeaning  assertion,  but  a  most  import- 
ant and  really  fundamental  truth. 

§  2.  The  notion  of  Cause  being  the  root  of  the  whole  theory  of  Induc- 
tion, it  is  indispensable  that  this  idea  should,  at  the  very  outset  of  our 
inquiry,  be,  with  the  utmost  practicable  degree  of  precision,  fixed  and 
determined.  If,  indeed,  it  were  necessary  for  the  purposes  of  induc- 
tive logic  that  the  strife  should  be  quelled,  which  has  so  long  raged 
among  the  different  schools  of  metaphysicians,  respecting  the  origin 
and  analysis  of  our  idea  of  causation  ;  the  promulgation,  or  at  least 
the  general  reception,  of  a  true  theory  of  induction,  might  be  con- 
sidered desperate,  for  a  long  time  to  come.  But  in  this  as  in  most 
other  respects,  the  science  of  the  Investigation  of  Truth  by  means  of 
Evidence,  has  no  need  to  bon-ow  any  premisses  from  the  science  of 
the  ultimate  constitution  of  the  human  mind,  except  such  as  have  at 
last,  though  often  after  long  controversy,  been  incoi-porated  into  all  the 
existing  systems  of  mental  philosophy,  or  all  but  such  as  may  be  re- 
garded as  essentially  effete. 

I  premise,  then,  that  when  in  the  course  of  this  inquiry  I  speak  of 
the  cause  of  any  phenomenon,  I  do  not  mean  a  cause  which  is  not 
itself  a  phenomenon  ;  I  make  no  research  into  the  ultimate,  or  ontolo- 
gical  cause  of  anything.  To  adopt  a  distinction  familiar  in  the  wri- 
tings of  the  Scotch  metaphysicians,  and  especially  of  Reid,  the  causes 
with  which  I  concern  myself  are  not  efficient,  but  physical  causes. 
They  are  causes  in  that  sense  alone,  in  which  one  physical  fact  may  be 
said  to  be  the  cause  of  another.  Of  the  efficient  causes  of  phenomena, 
or  whether  any  such  causes  exist  at  all,  I  am  not  called  upon  to  give 
an  opinion.  The  notion  of  causation  is  deemed,  by  the  schools  of 
metaphysics  most  in  vogue  at  the  present  moment,  to  imply  a  myste- 
rious and  most  powerful  tie,  such  as  cannot,  or  at  least  does  not,  exist 
between  any  physical  fact  and  that  other  physical  fact  upon  which  it  is 
invariably  consequent,  and  which  is  popularly  termed  its  cause  :  and 
thence  is  deduced  the  supposed  necessity  of  ascending  higher,  into  the 
essences  and  inherent  constitution  of  things,  to  find  the  tiue  cause,  the 
cause  which  is  not  only  followed  by,  but  actually  produces,  the  effect. 
No  such  necessity  exists  for  the  purposes  of  the  present  inquiry,  nor 
will  any  such  doctrine  be  found  in  the  following  pages.  But  neither 
\\\\\  there  be  found  anything  incompatible  with  it.     We  are  in  no  way 


LAW    OF    CAUSATION.  197 

concerned  in  the  question.  The  only  notion  of  a  cause,  which  the 
theory  of  induction  requires,  is  such  a  notion  as  can  be  gained  from 
experience.  The  Law  of  Causation,  the  recognition  of  wliicli  is  the 
main  pillar  of  inductive  philosophy,  is  but  the  familiar  truth,  that  inva- 
riability of  succession  is  found  by  observation  to  obtain  between  every 
fact  in  nature  and  some  other  fact  which  has  preceded  it ;  independ- 
ently of  all  consideration  respecting  the  ultimate  mode  of  production 
of  phenomena,  and  of  every  other  question  regarding  the  nature  of 
"  Things  in  themselves." 

Between  the  phenomena,  then,  which  exist  at  any  instant,  and  the 
phenomena  which  exist  at  the  succeeding  instant,  there  is  an  invariable 
order  of  succession ;  and,  as  wo  said  in  speaking  of  the  general  uni- 
formity of  the  course  of  nature,  this  web  is  composed  of  separate  fibres  ; 
this  collective  order  is  made  up  of  particular  sequences,  obtaining  inva- 
riably among  the  separate  parts.  To  certain  facts,  certain  facts  always 
do,  and,  as  we  believe,  always  will,  succeed.  The  invariable  antece- 
dent is  termed  the  cause  ;  the  invariable  consequent,  the  effect.  And 
the  universality  of  the  law  of  causation  consists  in  this,  that  every  con- 
sequent is  connected  in  this  manner  with  some  particular  antecedent, 
or  set  of  antecedents.  Let  the  fact  be  what  it  may,  if  it  has  begun  to 
exist,  it  was  preceded  by  some  fact  or  facts,  with  which  it  is  invaria- 
bly connected.  For  every  event,  there  exists  some  combination  of 
objects  or  events,  some  given  concurrence  of  circumstances,  positive 
and  negative,  the  occurrence  of  which  will  always  be  followed  by  that 
phenomenon.  We  may  not  have  found  out  what  this  concurrence  of 
circumstances  may  be ;  but  we  never  doubt  that  there  is  such  a  one, 
and  that  it  never  occurs  without  having  the  phenomenon  in  question 
as  its  effect  or  consequence.  Upon  the  universality  of  this  truth  de- 
pends the  possibility  of  reducing  the  inductive  process  to  rules.  The 
undoubted  assurance  we  have  that  there  is  a  law  to  be  found  if  we  only 
knew  how  to  find  it,  will  be  seen  presently  to  be  the  source  from  which 
the  canons  of  the  Inductive  Logic  derive  their  validity. 

§  3.  It  is  seldom,  if  ever,  between  a  consequent  and  one  single  an- 
tecedent, that  this  invariable  sequence  subsists.  It  is  usually  between 
a  consequent  and  the  sum  of  several  antecedents ;  the  concurrence  of 
them  all  being  requisite  to  produce,  that  is,  to  be  certain  of  being  fol- 
lowed by,  the  consequent.  In  such  cases  it  is  very  common  to  single 
out  one  only  of  the  antecedents  under  the  denomination  of  Cause,  call- 
ing the  others  merely  Conditions.  Thus  if  a  man  eats  of  a  particular 
dish,  and  dies  in  consequence,  that  is,  would  not  have  died  if  be  had 
not  eaten  of  it,  people  would  be  apt  to  say  that  eating  of  that  dish 
was  the  cause  of  his  death.  There  needs  not,  however,  be  any  inva- 
riable connexion  between  eating  of  the  dish  and  death  ;  but  thex'e 
certainly  is,  among  the  circumstances  which  took  place,  some  combi- 
nation or  other  upon  which  death  is  invariably  consecjuent :  as,  for 
instance,  the  act  of  eating  of  the  dish,  comliined  with  a  particular  bodily 
constitution,  a  particular  state  of  present  health,  and  perhaps  even  a 
certain  state  of  the  atmosphere  ;  the  whole  of  which  circumstances 
perhaps  constituted  in  this  particular  case  the  conditions  of  the  phenom- 
enon, or  in  other  words  the  set  of  antecedents  which  determined  it, 
and  but  for  which  it  would  not  have  happened.  The  real  Cause,  is 
the  vyhole  of  these  antecedents  ;  and  we  have,  philosophically  speak- 


198  INDUCTION. 

ino-,  no  right  to  give  the  name  of  cause  to  one  of  them,  exclusively  of 
the  others.  What,  in  the  case  we  have  supposed,  disguises  the  incor- 
rectness of  the  expression,  is  this  :  that  the  various  conditions,  except 
the  single  one  of  eating  the  food,  were  not  events  (that  is,  instantaneous 
chano-es,  or  successions  of  instantaneous  changes)  but  states,  possessing 
more  or  less  of  permanency  ;  and  might  therefore  have  preceded  the 
effect  by  an  indefinite  length  of  duration,  for  want  of  the  event  which 
was  requisite  to  complete  the  required  concurrence  of  conditions : 
while  as  soon  as  that  event,  eating  the  food,  occurs,  no  other  cause  is 
waited  for,  but  the  effect  begins  immediately  to  take  place :  and  hence 
the  appearance  is  presented  of  a  more  immediate  and  closer  connexion 
between  the  effect  and  that  one  antecedent,  than  between  the  effect 
and  the  remaining  conditions.  But  although  we  may  think  proper  to 
give  the  name  of  cause  to  that  one  condition,  the  fulfilment  of  which 
completes  the  tale,  and  brings  about  the  effect  without  further  delay ; 
this  condition  has  really  no  closer  relation  to  the  effect  than  any  of  the 
other  conditions  has.  The  production  of  the  consequent  required 
that  they  should  all  exist  immediately  previous,  though  not  that  they 
should  all  begi7i  to  exist  immediately  previous.  The  statement  of  the 
cause  is  incomplete,  unless  in  some  shape  or  other  we  introduce  all 
the  conditions.  A  man  takes  mercury,  goes  out  of  doors,  and  catches 
cold.  We  say,  perhaps,  that  the  cause  of  his  taking  cold  was  ex- 
posure to  the  air.  It  is  clear,  however,  that  his  having  taken  mercury 
may  have  been  a  necessary  condition  of  his  catching  cold;  and  though 
it  might  consist  with  usage  to  say  that  the  caiise  of  his  attack  was  ex- 
posure to  the  air,  to  be  accurate  we  ought  to  say  that  the  cause  was 
exposure  to  the  air  while  under  the  effect  of  mercury. 

If  we  do  not,  when  aiming  at  accuracy,  enumerate  all  the  condi- 
tions, it  is  only  because  some  of  them  will  in  most  cases  be  imder- 
stood  without  being  expressed,  or  because  for  the  purpose  in  view 
they  may  without  detriment  be  overlooked.  For  example,  when  we 
say,  the  cause  of  a  man's  death  was  that  his  foot  slipped  in  climbing  a 
ladder,  we  omit  as  a  thing  unnecessary  to  be  stated  the  circumstance 
of  his  weight,  though  quite  as  indispensable  a  condition  of  the  effect 
which  took  place.  When  we  say  that  the  assent  of  the  crown  to  a 
bill  makes  it  law,  we  mean  that  the  assent,  being  never  given  until  all 
the  other  conditions  are  fulfilled,  makes  up  the  sum  of  the  conditions, 
although  no  one  now  regards  it  as  the  principal  one.  When  the  deci- 
sion of  a  legislative  assembly  has  been  detennined  by  the  casting  vote 
of  the  chaimian,  we  often  say  that  this  one  person  was  the  cause  of  all 
the  effects  which  resulted  from  the  enactment.  Yet  we  do  not  really 
suppose  that  his  single  vote  contributed  more  to  the  result  than  that 
of  any  other  person  who  voted  in  the  affirmative  ;  but,  for  the  purpose 
we  have  in  view,  which  is  that  of  fixing  him  with  the  responsibility,  the 
share  which  any  other  person  took  in  the  transaction  is  not  material. 

In  all  these  instances  the  fact  which  was  dignified  by  the  name  of 
cause,  was  the  one  condition  which  came  last  into  existence.  But  it 
must  not  be  supposed  that  in  the  employment  of  the  term  this  or  any 
other  rule  is  always  adhered  to.  Nothing  can  better  show  the  absence 
of  any  scientific  ground  for  the  distinction  between  the  cause  of  a  phe- 
nomenon and  its  conditions,  than  the  capricious  manner  in  which  we 
select  from  among  the  conditions  that  which  we  choose  to  denominate 
the  cause.     However  numerous  the  conditions  may  be,  there  is  hardly 


LAW    OF    CAUSATION.  199 

any  of  them  which  may  not,  according  to  the  purpose  of  our  immediate 
discourse,  obtain  that  nominal  preeminence.  This  will  be  seen  by 
analyzing  the  conditions  of  some  one  familiar  phenomenon.  For 
example,  a  stone  thrown  into  water  falls  to  the  bottom.  What  are  the 
conditions  of  this  event]  In  the  first  place  there  must  be  a  stone,  and 
water,  and  the  stone  must  be  thrown  into  the  water ;  but,  these  suppo- 
sitions forming  part  of  the  enunciation  of  the  phenomenon  itself,  to 
include  them  also  among  the  conditions  would  be  a  vicious  tautology, 
and  this  class  of  conditions,  therefore,  have  never  received  the  name  of 
cause  from  any  but  the  schoolmen,  by  whom  they  were  called  the  ma- 
terial cause,  causa  materialis.  The  next  condition  is,  there  must  be 
an  earth :  and  accordingly  it  is  often  said,  that  the  fall  of  a  stone  is 
caused  by  the  earth ;  or  by  a  power  or  property  of  the  earth,  or  a  force 
exerted  by  the  earth,  all  of  which  are  merely  roundabout  ways  of  say- 
ing that  it  is  caused  by  the  earth  ;  or,  lastly,  the  earth's  atti-action;  which 
also  is  only  a  technical  mode  of  saying  that  the  earth  causes  the  motion, 
with  the  additional  particularity  that  the  motion  is  towards  the  earth, 
which  is  not  a  character  of  the  cause,  but  of  the  effect.  Let  us  now 
pass  to  another  condition.  It  is  not  enough  that  the  earth  should  exist; 
the  body  must  be  within  that  distance  fi'om  it,  in  which  the  earth's 
attraction  preponderates  over  that  of  any  other  body.  Accordingly  we 
may  say,  and  the  expression  would  be  confessedly  correct,  that  the 
cause  of  the  stone's  falling  is  its  being  within  the  sphere  of  the  earth's 
attraction.  We  proceed  to  a  further  condition.  The  stone  is  immersed 
in  water  :  it  is  therefore  a  condition  of  its  reaching  the  ground,  that  its 
specific  gravity  exceed  that  of  the  surrounding  fluid,  or  in  other  woi'ds 
that  it  surpass  in  weight  an  equal  volume  of  water.  Accordingly,  any 
one  would  be  acknowledged  to  speak  correctly  who  said,  that  the  cause 
of  the  stone's  going  to  the  bottom  is  its  exceeding  in  specific  gravity 
the  fluid  in  which  it  is  immersed. 

Thus  we  see  that  each  and  every  condition  of  the  phenomenon  may 
be  taken  in  its  turn,  and  with  equal  propriety  in  common  parlance,  but 
with  equal  impropriety  in  scientific  discourse  may  be  spoken  of  as  if 
it  were  the  entire  cause.  And  in  practice  that  particular  condition  is 
usually  styled  the  cause,  whose  share  in  the  matter  is  superficially  the 
most  conspicuous,  or  whose  requisiteness  to  the  production  of  the  effect 
we  happen  to  be  insisting  upon  at  the  moment.  So  great  is  the  force 
of  this  last  consideration,  that  it  often  induces  us  to  give  the  name  of 
cause  even  to  one  of  the  negative  conditions.  We  say,  for  example, 
The  cause  of  the  army's  being  surprised  was  the  sentinel's  being  oft' 
his  post.  But  since  the  sentinel's  absence  was  not  what  created  the 
enemy,  or  made  the  soldiers  to  be  asleep,  how  did  it  cause  them  to  be 
surprised  ?  All  that  is  really  meant  is,  that  the  event  would  not  have 
happened  if  he  had  been  at  his  duty.  His  being  off  his  post  was  no 
producing  cause,  but  the  mere  absence  (^  a  preventing  cause :  it  was 
simply  equivalent  to  his  non-existence.  From  nothing,  from  a  mere 
negation,  no  consequences  can  proceed.  All  effects  are  connected,  by 
the  law  of  causation,  with  some  set  oi positive  conditions  ;  negative  ones, 
it  is  true,  being  almost  always  required  in  addition.  In  other  words, 
every  fact  or  phenomenon  which  has  a  beginning,  invariably  arises 
when  some  certain  combination  of  positive  facts  exists,  provided  cer- 
tain other  positive  facts  do  not  exist. 

Since,  then,  mankind  are  accustomed,  with  acknowledged  propriety 


200  INDUCTION. 

SO  far  as  the  ordinances  of  language  are  concerned,  to  give  the  name 
of  cause  to  almost  any  one  of  the  conditions  of  a  phenomenon,  or  any 
portion  of  the  whole  number,  arbitrarily  selected,  without  excepting 
even  those  conditions  which  are  purely  negative,  and  in  themselves 
incapable  of  causing  anything ;  it  will  probably  be  admitted  without 
longer  discussion,  that  no  one  of  the  conditions  has  more  claim  to  that 
title  than  another,  and  that  the  real  cause  of  the  phenomenon  is  the  as- 
semblage of  all  its  conditions.  There  is,  no  doubt,  a  tendency  (which 
our  first  example,  that  of  death  from  taking  a  particular  food,  suffi- 
ciently illustrates)  to  associate  the  idea  of  causation  with  the  proximate 
antecedent  event,  rather  than  with  any  of  the  antecedent  states,  or 
permanent  facts,  which  may  happen  also  to  be  conditions  of  the  phe- 
nomenon ;  the  reason  being  that  the  event  not  only  exists,  but  begins 
to  exist  immediately  previous  :  while  the  other  conditions  may  have 
preexisted  for  an  indefinite  time.  And  this  tendency  shows  itself  very 
visibly  in  the  different  logical  fictions  which  are  resorted  to  even  by 
philosophers,  to  avoid  the  necessity  of  giving  the  name  of  cause  to 
anything  which  had  existed  for  an  indeterminate  length  of  time  before 
the  effect.  Thus,  rather  than  say  that  the  earth  causes  the  fall  of 
bodies,  they  ascribe  it  to  ^  force  exerted  by  the  earth,  or  an  attraction 
by  the  earth,  abstractions  which  they  can  represent  to  themselves  as 
exhausted  by  each  eftbrt,  and  therefore  constituting  at  each  successive 
instant  a  fresh  act,  simultaneous  with,  or  only  immediately  preceding, 
the  effect.  Inasmuch  as  the  coming  of  the  circumstance  which  com- 
pletes the  assemblage  of  conditions,  is  a  change  or  event,  it  thence 
happens  that  an  event  is  always  the  antecedent  in  closest  apparent 
proximity  to  the  consequent :  and  this  may  account  for  the  illusion 
which  disposes  us  to  look  upon  the  proximate  event  as  standing  more 
peculiarly  in  the  position  of  a  cause  than  any  of  the  antecedent  states. 
But  even  this  peculiarity  of  being  in  closer  proximity  to  the  effect 
than  any  other  of  its  conditions,  is,  as  we  have  already  seen,  far 
from  being  necessary  to  the  common  notion  of  a  cause ;  with  which 
notion,  on  the  contiary,  any  one  of  the  conditions,  either  positive  or 
negative,  is  found,  upon  occasion,  completely  to  accord. 

The  cause,  then,  philosophically  speaking,  is  the  sum  total  of  the  con- 
ditions, positive  and  negative,  taken  together ;  the  whole  of  the  contin- 
gencies of  every  description,  which  being  realized,  the  consequent 
invariably  follows.  The  negative  conditions,  however,  of  any  phenom- 
enon, a  special  enumeration  of  which  would  generally  be  very  prolix, 
may  be  all  summed  up  under  one  head,  namely,  the  absence  of  pre- 
venting or  counteracting  causes.  The  convenience  of  this  mode  of 
expression  is  grounded  mainly  upon  the  fact,  that  the  effects  of  any 
cause  in  counteracting  another  cause  may  in  most  cases  be,  with  strict 
scientific  exactness,  regarded  as  a  mere  extension  of  its  own  proper  and 
separate  effects.  If  gravity  retards  the  upward  motion  of  a  projectile, 
and  deflects  it  into  a  parabolic  trajectory,  it  produces,  in  so  doing,  the 
very  same  kind  of  effect,  and  even  (as  mathematicians  know)  the  same 
quantity  of  eftect,  as  it  does  in  its  ordinary  operation  of  causing  the 
fall  of  bodies  when  simply  deprived  of  their  support.  If  an  alkaline 
solution  mixed  with  an  acid  destroys  its  sourness,  and  prevents  it  from 
reddening  vegetable  blues,  it  is  because  the  specific  effect  of  the  alkali 
is  to  combine  with  the  acid,  and  form  a  compound  with  totally  different 
qualities.     This  property,  which  causes  of  all  descriptions  possess,  of 


LAW    OF    CAUSATION.  201 

preventing  the  effects  of  other  causes  by  virtue  (for  the  most  part)  of 
the  same  laws,  according  to  which  they  produce  their  own,*  enables 
us,  by  establishing  the  general  axiom  that  all  causes  are  liable  to  be 
counteracted  in  their  effects  by  one  another,  to  dispense  with  the  con- 
sideration of  negative  conditions  entirely,  and  limit  the  notion  of  cause 
to  the  assemblage  of  the  positive  conditions  of  the  phenomenon :  one 
negative  condition  invariably  understood,  and  the  same  in  all  instances 
(namely,  the  absence  of  all  counteracting  causes)  being  sufficient,  along 
with  the  sum  of  the  positive  conditions,  to  make  up  the  whole  set  of 
circumstances  upon  which  the  phenomenon  is  dependent. 

§  4.  Among  the  positive  conditions,  as  we  have  seen  that  there  are 
some  to  which,  in  common  parlance,  the  term  cause  is  more  readily 
and  frequently  awarded,  so  there  are  others  to  which  it  is,  in  ordinary 
circumstances,  refused.  In  most  cases  of  causation  a  distinction  is 
commonly  dra\vn  between  somethhig  which  acts,  and  some  other  thing 
which  is  acted  upon,  between  an  agent  and  a  patient.  Both  of  these, 
it  would  be  universally  allowed,  are  conditions  of  the  phenomenon  ; 
but  it  would  be  thought  absurd  to  call  the  latter  the  cause,  that  title 
being  reserved  for  the  former.  The  distinction,  however,  vanishes  on 
examination,  or  rather  is  found  to  be  only  verbal ;  arising  from  an  in- 
cident of  mere  expression,  namely,  that  the  object  said  to  be  acted  upon., 
and  which  is  considered  as  the  scene  in  which  the  effect  takes  place,  is 
commonly  included  ia  the  phrase  by  which  the  effect  is  spoken  of,  so 
that  if  it  were  also  reckoned  as  part  of  the  cause,  the  seeming  incon- 
gruity would  arise  of  its  being  supposed  to  cause  itself.  In  the  in- 
stance which  we  have  already  had,  of  falling  bodies,  the  question  was 
thus  put : — What  is  the  cause  which  makes  a  stone  fall  1  and  if  the 
answer  had  been  "the  stone  itself,"  the  expression  would  have  been 
in  apparent  contradiction  to  the  meaning  of  the  word  cause.  The 
stone,  therefore,  is  conceived  as  the  patient,  and  the  earth  (or,  accord- 
ing to  the  common  and  most  unphilosophical  practice,  some  occult 
quality  of  the  earth)  is  represented  as  the  agent,  or  cause.  But  that 
there  is  nothing  fundamental  in  the  distinction  may  be  seen  from  this, 
that  if  we  do  but  alter  the  mere  wording  of  the  question,  and  express 
it  thus,  What  is  the  cause  which  produces  vertical  motion  towards  the 
earth  ?  we  might  now,  without  any  incongruity,  speak  of  the  stone  or 
other  heavy  body  as  the  agent,  which,  by  virtue  of  its  own  laws  or 
properties,  commences  moving  towards  the  earth  ;  although  to  save  the 
established  doctrine  of  the  inactivity  of  matter,  men  usually  prefer  here 
also  to  ascribe  the  effect  to  an  occult  quality,  and  say  that  the  caase  is 
not  the  stone  itself,  but  the  weight  or  gravitation  of  the  stone. 

*  There  are  a  few  exceptions  ;  for  there  are  some  properties  of  objects  which  seem  to  be 
purely  preventive  ;  as  the  property  of  opaque  bodies,  by  which  they  intercept  the  passage 
of  light.  This,  so  far  as  we  are  able  to  understand  it,  appears  an  instance  not  of  one  cause 
counteracting  another  by  the  same  law  whereby  it  produces  its  own  efl'ects,  but  of  an 
agency  vvhicfi  manifests  itself  in  no  other  way  than  in  defeating  the  effects  of  another 
agency.  If  we  knew  upon  wnat  other  relations  to  light,  or  upon  what  peculiarities  of 
structure  opacity  depends,  we  might  find  that  this  is  only  an  apparent,  not  a  real,  excep- 
tion to  the  general  proposition  in  the  text.  In  any  case  it  needs  not  affect  the  practical 
application.  The  formula  which  includes  all  the  negative  conditions  of  an  effect  in  the 
single  one  of  the  absence  of  counteracting  causes,  is  not  violated  by  such  cases  as  this; 
although,  if  all  counteracting  agencies  were  of  this  description,  there  would  be  no  pur- 
pose served  by  employing  the  formula,  since  we  should  still  have  to  enumerate  specially 
the  negative  conditions  of  each  phenomenon,  instead  of  regarding  them  as  implicitly  con- 
tained in  the  positive  laws  of  the  various  other  agencies  in  nature. 

Cc 


202  INDUCTION. 

Those  who  have  contended  for  a  radical  distinction  between  agent 
and  patient,  have  generally  conceived  the  agent  as  that  which  causes 
some  state  of,  or  some  change  in  the  state  of,  another  object  which  is 
called  the  patient.  But  a  little  reflection  will  show  that  the  license 
we  assume  of  speaking  of  phenomena  as  states  of  the  various  objects 
which  take  part  in  them,  (an  artifice  of  which  so  much  use  has  been 
made  by  some  philosophers.  Brown  in  particular,  for  the  apparent 
explanation  of  phenomena,)  is  simply  a  sort  of  logical  fiction,  useful 
sometimes  as  one  among  several  modes  of  expression,  but  which 
should  never  be  supposed  to  be  the  statement  of  a  philosophical  truth. 
Even  those  of  the  attributes  of  an  object  which  might  seem  with 
greatest  propriety  to  be  called  states  of  the  object  itself,  its  sensible 
qualities,  its  color,  hardness,  shape,  and  the  like,  are,  in  reality,  (as  no 
one  has  pointed  out  more  clearly  than  Brown  himself,)  phenomena  of 
causation,  in  which  the  substance  is  distinctly  the  agent,  or  producing 
cause,  the  patient  being  our  own  organs,  and  those  of  other  sentient 
beings.  What  we  call  the  states  of  objects,  are  always  sequences  into 
which  those  objects  enter,  generally  as  antecedents  or  causes;  and 
things  are  never  more  active  than  in  the  production  of  those  phenomena 
in  which  they  are  said  to  be  acted  upon.  Thus,  in  the  last  example, 
that  of  a  sensation  produced  in  our  organs,  are  not  the  laws  of  our 
organization,  and  even  those  of  our  minds,  as  directly  operative  in 
determining  the  effect  produced,  as  the  laws  of  the  outward  object] 
Though  we  call  prussic  acid  the  agent  of  a  man's  death,  are  not  the 
whole  of  the  vital  and  organic  properties  of  the  patient  as  actively 
instrumental  as  the  poison,  in  the  chain  of  effects  which  so  rapidly 
terminates  his  sentient  existence  1  In  the  process  of  education,  we 
may  call  the  teacher  the  agent,  and  the  scholar  only  the  matei'ial  acted 
upon ;  yet  in  truth  all  the  facts  which  preexisted  in  the  scholar's  mind 
exert  either  cooperating  or  counteracting  agencies  in  relation  to  the 
teacher's  efforts.  It  is  not  light  alone  which  is  the  agent  in  vision,  but 
light  coupled  with  the  active  properties  of  the  eye  and  brain,  and  with 
those  of  the  visible  object.  The  distinction  between  agent  and  patient 
is  merely  verbal :  patients  are  always  agents ;  in  a  great  proportion, 
indeed,  of  all  natural  phenomena,  they  are  so  to  such  a  degi'ee  as 
to  react  most  forcibly  upon  the  causes  which  acted  upon  them  :  and 
even  when  this  is  not  the  case,  they  contribute,  in  the  same  manner  as 
any  of  the  other  conditions,  to  the  production  of  the  effect  of  which 
they  are  vulgarly  treated  as  the  mere  theatre.  All  the  positive  con- 
ditions of  a  phenomenon  are  alike  agents,  alike  active ;  and  in  any 
expression  of  the  cause  which  professes  to  be  a  complete  one,  none  of 
them  can  with  reason  be  excluded,  except  such  as  have  already  been 
implied  in  the  words  used  for  describing  the  effect ;  nor  by  including 
even  these  would  there  be  incurred  any  but  a  merely  verbal  incon- 
sistency. 

§  5.  It  now  remains  to  advert  to  a  distinction  which  is  of  first-rate 
importance  both  for  clearing  up  the  notion  of  cause,  and  for  obviating 
a  very  specious  objection  often  made  against  the  view  which  we  have 
taken  of  the  subject. 

When  we  define  the  cause  of  anything  (in  the  only  sense  in  which 
the  present  inquiry  has  any  concern  with  causes)  to  be  "  the  antecedent 
which  it  invariably  follows,"  we  do  not  use  thi;:  phrase  as  exactly 


LAW    OF    CAUSATION.  203 

synonymous  with  "  tlie  antecedent  which  it  invariably  has  followed  in 
our  past  experience."  Such  a  mode  of  viewing  causation  would  be 
liable  to  the  objection  very  plausibly  urged  by  Dr.  Reid,  namely,  that 
according  to  this  doctrine  night  must  be  the  cause  of  day,  and  day  the 
cause  of  night ;  since  these  phenomena  have  invariably  succeeded  one 
another  from  the  beginning  of  the  world.  But  it  is  necessary  to  our 
using  the  word  cause,  that  we  should  believe  not  only  that  the  ante- 
cedent always  has  been  followed  by  the  consequent,  but  that,  as  long 
as  the  present  constitution  of  things  endurcss,  it  always  will  be  so.  And 
this  would  not  be  true  of  day  and  night.  We  do  not  believe  that  night 
will  be  followed  by  day  under  any  imaginable  circumstances,  but  only 
that  it  will  be  ?>o,prov.idcd  the  sun  rises  above  the  horizon.  If  the  sun 
ceased  to  rise,  which,  for  aught  we  know,  may  be  perfectly  compatible 
with  the  general  laws  of  matter,  night  would  be,  or  might  be,  eternal. 
On  the  other  hand,  if  the  sun  is  above  the  horizon,  his  light  not  extinct, 
and  no  opaque  body  between  us  and  him,  we  believe  firmly  that  unless 
a  change  takes  place  in  the  properties  of  matter,  this  combination  of 
antecedents  will  be  followed  by  the  consequent,  day ;  that  if  the  com- 
bination of  antecedents  could  be  indefinitely  prolonged,  it  would  be 
always  day ;  and  that  if  the  same  combination  had  always  existed,  it 
would  always  have  been  day,  quite  independently  of  night  as  a  previous 
condition.  Therefore  is  it  that  we  do  not  call  night  the  cause,  nor  even 
a  condition  of  day.  The  existence  of  the  sun  (or  some  such  luminous 
body),  and  there  being  no  opaque  medium  in  a  straight  line*  between 
that  body  and  the  part  of  the  earth  where  we  are  situated,  are  the  sole 
conditions  ;  and  the  union  of  these,  without  the  addition  of  any  super- 
fluous circumstance,  constitutes  the  cause.  This  is  what  writers  mean 
when  they  say  that  the  notion  of  cause  involves  the  idea  of  necessity. 
If  there  be  any  meaning  which  confessedly  belongs  to  the  term  neces- 
sity, it  is  unconditionalmss.  That  which  is  necessary,  that  which  must 
be,  means  that  which  will  be,  whatever  supposition  we  may  make  in 
regard  to  all  other  things.  The  succession  of  day  and  night' evidently 
is  not  necessary  in  this  sense.  It  is  conditional  upon  the  occurrence  of 
other  antecedents.  That  which  wDl  be  followed  by  a  given  consequent 
when,  and  only  when,  some  third  circumstance  also  exists,  is  not  the 
cause,  oven  although  no  case  should  have  ever  occuiTed  in  which  the 
phenomenon  took  place  without  it. 

Invariable  sequence,  therefore,  is  not  synonymous  with  causation, 
unless  the  sequence,  besides  being  invariable,  is  unconditional.  There 
are  sequences  as  uniform  in  past  experience  as  any  others  whatever, 
which  yet  we  do  not  regard  as  cases  of  causation,  but  as  conjunctions, 
in  some  sort  accidental.  Such,  to  a  philosopher,  is  that  of  day  and 
night.  The  one  might  have  existed  for  any  length  of  time,  and  the 
other  not  have  followed  the  sooner  for  its  existence  ;  it  fi)llows  only  if 
certain  other  antecedents  exist ;  and  where  those  antecedents  existed, 
it  would  follow  in  any  case.  No  one,  probably,  ever  called  night  the 
cause  of  day ;  mankind  must  so  soon  have  arrived  at  the  very  obvious 
generalization,  that  the  state  of  general  illumination  which  we  call  day 

*  I  use  the  words  "  straight  line"  for  brevity  and  simplicity.  In  reality  the  line  in  ques- 
tion is  not  exactly  straight,  for,  from  the  effects  of  refraction,  we  actually  see  the  snn  for  a 
short  interval  during  which  the  opaque  mass  of  the  earth  is  interposed  in  a  direct  line  be- 
tween the  sun  and  our  eyes ;  thus  realizing,  though  but  to  a  limited  extent,  the  coveted 
desideratum  of  seeing  round  a  corner. 


204  INDUCTION. 

would  follow  tlie  presence  of  a  sufficiently  luminous  body,  whether 
darkness  had  preceded  or  not. 

We  may  define,  therefore,  the  cause  of  a  phenomenon  to  be  the  an- 
iecedent,  or  the  concurrence  of  antecedents,  upon  which  it  is  invariatly 
and  uncondUionally  consequent.  Or  if  we  adopt  the  convenient  modi- 
fication of  the  meaning  of  the  word  cause,  which  confines  it  to  the  as- 
semblage of  positive  conditions,  without  the  negative,  then  instead  of 
"unconditionally,"  we  must  say,  "subject  to  no  other  than  negative 
conditions." 

It  is  evident,  that  from  a  limited  number  of  unconditional  sequences, 
there  will  result  a  much  greater  number  of  conditional  ones.  Certain 
causes  being  given,  that  is,  certain  antecedents  which  are  uncondition- 
ally followed  by  certain  consequents ;  the  mere  coexistence  of  these 
causes  will  give  rise  to  an  unlimited  number  of  additional  uniformities. 
If  two  causes  exist  together,  the  effects  of  both  ^vill  exist  together  ; 
and  if  many  causes  coexist,  these  causes  (by  what  we  shall  term  here- 
after, the  intermixture  of  their  laws)  will  give  rise  to  new  effects, 
accompanying  or  succeeding  one  another  in  some  particular  order, 
which  order  will  be  invariable  while  the  causes  continue  to  coexist,  but 
no  longer.  The  motion  of  the  earth  in  a  given  orbit  round  the  sun  is 
a  series  of  changes  which  follow  one  another  as  antecedents  and  con- 
sequents, and  will  continue  to  do  so  while  the  sun's  attraction,  and  the 
force  with  which  the  earth  tends  to  advance  in  a  direct  line  through 
space,  continue  to  coexist  in  the  same  quantities  as  at  present.  But 
vary  either  of  these  causes,  and  the  unvarying  succession  of  motions 
would  cease  to  take  place.  The  series  of  the  earth's  motions,  there- 
fore, though  a  case  of  sequence  invariable  within  the  limits  of  human 
experience,  is  not  a  case  of  causation.     It  is  not  unconditional. 

To  distinguish  these  conditionally  uniform  sequences  from  those 
which  are  uniform  unconditionally  ;  to  ascertain  whether  an  apparently 
invariable  antecedent  of  some  consequent  is  really  one  of  its  conditions, 
or  whether,  in  the  absence  of  that  antecedent,  the  effect  would  equally 
have  followed  from  some  other  portion  of  the  circumstances  which  are 
present  whenever  it  occurs ;  is  a  principal  part  of  the  great  problem 
of  Induction ;  and  is  one  of  those  questions,  the  principles  of  the  solu- 
tion of  which  will,  it  is  to  be  hoped,  result  from  the  inquiry  we  have 
undertaken. 

§  6.  Does  a  cause  always  stand  \%ath  its  effect  in  the  relation  of  an- 
tecedent and  consequent]  Do  we  not  often  say  of  two  simultaneous 
facts  that  they  are  cause  and  effect — as  when  we  say  that  fire  is  the 
cause  of  warmth,  the  sun  and  moisture  the  cause  of  vegetation,  and  the 
like  1  It  is  certain  that  a  cause  does  not  necessarily  perish  because 
its  effect  has  been  produced ;  the  two,  therefore,  do  very  generally 
coexist ;  and  there  are  some  appearances,  and  some  common  expres- 
sions, seeming  to  imply  not  only  that  causes  may,  but  that  they  must, 
be  contemporaneous  with  their  effects.  Cessante  causd,  cessat  ct  effec- 
tus,  has  been  a  dogma  of  the  schools  :  the  necessity  for  the  continued 
existence  of  the  cause  in  order  to  the  continuance  of  the  effect,  seems 
to  have  been  once  a  general  doctrine  among  philosophers.  Mr.  Whe- 
well  observes  that  Kepler's  numerous  attempts  to  account  for  the 
motion  of  the  heavenly  bodies  on  mechanical  principles,  were  rendered 
abortive  by  his  always  supposing  that  the  force  which  set  those  bodiea 


LAW    OF    CAUSATION.  205 

in  motion  must  continue  to  operate  in  order  to  keep  up  the  motion 
which  it  at  first  produced.  Yet  there  were  at  all  times  many  familiar 
instances  in  open  contradiction  to  this  supposed  axiom.  A  coup  de 
soleil  gives  a  man  a  brain  fever :  will  the  fever  go  off  as  soon  as  he  is 
moved  out  of  the  sunshine  ]  A  sword  is  run  through  his  body  :  must 
the  sword  remain  in  his  body  in  order  that  he  may  continue  dead  ] 
A  ploughshare  once  made,  remains  a  ploughshare,  without  any  contin- 
uance of  heating  and  hammering,  and  even  after  the  man  who  heated 
and  hammered  it  has  been  gathered  to  his  fathers.  On  the  other  hand, 
the  pressure  which  forces  up  the  mercury  in  an  exhausted  tube  must 
be  continued  in  order  to  sustain  it  in  the  tube.  This  (it  may  be 
replied,)  is  because  another  force  is  acting  without  intermission,  the 
force  of  gravity,  which  would  restore  it  to  its  level,  unless  counter- 
poised by  a  force  equally  constant.  But  again ;  a  tight  bandage 
causes  pain,  which  pain  will  sometimes  go  off  as  soon  as  the  bandage 
is  removed.  The  illumination  which  the  sun  diffuses  over  the  earth 
ceases  when  the  sun  goes  down. 

The  solution  of  these  difficulties  will  be  found  in  a  very  simple  dis- 
tinction. The  conditions  which  are  necessary  for  the  first  production 
of  a  phenomenon,  are  occasionally  also  necessary  for  its  continuance; 
but  more  commonly  its  continuance  requires  no  condition  except  neg- 
ative ones.  Most  things,  once  produced,  continue  as  they  are,  until 
something  changes  or  destroys  them ;  but  some  require  the  permanent 
presence  of  the  agencies  which  produced  them  at  first.  These  may, 
if  we  please,  be  considered  as  instantaneous  phenomena,  requiring  to 
be  renewed  at  each  instant  by  the  cause  by  which  they  were  at  first 
generated.  Accordingly,  the  illumination  of  any  given  point  of  space 
has  always  been  looked  upon  as  an  instantaneous  fact,  which  perishes 
and  is  perpetually  renewed  as  long  as  the  necessary  conditions  subsist.. 
If  we  adopt  this  language  we  are  enabled  to  avoid  admitting  that  the 
continuance  of  the  cause  is  ever  required  to  maintain  the  effect.  We 
may  say,  it  is  not  required  to  maintain  but  to  reproduce  the  effect,  or 
else  to  counteract  some  force  tending  to  destroy  it.  And  this  may  be 
a  convenient  phraseology.  But  it  is  only  a  phraseology.  The  fact 
remains,  that  in  some  cases  (though  these  are  a  minority),  the  continu- 
ance of  the  conditions  which  produced  an  effect  is  necessary  to  the 
continuance  of  the  effect. 

As  to  the  ulterior  question,  whether  it  is  strictly  necessary  that  the 
cause,  or  assemblage  of  conditions,  should  precede,  by  ever  so  short  an 
instant,  the  production  of  the  effect,  (a  question  raised  and  argued  with 
much  ingenuity  by  a  writer  from  whom  we  have  quoted,*)  we  think 
the  inquiry  an  unimportant  one.  There  certainly  are  cases  in  which 
the  effect  follows  without  any  interval  perceptible  to  our  faculties  ;  and 
when  there  is  an  interval  we  cannot  tell  by  how  many  intermediate 
links  imperceptible  to  us  that  interval  may  really  be  filled  up.  But 
even  granting  that  an  effect  may  commence  simultaneously  with  its 
cause,  the  view  I  have  taken  of  causation  is  in  no  way  practically  af- 
fected. Whether  the  cause  and  its  effect  be  necessarily  successive  or 
not,  causation  is  still  the  law  of  the  succession  of  phenomena.  Every- 
thing which  begins  to  exist  must  have  a  cause  ;  what  does  not  begin  to 
exist  does  not  need  a  cause  ;  what  causation  has  to  account  for  is  the 

*  The  reviewer  of  Mr.  Whewcll  in  the  Quarterly  Review. 


206  INDUCTION. 

origin  of  phenomena,  and  all  the  successions  of  phenomena  must  be 
resolvable  into  causation.  These  are  the  axioms  of  our  doctrine.  If 
these  be  gi-anted,  we  can  afford,  though  I  see  no  necessity  for  doing 
so,  to  drop  the  words  antecedent  and  consequent  as  applied  to  catrse 
and  effect.  I  have  no  objection  to  define  a  cause,  the  assemblage  of 
phenomena,  which  occuning,  some  otlier  phenomenon  invariably  com- 
mences, or  has  its  origin.  Whether  the  effect  coincides  in  point  of 
time  with,  or  immediately  follows,  the  hindmost  of  its  conditions, 
is  immaterial.  At  all  events  it  does  not  precede  it ;  and  when  we  are 
in  doubt,  between  two  coexistent  phenomena,  which  is  cause  and  which 
effect,  we  rightly  deem  the  question  solved  if  we  can  ascertain  which 
of  them  preceded  the  other. 

§  7.  It  continually  happens  that  several  different  phenomena,  which 
are  not  in  the  slightest  degi-ee  dependent  or  conditional  upon  one 
another,  are  found  all  to  depend,  as  the  phrase  is,  upon  one  and  the 
same  agent ;  in  other  words,  one  and  the  same  phenomenon  is  seen  to 
be  followed  by  several  sorts  of  effects  quite  heterogeneous,  but  w^hich 
go  on  simultaneously  one  with  another ;  provided,  of  course,  that  all 
other  conditions  requisite  for  each  of  them  also  exist.  Thus,  the  sun 
produces  the  celestial  motions,  it  produces  daylight,  and  it  produces 
heat.  The  earth  causes  the  fall  of  heavy  bodies,  and  it  also,  in  its 
capacity  of  an  immense  magnet,  causes  the  phenomena  of  the  magnetic 
needle.  A  crystal  of  galena  causes  the  sensations  of  hardness,  of 
weight,  of  cubical  form,  of  gray  color,  and  many  others  between  w^hich 
we  can  trace  no  interdependence.  The  pui-pose  to  which  the  phraseol- 
ogy of  Properties  and  Powers  is  specially  adapted,  is  the  expression  of 
this  sort  of  cases.  When  the  same  phenomenon  is  followed  (either 
subject  or  not  to  the  presence  of  other  conditions)  by  effects  of  differ- 
ent and  dissimilar  orders,  it  is  usual  to  say  that  each  different  sort  of 
effect  is  produced  by  a  different  property  of  the  cause.  Thus  we  dis- 
tinguish the  attractive,  or  gravitative,  property  of  the  earth,  and  its 
magnetic  property ;  the  gravitative,  luminiferous,  and  calorific  proper- 
ties of  the  sun  ;  the  color,  shape,  weight,  and  hardness  of  the  crys- 
tal. These  are  mere  phrases,  wdiich  explain  nothing,  and  add  nothing 
to  our  knowdedge  of  the  subject;  but  considered  as  absti'act  names 
denoting  the  connexion  between  the  different  effects  produced  and  the 
object  which  produces  them,  they  are  a  very  powerful  instrument  of 
abridgment,  and  of  that  acceleration  of  the  process  of  thought  which 
abridgment  accomplishes. 

This  class  of  considerations  leads  us  to  a  conception  which  we  shall 
find  of  great  importance  in  the  interpretation  of  nature  ;  that  of  a  Per- 
manent Cause,  or  original  natural  agent.  There  exist  in  nature  a  num- 
ber of  permanent  causes,  which  have  subsisted  ever  since  the  human 
race  has  been  in  existence,  and  for  an  indefinite  and  probably  enonnous 
length  of  time  previous.  The  sun,  the  earth  and  jilanets,  with  their 
various  constituents,  air,  water,  and  the  other  distinguishable  substances, 
whether  simple  or  compound,  of  which  nature  is  made  up,  are  such 
Peraianent  Causes.  These  have  existed,  and  the  effects  or  consequen- 
ces which  they  were  fitted  to  produce  have  taken  place,  (as  often  as  the 
other  conditions  of  the  production  met,)  from  the  very  beginning  of  our 
experience.  But  we  can  give,  scientifically  speaking,  no  account  of  the 
origin  of  the  Permanent  Causes  themselves.     Wliy  these  particular  nat- 


LAW    OF    CAUSATION.  207 

ural  agents  existed  originally  and  no  others,  or  why  they  are  commin- 
gled in  such  and  such  proportions,  and  distributed  in  such  and  such  a 
manner  throughout  space,  is  a  question  we  cannot  answer.  More  than 
this  :  we  can  discover  nothing  regular  in  the  distribution  itself;  we  can 
reduce  it  to  no  uniformity,  to  no  law.  There  are  no  means  by  which, 
from  the  distribution  of  these  causes  or  agents  in  one  part  of  spaco,  we 
could  conjecture  whether  a  similar  distribution  prevails  in  another. 
The  coexistence,  therefore,  of  Primeval  Causes,  tanks,  to  us,  among 
merely  casual  concurrences :  and  all  those  sequences  or  coexistences 
among  the  effects  of  several  such  causes,  which,  though  invariable  while 
those  causes  coexist,  would,  if  the  coexistence  terminated,  terminate 
along  with  it,  we  do  not  class  as  cases  of  causation,  or  laws  of  nature : 
we  can  only  calculate  upon  finding  these  sequences  or  coexistences 
where  we  know,  by  direct  evidence,  that  the  natural  agents  on  the 
properties  of  which  they  ultimately  depend,  are  distributed  in  the  re- 
quisite manner.  These  Permanent  Causes  are  not  always  objects ; 
they  are  sometimes  events,  that  is  to  say,  periodical  cycles  of  events, 
that  being  the  only  mode  in  which  events  can  possess  the  property  of 
permanence.  Not  only,  for  instance,  is  the  earth  itself  a  permanent 
cause,  or  primitive  natural  agent,  but  the  earth's  rotation  is  so  too :  it 
is  a  cause  which  has  produced,  from  the  earliest  period  (by  the  aid  of 
other  necessary  conditions),  the  succession  of  day  and  night,  the  ebb 
and  flow  of  the  sea,  and  many  other  effects,  while,  as  we  can  assign  no 
cause  (except  conjectm-ally)  for  the  rotation  itself,  it  is  entitled  to  be 
ranked  as  a  pi'imeval  cause.  It  is,  however,  only  the  origin  of  the  ro- 
tation which  is  mysterious  to  us :  once  begun,  its  continuance  is  account- 
ed for  by  the  first  law  of  motion  (that  of  the  permanence  of  rectilineal 
motion  once  impressed)  combined  with  the  gi-avitation  of  the  parts  of 
the  earth  towards  one  another. 

All  phenomena  without  exception  which  begin  to  exist,  that  is,  all 
except  the  primeval  causes,  are  effects  either  immediate  or  remote  of 
those  primitive  facts,  or  of  some  combination  of  them.  There  is  no 
Thing  produced,  no  event  happening,  in  the  universe,  which  is  not  con- 
nected by  an  uniformity,  or  invariable  sequence,  with  some  one  or  more 
of  the  phenomena  which  preceded  it ;  insomuch  that  it  will  happen  again 
as  often  as  those  phenomena  occur  again,  and  as  no  other  phenomenon 
having  the  character  of  a  counteracting  cause  shall  coexist.  These  an- 
tecedent phenomena,  again,  were  connected  in  a  similar  manner  with 
some  that  preceded  them;  and  so  on,  until  we  reach,  as  the  ultimate 
step,  either  the  properties  of  some  one  primeval  cause,  or  the  conjunc- 
tion of  several.  The  whole  of  the  phenomena  of  nature  were  therefore 
the  necessary,  or  in  other  words,  the  unconditional,  consequences  of 
the  original  collocation  of  the  Permanent  Causes. 

The  state  of  the  whole  universe  at  any  instant,  we  believe  to  be  the 
consequence  of  its  state  at  the  previous  instant:  insomuch  that  if  we 
knew  all  the  agents  which  exist  at  the  present  moment,  their  colloca- 
tion in  space,  and  their  properties,  in  other  words  the  laws  of  their 
agency,  we  could  predict  the  whole  subsequent  history  of  the  universe, 
at  least  unless  some  new  volition  of  a  power  capable  of  controlHng  the 
universe  should  supei-vene.*     And  if  any  particular  state  of  the  entire 

*  To  the  universality  which  mankind  are  agreed  in  ascribing  to  the  Law  of  Causation, 
there  is  one  claim  of  exception,  one  disputed  case,  that  of  the  Human  Will ;  the  detennina- 
tions  of  which  a  large  class  of  metaphysicians  are  not  willing  to  regard  as  following  the 


208  INDUCTION. 

universe  should  ever  recur  a  second  time,  (which,  however,  all  experi- 
ence combines  to  assure  us  will  never  happen,)  all  subsequent  states 
would  retui-n  too,  and  history  would,  Uke  a  circulating  decimal  of  many- 
figures,  periodically  repeat  itself: — 

Jam  redit  et  \irgo,  redeunt  Saturnia  regna 

Alter  eiit  turn  Tiphvs,  et  altera  quae  vehat  Argo 
Delectos  heroas  ;  eruntqooque  altera  bella, 
Atque  iterum  ad  TrOiam  magnus  mittetur  Achilles. 

And  though  things  do  not  really  revolve  in  this  eternal  round,  the  whole 
series  of  events  in  the  history  of  the  universe,  past  and  future,  is  not  the 
less  capable,  in  its  own  nature,  of  being  constructed  a  priori  by  any 
one  whom  we  can  suppose  acquainted  with  the  original  distribution  of 
all  natural  agents,  and  with  the  whole  of  their  properties,  that  is,  the 
laws  of  succession  existing  between  them  and  their  effects  :  saving  the 
infinitely  more  than  human  powers  of  combination  and  calculation 
which  would  be  required,  even  in  one  possessing  the  data,  for  the  actual 
performance  of  the  task. 

§  8.  Since  everything  which  occurs  in  the  universe  is  determined  by 
laws  of  causation  and  collocations  of  the  original  causes,  it  follows  that 
the  coexistences  which  are  obsei-vable  among  effects  cannot  be  them- 
selves the  subject  of  any  similar  set  of  laws,  distinct  from  laws  of  causa- 
tion. Uniformities  there  are,  as  well  of  coexistence  as  of  succession, 
among  the  effects;  but  these  must  in  all  cases  be  a  mere  result  either 
of  the  identity  or  of  the  coexistence  of  their  causes :  if  the  causes  did 
not  coexist,  neither  could  the  effects.  And  these  causes  being  also 
effects  of  prior  causes,  and  these  of  others,  until  we  reach  the  primeval 
causes,  it  follows  that  (except  in  the  case  of  effects  which  can  be  traced 
immediately  or  remotely  to  one  and  the  same  cause),  the  coexistences 
of  phenomena  can  in  no  case  be  universal,  unless  the  coexistences  of 
the  pi-imeval  causes  to  which  the  effects  are  ultimately  traceable,  can 
be  reduced  to  an  universal  law :  but  we  have  seen  that'  they  cannot. 
There  are,  accordingly,  no  original  and  independent,  in  other  words, 
no  unconditional,  uniformities  of  coexistence  between  effects  of  different 
causes ;  if  they  coexist,  it  is  only  because  the  causes  have  casually  coex- 
isted. The  only  independent  and  unconditional  coexistences  which  are 
sufficiently  invai'iable  to  have  any  claim  to  the  character  of  laws,  are 
between  diff'erent  and  mutually  independent  effects  of  the  same  cause; 
in  other  words,  between  different  properties  of  the  same  natural  agent. 
This  portion  of  the  Laws  of  Nature  will  be  ti-eatedof  in  the  latter  part 

causes  called  motives,  according  to  as  strict  laws  as  those  which  they  suppose  to  exist  in 
the  world  of  mere  matter.  This  controverted  point  will  undergo  a  special  examination 
when  we  come  to  treat  particularly  of  the  Logic  of  the  Moral  Sciences  (Book  vi.,  ch.  3). 
In  the  mean  time  I  may  remark  that  these  metaphysicians,  who,  it  must  be  observed,  ground 
the  main  part  of  their  objection  upon  the  supposed  repugnance  of  the  doctrine  in  question 
to  our  consciousness,  seem  to  me  to  mistake  the  fact  which  consciousness  testifies  against. 
What  is  really  in  contradiction  to  consciousness,  they  would,  I  think,  on  strict  self-e.xam- 
ination,  find  to  be,  the  application  to  human  actions  and  volitions  of  the  ideas  involved  in 
the  common  use  of  the  term  Necessity  ;  which  I  agree  with  them  in  thinking  highly  objec- 
tionable. But  if  they  would  consider  that  by  saying  that  a  man's  actions  necessarily  follow 
from  his  character,  all  that  is  really  meant  (for  no  more  is  meant  in  any  case  whatever  of 
causation)  is  that  he  invariably  does  act  in  conformity  to  his  character,  ahd  that  any  one  who 
thoroughly  knew  his  character  could  certainly  predict  how  he  would  act  in  any  supposable 
case ;  they  probably  would  not  find  this  doctrine  either  contrary  to  their  experience  or 
revolting  to  their  feelings.  And  no  more  than  this  is  contended  for  by  any  one  but  an 
Asiatic  fatalist. 


LAW    OF    CAUSATION.  209 

of  the  pi-esent   Book,  under  the  name  of  the  Specific  Properties  of 
Kinds. 

§  9.  Before  concluding  this  chapter,  it  seems  desirable  to  take 
notice  of  an  apparent,  but  not  a  real  opposition  between  the  doctrines 
which  I  have  laid  down  respecting  causation,  and  those  maintained  in 
a  work  which  I  hold  to  be  far  the  greatest  yet  produced  on  the  Phi- 
losophy of  the  Sciences,  ]M.  Comte's  Cours  dc  Phdosophie  Positive. 
M.  Comte  asserts  as  his  first  principle,  that  the  causes  of  phenomena 
are  beyond  the  reach  of  the  human  faculties,  and  that  all  which  is  ac- 
cessible to  us  is  their  laws,  or,  as  he  explains  the  term,  their  constant 
relations  of  succession  or  of  similarity.  Accordingly  M.  Comte  sedu- 
lously abstains,  in  the  subsequent  part  of  his  work,  from  the  use  of  the 
word  Cause  :  an  example  which  I  have  not  followed,  for  reasons  which 
I  will  proceed  to  state.  I  most  fully  agree  with  M.  Comte  that  ulti- 
niatc,  or,  in  the  phraseology  of  metaphysicians,  efficient  causes,  which 
ai'e  conceived  as  liot  being  jjhenoraena,  nor  perceptible  by  the  senses 
at  all,  are  radically  inaccessible  to  the  human  faculties :  and  that  the 
"  constant  relations  of  succession  or  of  similarity"  which  exist  among 
phenomena  themselves,  (not  forgetting,  so  far  as  any  constancy  can  be 
traced,  their  relations  of  coexistence,)  are  the  only  subjects  of  rational 
investigation.  When  I  speak  of  causation,  I  have  nothing  in  view, 
other  than  those  constant  relations  :  but  I  think  the  terms  causation, 
and  cause  and  effect,  important  to  be  preserved,  for  the  purpose  of 
distinctively  designating  one  class  of  those  relations,  namely,  the  rela- 
tions of  succession  which  so  far  as  we  know  are  unconditional ;  as 
contrasted  with  those  which,  like  the  succession  of  day  and  night,  de- 
pend upon  the  existence  or  upon  the  coexistence  of  other  antecedent 
facts.  This  distinction  corresponds  to  the  great  division  which  Mr. 
Whewell  and  other  writers  have  made  of  the  field  of  science,  into  the 
investigation  of  what  they  term  the  Laws  of  Phenomena,  and  the 
investigation  of  causes ;  a  phraseology,  as  I  conceive,  altogether 
vicious,  inasmuch  as  the  ascertainment  of  causes,  sucli  causes  as  the 
human  faculties  can  ascertain,  namely,  causes  which  are  themselves 
phenomena,  is,  therefore,  merely  the  asceitaiimicnt  of  other  and  more 
universal  Laws  of  Phenomena.  And  I  cannot  but  look  upon  the 
revival,  on  English  soil,  of  the  doctrine  (not  only  refuted  by  the  school 
of  Locke  and  Hume,  but  given  up  by  their  great  rivals  Reid  and 
Stewart)  tliat  efficient  causes  are  within  the  reach  of  human  knowl- 
edge, as  a  remarkable  instance  of  what  hag  been  aptly  called  "  the 
peculiar  zest  which  the  spirit  of  reaction  against  modern  tendencies 
gives  to  ancient  absurdities." 

Yet  the  distinction  between  those  constant  relations  of  succession  or 
coexistence  which  Mr.  Whewell  tenns  Laws  of  Phenomena,  and 
those  which  he  tenns,  as  I  do.  Laws  of  Causation,  is  grounded  (how- 
ever incorrectly  expressed)  upon  a  real  difference.  It  is  no  doubt 
with  great  injustice  that  Mr.  Wliewell  (who  has  evidently  given  only 
a  most  partial  and  cursory  inspection  to  M.  Comte's  work,)  assumes 
that  M.  Comte  has  overlocdced  this  fundamental  distinction,  and  that 
by  excluding  the  investigation  of  causes,  he  excludes  that  of  all  the 
most  general  truths.  No  one  really  acfjuainted  with  M.  Comte's 
admirable  speculations  could  have  so  completely  misapj)rehended  their 
whole  spirit  and  purpoit.  But  it  does  appear  to  me  tlaat  his  disinclina- 
Dd 


210  INDUCTION. 

tion  to  employ  the  word  Cause  has  occasionally  led  him  to  attach  less 
importance  than  it  deserves  to  this  great  distinction,  upon  which  alone, 
I  am  convinced,  the  possibility  rests  of  framing  a  rigorous  Canon  of 
Induction.  Nor  do  I  see  what  is  gained  by  avoiding  this  particular 
■word,  when  M.  Comte  is  forced,  like  other  people,  to  speak  continually 
of  the  properties  of  things,  of  agents  and  their  action,  oi  forces,  and 
the  like ;  terms  equally  liable  to  perversion,  and  which  are  partial  and 
inadequate  expressions  for  what  no  word  that  we  possess,  except 
Cause,  expresses  in  its  frill  generality.  I  believe,  too,  that  when  the 
ideas  which  a  word  is  commonly  used  to  convey  are  overclouded  with 
mysticism,  the  obscurity  is  not  likely  to  be  so  effect,ually  dispelled  by 
abstaining  from  its  employment,  as  by  bringing  out  into  full  clearness 
the  poition  of  real  meaning  which  exists  in  the  various  cases  where 
the  terin  is  most  familiarly  employed,  and  therelay  giving  a  legitimate 
satisfaction  to  that  demand  of  the  intellect  which  has  caused  the  term 
to  remain  in  use. 


CHAPTER  VI. 

OF  THE   COMPOSITION*   OF   CAUSES. 


§  1.  To  complete  the  general  notion  of  causation  on  which  the  rules 
of  experimental  inquiry  into  the  laws  of  nature  must  be  founded, 
one  distinction  still  remains  to  be  pointed  out :  a  distinction  so  frinda- 
mental,  and  of  so  much  importance,  as  to  require  a  chapter  to  itself 

The  preceding  discussions  have  rendered  us  familiar  with  the  case 
in  which  several  agents,  or  causes,  concur  as  conditions  to  the  pro- 
duction of  an  effect ;  a  case,  in  truth,  almost  universal,  there  being 
very  few  effects  to  the  production  of  which  no  more  than  one  agent 
contributes.  Suppose,  then,  that  two  different  agents,  operating 
jointly,  are  followed,  under  a  certain  set  of  collateral  conditions,  by  a 
given  effect.  If  either  of  these  agents,  instead  of  being  joined  with 
the  other,  had  operated  alone,  under  the  same  set  of  conditions  in  all 
other  respects,  some  effect  would  probably  have  followed  ;  which 
would  have  been  different  from  the  joint  effect  of  the  two,  and  more 
or  less  dissimilar  to  it.  Now,  if  we  happen  to  kijow  what  would  be 
the  effects  of  each  cause  when  acting  separately'from  the  other,  we 
are  often  able  to  arrive  deductively,  or  a  priori,  at  a  correct  prediction 
of  what  will  arise  fi'om  their  conjunct  agency.  To  enable  us  to  do 
this,  it  is  only  necessary 'that  the  same  law  which  expresses  the  effect 
of  each  cause  acting  by  itself,  shall  also  coiTectly  express  the  part  due 
to  that  cause,  of  the  effect  which  follows  from  the  two  together.  This 
condition  is  realized  in  the  extensive  and  impoitant  class  of  phenomena 
commonly  called  mechanical,  namely,  the  phenomena  of  the  communi- 
cation of  motion  (or  of  pressure,  which  is  tendency  to  motion)  fr'om 
one  body  to  another.  In  this  important  class  of  cases  of  causation, 
one  cause  never,  properly  speaking,  defeats  or  frusti-ates  another ;  both 
have  their  full  effect.  If  a  body  is  propelled  in  two  directions  by  two 
forces,  one  tending  to  drive  it  to  the  north,  and  the  other  to  the  east,  , 
it  is  caused  to  move  in  a  given  time  exactly  as  far  in  both  du'ections  as 


COMPOSITION    OF    CAUSES.  211 

the  two  forces  would  separately  have  camcJ  it ;  and  is  left  precisely 
where  it  would  have  arrived  if  it  had  been  acted  upon  first  by  one  of 
the  two  forces,  and  afterwards  by  the  other.  This  law  of  nature  is 
called,  in  mechanical  philosophy,  the  principle  of  the  Composition  of 
Forces  :  and  in  imitation  of  that  well-chosen  expression,  I  shall  give 
the  name  of  the  Composition  of  Causes  to  the  principle  which  is 
exemplified  in  all  cases  in  which  the  joint  effect  of  several  causes  is 
identical  with  the  sum  of  their  separate  effects. 

This  principle;  however,  by  jio  means  prevails  in  all  departments  of 
the  field  of  natui'e.  The  chemical  combination  of  two  substances 
produces,  as  is  well  known,  a  third  substance  with  properties  entirely 
different  from  those  of  either  of  the  two  substances  separately,  or  of 
both  of  them  taken  together.  Not  a  trace  of  the  properties  of  hydro- 
gen or  of  oxygen  is  observable  in  those  of  their  compound,  water. 
The  taste  of  sugar  of  lead  is  not  the  sum  of  the  tastes  of  its  component 
elements,  acetic  acid  and  lead  or  its  oxide ;  nor  is  the  color  of  green 
viti-iol  a  mixture  of  the  colors  of  sulphuric  acid  and  copper.  This 
explains  why  mechanics  is  a  deductive  or  demonstrative  science,  and 
chemisti-y  not.  In  the  one,  we  can  compute  the  effects  of  all  combina- 
tions of  causes,  Avhether  real  or  hypothetical,  from  the  laws  which  we 
know  to  govern  those  causes  when  apting  sej?arately ;  because  they 
continue  to  obsei've  the  same  laws  when  in  combination,  which  they 
observed  when  separate ;  whatever  would  have  happened  in  conse- 
quence of  each  cause  taken  by  itself,  happens  when  they  are  together, 
and  we  have  only  to  cast  up  the  results.  Not  &o  in  the  phenomena 
which  are  the  peculiar  subject  of  the  science  of  chemistry.  There, 
most  of  the  uniformities  to  which  the  causes  conformed  when  separate, 
cease  altogether  when  they  are  conjoined ;  and  we  are  not,  at  least  in 
the  present  state  of  our  knowledge,  able  to  foresee  what  result  will 
follow  from  any  new  combination,  until  we  have  tried  it  by  specific 
experiment. 

If  this  be  true  of  chemical  combinations,  it  is  still  more  time  of  those 
far  more  complex  combinations  of  elements  which  constitute  organized 
bodies  ;  and  in  which  those  extraordinary  new  uniformities  arise,  which 
are  called  the  laws  of  life.  All  organized  bodies  are  composed  of 
parts,  similar  to  those  composing  inorganic  nature,  and  which  have 
even  themselves  existed  in  an  inorganic  state ;  but  the  phenomena  of 
iife,  which  result  from  the  juxtaposition  of  those  parts  in  a  certain 
manner,  bear  no  analogy  to  any  of  the  effects  which  would  be  produced 
by  the  action  of  the  component  substances  considered  as  mere  physical 
agents.  To  whatever  degree  we  might  imagine  our  knowledge  of  the 
properties  of  the  several  ingi-edients  of  a  living  body  to  be  extended 
and  perfected,  it  is  certain  that  no  mere  summing  up  of  the  separate 
actions  of  those  elements  will  ever  amount  to  the  action  of  the  living 
body  itself.  The  tongue,  for  instance,  is,  like  all  other  parts  of  the 
animal  frame,  composed  of  gelatine,  fibrin,  and  other  products  of  the 
chemistry  of  digestion,  but  from  no  knowledge  of  the  properties  of 
those  substances  could  wc  ever  predict  that  it  could  taste,  unless  gel- 
atine or  fibrin  could  themselves  taste  ;  for  no  elementary  fact  can  be  in 
the  conclusion,  which  was  not  first  in  the  premisses. 

There  are  thus  two  different  modes  of  the  conjunct  action  of  causes; 
from  which  arise  two  modes  of  conflict,  or  mutual  interference,  between 
laws  of  nature.     Suppose,  at  a  given  point  of  time  and  space,  two  or 


212  INDUCTION. 

more  causes,  which,  if  they  acted  separately,  would  produce  effects 
contrary,  or  at  least  conflicting  with  each  other ;  one  of  them  tending 
to  undo,  wholly  or  partially,  what  the  other  tends  to  do.  Thus,  the 
expansive  force  of  the  gases  generated  by  the  ignition  of  gunpow- 
der tends  to  project  a  bullet  towards  the  sky,  while  its  gravity  tends  to 
make  it  fall  to  the  ground.  A  stream  running  into  a  reservoir  at  one 
end  tends  to  fill  it  higher  and  higher,  while  a  drain  at  the  other  exJn-emity 
tends  to  empty  it.  Now,  in  such  cases  as  these,  even  if  the  two  causes 
which  are  in  joint  action  exactly  annul  one  another,  still  the  laws  of 
both  are  fulfilled;  the  effect  is  the  same  as  if  the  drain' had  been  open 
for  half  an  hour  first,*  and  the  stream  had  flowed  in  for  as  long  after- 
wards. Each  agent  produced  the  same  amount  of -effect  as  if  it  had 
acted  separately,  though  the  contrary  effect  which  was  taking  plafce 
during  the  same  time  obliterated  it  as  fast  as  it  was  produced.  Here, 
then,  we  have  two  causes,  producing  by  their  joint  operation  an  effect 
which  at  first  seems  quite  dissimilar  to  those  which  they  produce  sep- 
arately, but  which  on  examination  proves  to  be  really  the  sum  of  those 
separate  effects.  It  will  be  noticed  that  we  here  enlarge  the  idea  of  the 
sum  of  two  effects,  so  as  to  include  what  is  commonly  called  their  dif- 
ference, but  which  is  in  reality  the  result  of  the  addition  of  opposites  ; 
a  conception  to  which,  as  is  well  known,  mankind  are  indebted  for  that 
admirable  extension  of  the  algebraical  calculus,  which  has  so  vastly  in- 
creased its  powerxS  as  an  instrument  of  discovery,  by  introducing  into 
its  reasonings  (with  the  sign  of  subtraction  prefixed,  and  under  the 
name  of  Negative  Quantities)  every  description  whatever  of  positive 
phenomena,  provided  they  are  of  such  a  quality  in  reference  to  those 
previously  introduced,  that  to  add  the  one  is  equivalent  to  subtracting 
an  equal  quantity  of  the  other. 

There  is,  then,  one  mode  of  the  mutual  interference  of  laws  of  na- 
ture in  which,  even  when  the  eoncuiTent  causes  annihilate  each  other's 
effects,  each  exerts  its  full  efficacy  according  to  its  own  law,  its  law  as 
a  separate  agent.  But  in  the  other  description  of  cases,  the  two  agen- 
cies which  are  brought  together  cease  entirely,  and  a  totally  different 
set  of  phenomena  arise  :  as  in  the  experiment  of  two  liquids  which, 
when  mixed  in  certain  proportions,  instantly  become  a  solid  mass,  in- 
stead of  merely  a  larger  amount  of  liquid. 

§  2.  This  difference  between  the  case  in  which  the  joint  effect  of 
causes  is  the  sum  of  their  separate  effects,  and  the  ease  in  which  it  is 
heterogeneous  to  them ;  between  laws  which  work  together  without 
alteration,  and  laws  which,  when  called  upon  to  work  together,  cease 
and  give  place  to  others ;  is  one  of  the  fundamental  distinctions  in 
nature.  The  former  case,  that  of  the  Composition  of  Causes,  is  the 
general  one;  the  other  is  always  special  and  exceptional.  There  are 
no  objects  which  do  not,  as  to  some  of  their  phenomena,  obey  the  prin- 
ciple of  the  Composition  of  Causes  ;  none  that  have  not  some  laws 
which  are  rigidly  fulfilled  in  eveiy  combination  into  which  the  objects 
enter.  The  weight  of  a  body,  for  instance,  is  a  property  which  it 
retains  in  all  the  combinations  in  which  it  is  placed.  The  weight  of  a 
chemical  compound,  or  of  an  organized  body,  is  equal  to  the  sum  of 

*  I  omit,  for  simplicity,  to  take  into  account  the  effect,  in  this  latter  case,  of  the  diminu- 
tion of  pressure,  in  diminishing  the  flow  of  the  water  through  the  drain ;  which  evidently 
iu  no  way  allects  the  truth  or  applicability  of  the  principle. 


COMPOSITION    OF    CAUSES.  213 

the  weights  of  the  elements  which  compose  it.  The  weight  either 
of  the  elements  or.  of"  the  compound  will  vary,  if  they  be  carried  fur- 
ther from  their  centre  of  attraction,  or  brought  nearer  to  it ;  but  what- 
ever affects  the  one  affects  the  other.  They  always  remain  precisely 
equal.  So  again,  the  component  parts  of  a  vegetable  or  animal  sub- 
stance do  not  lose  their  mechanical  and  chemical  properties  as  sepa- 
rate agents,  when,  by  a  peculiar  mode  of  juxtaposition,  they,  as  an 
aggregate  whole,  acquire  physiological  or  vital  properties  in  addition. 
Those  bodies  continue,  as  before,  to  obey  mechanical  and  chemical 
laws,  in  so  far  as  the  operation  of  those  laws  is  not  counteracted  by  the 
jiew  laws  which  govern  them  as  organized  beings.  When,  in  short,  a 
concurrence  of  causes  takes  place  whicli  calls  into  action  new  laws, 
bearing  no  analogy  to  any  that  we  can  trace  in  the  separate  operation 
of  the  causes,  the  new  laws  may  supersede  one  portion  of  the  previous 
laws  but  coexist  with  ancither  portion,  and  may  even  com})ound  the 
effect  of  thosfe  previous  laws  with  their  own. 

Again,  laws  which  were  themselves  generated  in  the  second  mode, 
may  generate  others  in  the  fir^t.  Though  there  be  laws  which,  like 
those  of  chemistry  and  physiology,  owe  their  existence  to  a  breach  of 
the  principle  of  Composition  of  Causes,  it  does  not  follow  that  these 
peculiar,  or  as  they  might  be  termed,  het.eropathic  laws,  are  not  capa- 
ble of  composition  with  one  another.  The  causes  which  by  one  com- 
bination have  had  their  laws  altered,  may  carry  their  new  laws  with 
them  unaltered  into  their  ulterior  combinations.  And  hence  there  is 
no  reason  to  despair  of  ultimately  raising  chemistry  and  physiology  to 
the  condition  of  deductive  sciences ;  for  though  it  is  impossible  to  de- 
duce all  chemical  and  physiological  truths  from  the  laws  or  properties 
of  simple  substances  or  elementary  agents,  they  may  probably  be  de- 
ducible  from  laws  whicli  commence  when  these  elementary  agents  are 
brought  together  into  some  moderate  number  of  not  very  complex 
combinations.  The  Laws  of  Life  will  never  be  deducible  from  the 
mere  laws  of  the  ingi-edients,  but  the  prodigiously  complex  Facts  of 
Life  may  all  be  deducible  from  comparatively  simple  laws  of  life ; 
which  laws  (depending  indeed  upon  combinations,  but  upon  compara- 
tively simple  combinations,  of  antecedents),  may  in  more  complex 
circumstances  be  strictly  comjiounded  wjth  one  another,  and  with  the 
physical  and  chemical  laws  of  the  ingredients.  The  details  of  the 
vital  phenomena  even  now  afford  innumerable  exemplifications  of  the 
Composition  of  Causes;  and  in  pi'oportion  as  these  phenomena  are 
more  ac(;urately  studied,  there  aj)pears  more  and  more  reason  to 
believe  tliat  the  same  laws  which  operate  in  the  simpler  combinations 
of  circumstances  do,  in  fact,  continue  to  be  obsei-ved  in  the  more  com- 
plex. *  This  will  be  found  c(jually  true  in  the  phenomena  of  mind ; 
and  even  in  social  and  political  phenomena,  the  result  of  the  laws  of 
mind.     It  is  in  the  case  of  chemical  phenomena  that  the  least  progress 

*  For  abundant  illustrations  of  this  remark,  I  may  refer  to  the  writings  of  Dr.  W.  B. 
Carppnter,  of  Bristol,  and  ospecially  his  treatise  on  General  Physiology,  in  which  the  high- 
est generalizations  which  the  science  of  life  has  yet  reached,  and  the  best  modern  concep- 
tion of  that  science  as  a  whole,  are  exhibited  in  a  manner  equally  perspicuous  and  philo- 
sophical. On  the  details  of  such  a  treatise  the  present  writer  would  be  an  incompetent  wit- 
ness :  these  however  have  been  sufficiently  vouched  for  by  some  of  the  highest  living 
authorities ;  while  of  the  genuinely  scientific  spirit  which  pervades  it,  those  ipay  be  per- 
mitted to  express  an  opinion,  who  v/ould  not  be  entitled  to  ofler  to  a  work  on  such  a  sub- 
ject,  any  other  praise. 


214  INDUCTION. 

has  yet  been  made  in  bringing  the  special  laws  under  general  ones 
from  which  they  may  be  deduced ;  but  there  are  even  in  chemistry 
many  circumstances  to  encourage  the  hope  that  such  general  laws 
will  hereafter  be  discovered.  The  different  actions,  of  a  chemical 
compound  will  never,  undoubtedly,  be  found  to  be  the  sum  of  the 
actions  of  its  separate  elements;  but  there  may  exist,  between  the 
properties  of  the  compound  and  those  of  its  elements,  some  constant 
relation,  which  if  discoverable  by  a  sufficient  induction,  would  enable 
us  to  foresee  the  sort  of  compound  which  will  result  from  a  new  com- 
bination before  we  have  actually  tried  it,  and.to  jiulge  of  what  sort  of 
elements  some  new  substance  is-  compounded  before  we  have  analyzed 
it :  a  problem,  •  the  solution  of  which  has  been  propounded  by  M. 
Comte  as  the  ideal  aim  and  purpose  of  chemical  speculation.  The 
gi-eat  law  of  definite  proportions,  first  discovered  in  its  full  generality 
by  Dalton,  is  a  complete  solution  of  this  problem  in  one  single  aspect 
(of  secondary  importance  it  is  ti-ue),  that  of  quantity  :  and  in  respect 
to  quality,  we  have  already  some  partial  generalizations  sufficient  to 
indicate  "the  possibility  of  ultimately  proceeding  further.  We  can 
predicate  many  common  properties  of  the  kind  of  compounds  which 
result  from  the  combination,  in  each  of  the  small  number  of  possible 
proportions,  of  any  acid  whatever  with  any  base.  We  have  also  the 
very  curious  law,  discovered  by  Berthollet,  that  two  soluble  salts 
mutually  decompose  one  another  whenever  the  new  combinations 
w^hich  result  produce  an  insoluble  compound :  or  one  less  soluble 
than  the  two  former.  Another  imifonnity  has  been  obsei-v^ed,  com- 
monly called  the  law  of  isomorphism  ;  the  identity  of  the  crystalline 
forms  of  substances  which  possess  in  common  certain  peculiarities  of 
chemical  composition.  Thus'  it  appears  that  even  heteropathic  laws, 
such  laws  of  combined  agency  as  are  not  compounded  of  the  laws  of 
the  separate  agencies,  are  yet,  at  least  in  some  cases,  derived  from 
them  according  to  a  fixed  principle.  There  may,  therefore,  be  laws 
of  the  o-eneration  of  laws  from  others  dissimilar  to  them;  and  in  chem- 
istry, these  undiscovered  laws  of  the  dependence  of  the  properties  of 
the  compound  on  the  properties  of  its  elements,  may,  together  with 
the  laws  of  the  elements  themselves,  furnish  the  premisses  by  which 
the  science  is  destined  one  day  to  be  rendered  deductive. 

It  would  seem,  therefore,  that  there  is  no  class  of  phenomena  in 
which  the  Composition  of  Causes  does  not  obtain :  that  as  a  general 
rule,  causes  in  combination  produce  exactly  the  same  effects  as  when 
actino-  singly  :  but  that  this  rule,  though  genei'al,  is  not  universal ;  that 
in  some  instances,  at  some  particular  points  in  the  transition  fi'om  sep- 
arate to  united  action,  the  laws  change,  and  an  entirely  new  set  of 
effects  are  either  added  to,  or  take  the  place  of,  those  which  arise  fi'om 
the  separate  agency  of  the  same  causes ;  the  Ia\vs  of  these  new  effects 
being  again  susceptible  of  composition,  to  an  indefinite  extent,  like  the 
laws  which  they  superseded. 

§  3.  That  effects  are  proportional  to  their  causes  is  laid  down,  by 
some  writers,  as  an  axiom  in  the  theory  of  causation ;  and  great  use  is 
sometimes  made  of  this  principle  in  reasonings  respecting  the  laws  of 
nature,  although  it  is  encumbered  with  many  difficulties  and  apparent 
exceptions,  which  much  ingenuity  has  been  expended  in  showing  not 
to  be  real  ones.     This  proposition,  in  so  far  as  it  is  brue,  enters  as  a 


COMPOSITION    OF    CAUSES.  215 

particular  case  into  tlic  gcjioral  principle  of  the  Composition  of  Causes  : 
tlie  causes  compounded  being,  in  this  instance,  liompgeneous ;  in  which 
case,  if  in  any,  their  joint  elfect  might  be  expected  to"  be  identical  with 
the  sum  of  their  separate  eflects.  If  a  force  equal  to  one  hundred 
-weight,  will  raise  a  certain  body  along  an  inclined  plane,  a  force  equal 
to  two  hundred  weight  will,  we  know,  raise  two  bodies  exactly  similar, 
and  thus  the  effect  is  proportienal  to  the  cause.  But  does  not  a  force 
equal  to  two  hundred  weight,  actually  contain  in  itself  two  forces  each 
equal  to  one  hundred: weight,  which,  if  employed  apait,  would  sepa- 
rately raise  the  two  bodies  in  (juestion  i  The  fact,  therefore,  that 
wlien  exerted  jointly  they  raise  both  bodies  at  once,  results  from  the 
Composition  of  Causes,  and  is  a  mere  instance  of  the  general  fact  that 
mechanical  forces  are  subject  to  the  law  of  Composition.  And  so  in 
every  other  case  which  can  be  supposed.  For  the  doctrine  of  the 
proportionality  of  eflects  to  their  causes  cannot  of  course  be  applicable 
to  cases  in  which  the  augmentation  of  the  cause  alters  the  ki?id  of  effect; 
that  is,  in  which  the  su7-j)lus  quantity  superadded  to  the  cause  does  not 
become  compounded  with  it,  but  the  two  together  generate  an  alto- 
gether' new  phenomenon.  Su^jpose  that  the  application  of  a  certain 
quantity  of  heat  to  a  body  merely  increases  its  bulk,  that  a  double 
quantity  melts  it,  and  a  triple  quantity  decomposes  it:  these  three 
eflects  being  heterogeneous,  no  ratio,  whether  corresponding  or  not  to 
that  of  the  quantities  of  heat  applied,  can  be  established  between  them. 
Thus  we  see  that  the  supposed  axiom  of  the  proportionality  of  effects 
to  their  causes  fails  at  the  precise  point  whei?e  the  principle  of  the 
Composition  of  Causes  also  fails ;  viz.,  where  the  concuiTence  of 
causes  is  such  as  to  determine  a  change  in  the  properties  of  the  body 
generally,  and  render  it  subject  to  new  laws,  more  or  less  dissimilar 
to  those  to  which  it  conformed  in  its  previous  state  of  existence.  The 
recognition,  therefore,  of  any  such  law  of  proportionality,  is  superseded 
by  the  more  comprehensive  principle,  in  which  as  much  of  it  as  is  true 
is  implicitly  asserted. 

The. general  remarks  on  causation,  which  seqmed  necessary  as  an 
introduction  to  the  theory  of  the  inductive  process,  may  here  termi- 
nate. That  process  is  essentially  an  inquiry  into  cases  of  causation. 
All  the  uniformities  which  exist  in  the  succession  of  plienomena,  and 
most  of  those  which  prevail  in  their  coexistence,  are  either,  as  we  have 
seen,  themselves  laws  of  causation,  or  consequences  resulting  from, 
and  corollaries  capable  of  being  deduced  from,  such  laws.  If  we  could 
determine  what  causes  are  correctly  assigned  to  what  effects,  and  what 
effects  to  what  causes,  we  should  be  virtually  acquainted  with  the 
whole  course  of  nature.  All  those  uniformities  which  are  mere  results 
of  causation,  might  then  be  explained  and  accounted  for ;  and  every 
individual  fact  or  event  might  be  predicted,  provided  we  had  the 
requisite  data,  that  is,  the  recjuisite  knowledge  of  the  circumstances 
which,  in  the  particular  instance,  preceded  it. 

To  ascertain,  therefore,  what  are  the  laws  of  causation  which  exist 
in  nature ;  to  determine  the  effects  of  eveiy  cause,  and  the  causes  of 
all  effects,  is  the  main  business  of  Induction  ;  and  to  point  out  how  this 
is  done  is  the  chief  object  of  Inductive  Logic. 


216 


INDUCTION. 


CHAPTER  VII. 

OF   OBSERVATION   AND  EXPERIMENT, 


§  1.  It  results  from  the  preceding  exposition,  that  the  process  of 
ascertaining  what  consequents^  in  natui-e,  are  invariably  connected 
with  what  antecedents,  or  in  other  words  what  phenomena  are  related 
to  each  other  as  causes  and  effects,  is  in  some  sort  a  pi'ocess  of  analysis. 
Tha.t  every  fact  which  begins  to  exist  has  a  cause,  and  that  this  cause 
must  be  found  somewhere  among  the  facts  which  immediately  pre- 
ceded its  occuiTence,  may  be  taken  for  certain.  The  whole  of  the 
present  facts  are  the  infallible  result  of  all  past  facts,  and  more  inmie- 
diately  of  all  the  facts  which  existed  at  the  moment  previous.  Here, 
then,  is  a  great  sequence,  which  we  know  to  be  uniform.  If  the  whole 
prior  state  of  the  entire  universe  could  again  recur,  it  would  again  be 
followed  by  the  whole  present  state.  The  question  is,  how  to  resolve 
this  complex  uniformity  into  the  simpler  uniformities  which  compose 
it,  and  assign  to  each  portion  of  the  vast  antecedent  that  portion  of  the 
consequent  which  is  attendant  upon  it. 

This  operation,  -which  we  have  called  analytical,  inasmuch  as  it  is 
the  resolution  of  a  complex  whole  into  the  component  elements,  is 
more  than  a  merely  mental  analysis.  No  mere  contemplation  of  the 
phenomena,  and  partition  of  them  by  the  intellect  alone,  will  of  itself 
accomplish  the  end  we  have  now  in  view.  Nevertheless,  such  a  men- 
tal partition  is  an  indispensable  first  step.  The  order  of  nature,  as  per- 
ceived at  a  first  glance,  presents  at  every  instant  a  chaos  followed  by 
another  chaos.  We  must  decompose  each  chaos  into  single  facts,' 
We  must  leai-n  to  see  in  the  chaotic  antecedent  a  multitude  of  dis- ' 
tinct  antecedents,  in  the  chaotic  consequent  a  multitude  of  distinct 
consequents.  This,  supposing  it  done,  will  not  of  itself  tell  us  on 
which  of  the  antecedents  each  consequent  is  invariably  attendant.  To 
determine  that  point,  we  must  endeavor  to  effect  a  sej)aration  of  the 
facts  from  one  another,  not  in  our  minds  only,  but  in  nature.  The 
mental  analysis,  however,  must  take  ]ilace  first.  And  every  one 
knows  that  in  the  mode  of  performing  it,  one  intellect  diflers  im- 
mensely fi-om  another.  It  is  the  essence  of  the  act  of  obsei-\'ing  ;  for  the 
observer  is  not  he  who  merely  sees  the  thing  which  is  before  his  eyes, 
but  he  who  sees  what  parts  that  thing  is  composed  of  To  do  this 
well  is  a  rare  talent.  One  person,  from  inattention,  or  attending  only 
in  the  wrong  place,  overlooks  half  of  what  he  sees ;  another  sets  down 
much  more  than  he  sees,  confounding  it  with  what  he  imagines,  or 
with  what  he  infers;  another  takes  note  of  the  hind  of  all  the  circum- 
stances, but  being  inexpert  in  estimating  their  degree,  leaves  the 
quantity  of  each  vague  and  uncertain;  another  sees  indeed  the  whole, 
but  makes  such  an  awkward  division  of  it  into  parts,  throwing  things 
into  one  mass  which  require  to  be  separated,  and  separating  others 
which  might  more  conveniently  be  considered  as  one,  that  the  result 
is  much  the  same,  sometimes  even  worse,  than  if  no  analysis  had  been 
attempted  at  all.  It  would  be  possible  to  point  out  what  qualities  of 
mind,  and  modes  of  mental  culture,  fit  a  person  for  being  a  good 
obsei-ver ;  that,  however,  is  a  question  not  of  Logic,  but  of  the.  theory 


OBSERVATION    AND    EXPEUIMRNT.  217 

of  Education,  in  the  most  enlarged  sense  of  the  term.  There  is  not 
properly  an  Art  of  Observing.  There  may  be  rules  for  observing. 
J)ut  these,  like  rules  for  inventing,  are  projjorly  instructions  for  the 
preparation  of  one's  own  mind ;  for  putting  it  into  the  state  in  which 
it  will  be  mnst  fitted  to  observe,  or  most  likely  to  invent.  They  are, 
therefore,  essentially  rules  of  self-education,  which  is  a  different  thing 
from  Logic.  They  do  not  teach  how  to  do  the  thing,  but  how  to  make 
ourselves  capable  of  doing  it.  They  are  an  art  of  strengthening  the 
limlTS,  not  an  art  of  using  them. 

The  extent  and  minuteness  of  observation  which  may  be  requisite, 
and  the  degree  of  decomposition  to  which  it  may  be  necessary  to  carry 
the  njental  analysis,  depend  upon  the  particular  purpose  in  view.  To 
ascertain  the  state  of  the  whole  universe  at  any  particular  m-oment  is 
impossible,  but  would  also  be  useless.  In  making  chemical  experi- 
ments, we  should  not  think  it  necessary  to  note  the  position  of  the 
planets;  because  experience  has  shown,  as  a  very  superficial  experi- 
ence is  sufficient  to  show,  that  in  such  cases  that  circumstance  is  not 
material  to  the  j-esult :  and,  accordingly,  in  the  age  when  men  believed 
in  the  occult  influences  of  the  heavenly  bodies,  it  might  have  been  un- 
philosophical  to  omit  ascertaining  the  precise  condition  of  those  bodies  . 
at  the  momeirt  of  the  experiment.  As  to  the  degree  of  minuteness  of 
the  mental  subdivision  ;  if  we  were  obliged  to  break  down  what  we 
obsen^e  into  its  very  simplest  elements,  that  is,  literally  into  single  facts, 
it  would  be  difficult  to  say  where  we.  should  find  them  :  we  can  hardly 
ever  affirm  that  our  divisions  of  any  kind  have  reached  the  ultimate 
unit.  But  this,  too,  is  fortunately  unnecessary.  The  only  object  of  the 
mental  separation  is  to  suggest  the  requisite  physical  separation,  so  ■ 
that  we  may  either  accomplish  it  ourselves,  or  seek  for  it  in  nature ; 
and  we  have  done  enough  when  we  have  can-ied  the  subdivision  as  far 
as  the  point  at  which  we  are  able  to  see  what  observations  or  ex})eri- 
ments  we  require.  It  is  only  essential,  at  whatever  point  our  mental 
decomposition  of  facts  may  for  the  present  have  stopped,  that  we  should 
hold  ourselves  ready  and  able  to  cany  it  further  as  occasion  requires, 
and  should  not  allow  the  freedom  of  our  discriminating  faculty  to  be 
im})risoned  by  the  swathes  and  bands  of  ordinary  classification  ;  as  was 
the  case  with  all  early  speculative  inquirers,  not  excepting  the  Greeks, 
to  whom  it  hardly  ever  occurred  that  what  was  called  by  one  abstract 
name  might,  in  reality,  be  several  phenomena,  or  that  there  was  a" pos- 
sibility of  decomposing  the  facts  of  the  universe  into  any  elements  but 
those  which  ordinaiy  language  already  recognized. 

§  2.  The  different  antecedents  and  consequents  being,  then,  supposed 
to  be,  so  far  as  the  case  requires,  ascertained  and  discriminated  from 
one  another  ;  we  are  to  inquire  which  is  connected  with  which.  In 
every  instance  which  comes  under  our  observation,  there  are  many 
antecedents  and  many  consequents.  If  those  antecedents  could  not  be 
severed  fi'om  one  another  except  in  thought,  or  if  those  consecjuents 
never  were  found  apart,  it  would  be  impossible  for  us  to  distinguish 
(a  posteriori  at  least)  the  real  laws,  or  to  assign  to  any  cause  its  eil'ect, 
or  to  any  effect  its  cause.  To  do  so,  we  must  be  able  to  meet  with 
some  of  the  antecedents  apart  from  the  rest,  and  observe  what  follows 
from  them;  or  some  of  the  consctpients,  and^  observe  by  what  they  are 
preceded.  We  must,  in  short,  follow  the  Baconian  rule  of  varying 
E  E 


218  INDUCTION. 

the  circumstances.  This  is,  indeed,  only  the  Jirst  rule  of  physical  inqui- 
ry, and  not,  as  some  have  thought,  the  sole  rule  ;  but  it  is  the  founda- 
tion of  all  the  rest. 

Foi-  the  purpose  of  varying  the  circumstances,  we  may  have  recourse 
(according  to  a  distinction  commonly  made)  either  to  observation  or  to 
experiment ;  we  may  either  find  an  instance  in  nature,  suited  to  our . 
purposes,  or,  by  an  artificial  arrangement  of  circumstances,  make  one. 
The  value  of  the  instance  depends  upon  what  it  is  in  itself,  not  upon 
the  mode  in  which  it  is  obtained  :  its  employment  for  the  puqioses  of 
induction  depends  upon  the  same  principles  in  the  one  case  and  in  the 
other;  as  the  uses  of  money  are  the  same  whether  it  is  inherited  or 
acquired.  There  is,  in  short,  no  difference  in  kind,  no  real  logical 
distinction,  between  the  two  processes  of  investigation.  There  are, 
however,  practical  distinctions  to  which  it  is  of  considerable  importance 
to  advert. 

§  3.  The  first  and  most  obvious  distinction  between  Observation  and 
Experiment  is,,  that  the  latter  is  an  immense  extension  of  the  former. 
It  not  only  enables  us  to  produce  a  much  greater  number  of  variations 
in  the  circumstances  than  nature  spontaneously  offers,  but,  moreover, 
in  thousands  of  cases,  to  produce  the  precise  sort  of  variation  which 
we  are  in  want  of  for  discovering  the  law  of  the  phenomenon ;  a  ser- 
vice which  nature,  being  constrvicted  on  a  quite  different  scheme  from 
that  of  facilitating  our  studies,  is  seldom  so  friendly  as  to  bestow  upon 
us.  For  example,  in  order  to  ascertain  what  principle  in  the  atmos- 
phere enables  it  to  sustain  life,  the  variation  we  require  is  that  a  living 
animal  should  be  immersed  in  each  component  element  of  the  atmos- 
phere separately.  But  nature  does  not  supply  either  oxygen  or  azote 
in  a  separate  state.  We  are  indebted  to  artificial  experiment  for  our 
knowledge  that  it  is  the  former,  and  not  the  latter,  which  supports 
respiration ;  and  even  for  our  knowledge  of  the  very  existence  of  the 
two  ingredients. 

Thus  far  the  advantage  of  experimentation  over  simple  obsez'vation 
is  universally  recognized  :  all  are  aware  that  it  enables  us  to  obtain 
innumerable  combinations  of  circumstances  which  are  not  to  be  found 
in  nature,  and  so  add  to  nature's  experiments  a  multitude  of  experi- 
ments of  our  own.  But  there  is  another  superiority  (or,  as  Bacon 
would  have  expressed  it,  another  prerogative),  of  instances  artificially 
obtained  over  spontaneous  instances — of  our  own  experiments  over 
even  the  same  experiments  when  made  by  nature — which  is  not  of  less 
importance,  and  which  is  far  from  being  felt  and  acknowledged  in  the 
same  degree. 

"When  we  can  produce  a  phenomenon  artificially,  we  can  take  it,  as 
it  were,  home  with  us,  and  observe  it  in  the  midst  of  circumstances 
with  which  in  all  other  respects  we  are  accurately  acquainted.  If  we 
desire  to  know  what  are  the  effects  of  the  cause  A,  and  are  able  to 
produce  A  by  any  means  at  our  disposal,  we  can  generally  determine 
at  our  own  discretion,  so  far  as  js  compatible  with  the  nature  of  the 
phenomenon  A,  the  whole  of  the  circumstances  which  shall  be  present 
along  with  it :  and  thus,  knowing  exactly  the  simultaneous  state  of  every- 
thing else  which  is  within  the  reach  of  A's  influence,  we  have  only  to 
observe  what  alteration  is  made  in  that  state  by  the  prissence  of  A. 

For  example,  by  the  electrical  machine  we  can  produce  in  the  midst 


OBSERVATION  AND  EXPERIMENT.  219 

of  known  circumstances,  the  plienomena  which  nature  exhibits  on  a 
grander  scale  uncUn-  the  form  of  lii^hrniniT  and  thunder.  Now  let  any 
one  consider  wirat  amount  of  kiu)wled'u;e  ot'riie  etfects  and  laws  of  elec- 
tric agency  mankind  could  ever  have  obtained  from  the  mere  observation 
of  thunder-storms,  and  compare  it  with  that  which  they  have  gained, 
and  may  expect  to  gain,  from  electrical  and  galvanic  experiments. 
This  example  is  the  more  striking,  now  that  we  have  reason  to  believe 
that  electric  action  is  of  all  natural  phenomena  (except  heat)  the  most 
pervading  and  universal,  which,  therefore,  it  might  antecedently  have 
been  supposed  could  stand  least  in  need  of  artificial  means  of  produc- 
tion to  enable  it  to  be  studied  ;  while  the  fact  is  so  much  tlie  contrary, 
that  without  the  electric  machine,  the  voltaic  l?attery,  and  the  Leyden 
jar,  we  should  never  have  suspected  tile  existence  of  electricity  as  one 
of  the  great  agents  in  nature ;  the  few  electric  phenomena  we  should 
have  known  of  would  have  continued  to  be  regarded  either  as  super- 
natural, or  as  a  sort  of  anomalies  and  eccentricities  in  the  order  of  the 
universe. 

When  we  have  succeeded  in  insulating  the  phenomenon  which  is  the 
subject  of  inquiry,  by  placing  it  among  known  circumstances,  we  may 
produce  further  variations  of  circumstances  to  any  extent,  and  of  such 
kinds  as  we  think  best  calculated  to  bring  the  laws  of  the  phenomenon 
into  a  clear  light.  By  introducing  one  well  defined  circumstance  after 
another  into  the  experiment,  we  obtain  assurance  of  the  manner  in 
which  the  phenomenon  behaves  under  an  indefinite  variety  of  possible 
circumstances.  Thus,  chemists,  after  having  obtained  some  newly-dis- 
covered substance  in  a  pure  state,  (that  is,  having  made  sure  that  there 
is  nothing  present  whicn  can  interfere  with  and  modify  its  agency,) 
introduce  various  other  substances,  one  by  one,  to  ascertain  whether  it 
will  combine  with  them,  or  decompose  them,  and  with  what  result; 
and  also  apply  heat,  or  electricity,  or  pressure,  to  discover  what  will 
happen  to  the  substance  under  each  of  these  circumstances. 

But  if,  on  the  other  hand,  it  is  out  of  our  power  to  produce  the  phe- 
nomenon, and  we  have  to  seek  for  instances  in  which  nature  produces 
it,  the  task  before  us  is  one  of  quite  another  kind.  Instead  of  being 
able  to  choose  what  thq  concomitant  circumstances  shall  be,  we  now 
have  to  discover  what  they  are ;  which,  when  we  go  beyond  the  sim- 
plest and  most  accessible  cases,  it  is  next  to  impossible  to  do,  with  any 
precision  and  completeness.  Let  us  take,  as  an  exemplification  of  a  phe- 
nomenon which  we  have  no  means  of  fabricating  artificially,  a  human 
mind.  Nature  produces  many  ;  but  the  consequence  of  our  not  being 
able  to  produce  it  by  art  is,  that  in  every  instance  in  which  we  see  a 
human  mind  developing  itself,  or  acting  upon  other  things,  we  see  it 
surrounded  and  obscured  by  an  indefinite  multitude  of  unascertainable 
circumstances,  rendering  the  use  of  the  common  experimental  methods 
almost  delusive.  We  may  conceive  to  what  extent  this  is  true,  if  we 
consider,  among  other  things,  that  whenever  nature  produces  a  human 
mind,  she  produces,  in  close  connexion  with  it,  also  a  body  :  that  is,  a 
vast  complication  of  physical  facts,  in  no  two  cases  perhaps  exactly 
similar,  and  most  of  which  (except  the  mere  structure,  which  we  can 
examine  in  a  sort  of  coarse  way  after  it  has  ceased  to  act)  are  radically 
out  of  the  reach  of  our  means  of  exploration.  If,  instead  of  a  human 
mind,  we  suppo.se  the  subject  of  investigation  to  be  a  human  society 
or  State  all  the  same  difficulties  recur  in  a  greatly  augmented  degree. 


220  INDUCTION. 

We  have  thus  ah-eady  come  within  sight  of  a  conclusion,  which  the 
progress  of  the  inquiry  will,  I  think,  bring  before  us  with,  the  clearest 
evidence  :  namely,  that  in  the  sciences  which  deal  with  phenomena  in 
which  artificial  experiments  are  impossible  (as  in  the  case  of  astron- 
omy), or  in  which  they  have  a  very  limited  range  (as  in  physiology,' 
m^'ental  philosophy,  and  the  social  science),  indviction  from  dhect 
experience  is  practised  at  a  disadvantage  generally  equivalent  to 
impracticability :  from  which  it  follows  that  the  methods  of  those 
sciences,  in  order  to  accomplish  anything  worthy  of  attainment,  must 
be  to  a  great  extent,  if  not  principally,  deductive.  This  is  already 
known  to  be  the  case  with  tlie  first  of  the  sciences  we  have  men- 
tioned, astronomy ;  that  it  is  not  generally  recognized  as  true  of  the 
others,  is  probably  one  of  the  reasons  why  they  are  still  in  their 
infancy.  But  any  further  notice  of  this  topic  would  at  present  be 
premature. 

§  4.  If  what  is  called  pure  Observation  is  at  so  great  a  disadvantage 
compared  with  artificial  experimentation,  in  one  department  of  the 
direct  exploration  of  phenomena,  there  is  another  branch  in  which  the 
advantage  is  all  on  the  side  of  the  former. 

Inductive  inquiry  having  for  its  object  to  ascertain  what  causes  are 
connected  with  what  effects,  we  may  begin  this  search  at  either  end  of 
the  road  which  leads  from  the  one  point  to  the  other :  we  may  either 
inquire  into  the  effects  of  a  given  cause,  or  into  the  caiises  of  a  given 
effect.  The  fact  that  light  blackens  chloride  of  silver  might  have  been 
discovered,  either  by  experiments  upon  light,  trying  what  effect  it 
would  produce  on  various  substances,  or  by  observing  that  portions  of 
the  chloride  had  repeatedly  become  black,  and  inquiring  into  the 
circumstances.  The  effect  of  the  urali  poison  might  have  become 
known  either  by  administering  it  to  animals,  or  by  examining  how  it 
happened  that  the  wounds  which  the  Indians  of  Guiana  inflict  with 
their  arrows  prove  so  uniformly  mortal.  Now  it  is  manifest  from  the 
mere  statement  of  the  examples,  without  any  dieorotical  discussion, 
that  artificial  experimentation  is  applicable  only  to  the  former  of  these 
modes  of  investigEttion.  We  can  take  a  cause,  and  try  what  it  will 
produce  :  but  we  cannot  take  an  effect,  and  try  what  it  will  be  pro- 
duced by.  We  can  only  watch  till  we  see  it  ]iroduced,  or  are  enabled 
to  produce  it  by  accident. 

This  would  be  of  little  importance,  if  it  always  depended  upon  our 
choice  from  which  of  the  two  ends  of  the  sequence  we  would  under- 
take our  inquiries.  But  we  have  seldom  any  option.  As  we  can  only 
travel  from  the  known  to  the  unknown,  we  are  obliged  to  commence 
at  whichever  end  we  are  best  acquainted  with.  If  the  agent  is  more 
familiar  to  us  than  its  effects,  we  watch  for,  or  contiive,  instances  of 
th,e  agent,  under  such  varieties  of  circumstances  as  are  open  to  us,  and 
observe  the  result.  If,  on  the  contrary,  the  conditions  on  which  a 
phenomenon  depends  are  obscure,  but  the  phenomenon  itself  familiar, 
we  must  commence  our  inquiry  from  the  effect.  If  we  are  struck  with 
the  fact  that  chloride  of  silver  has  been  blackened,  and  have  no 
suspicion  of  the  cause,  we  have  no  resoui'ce  but  to  comjiare  instances 
in  which  the  fact  has  chanced  to  occur,  until  by  that  comparison  we 
discover  that  in  all  those  instances  the  substance  had  been  exposed  to 
the  light.     If  we  knew  nothing  of  the  Indian  arrows  but  their  fatal 


OBSERVATION    AND    EXPERIMENT  221 

effect,  accident  alone  could  turn  our  attention  to  experiments  on  the 
urali :  in  the  regular  course  ofinvestisration,  we  could  only  inquire,  or 
try  to  observe,  what  had  been  done  to  the  arrows  in  particular  instances. 

Wherever,  having  nothing  to  guide  us  to  the  cause,  we  are  o])liged 
to  set  out  from  the  eftect,  and  to  apply  the  rule  of  varying  the  circum- 
stances to  the  consequents,  not  the  antecedents,  we  are  necessarily 
destitute  of  the  resource  of  artificial  experimentation.  We  cannot,  at 
our  choice,  obtain  consequents,  as  we  can  antecedents,  under  any  set 
of  circumstances  compatible  with  their  nature.  There  are  no  means  of 
producing  effects  but  through  their  causes,  and  by  the  supposition  the 
causes  of  the  effect  in  question  are  not  known  to  us.  We  have  there- 
fore no  expedient  but  to  study  it  where  it  offers  itself  spontaneously. 
If  nature  happens  to  present  us  with  instances  sufficiently  varied  in 
their  circumstances,  and  if  we  are  able  to  discover  either  among  the 
proximate  antecedents,  or  among  some  other  order  of  antecedents, 
something  which  is  always  found  when  the  effect  is  found,  however 
various  the  circumstances,  and  never  found  when  it  is  not ;  we  may 
discover,  by  mere  observation  without  experiment,  a  real  uniformity  in 
nature. 

But  although  this  is  certainly  the  most  favorable  case  for  sciences  of 
pure  observation,  as  contrasted  with  those  in  which  artificial  experi- 
ments are  possible,  there  is  in  reality  no  case  which  more  strikingly 
illustrates  the  inherent  imperfection  of  direct  induction  when  not 
founded  upon  experimentation.  Suppose  that,  by  a  comparison  of 
cases  of  the  effect,  we  have  found  an  antecedent  which  appears  to  be, 
and  perhaps  is,  invariably  connected  with  it :  we  have  not  yet  proved 
that  antecedent  to  be  the  cause,  until  we  have  reversed  the  process, 
and  produced  the  effect  by  means  of  that  antecedent.  If  we  can  pro- 
duce the  antecedent  artificially,  and  if,  when  we  do  so,  the  effect  fol- 
lows, the  induction  is  complete;  that  antecedent  is  the  cause  of  that 
consequent.*  But  we  then  have  added  the  evidence  of  experiment  to 
that  of  simple  observation.  Until  we  had  done  so,  we  had  only  proved 
invariaole  antecedence,  but  not  unconditional  antecedence,  or  causa- 
tion. Until  it  had  been  shown  by  the  actual  production  of  the  antece- 
dent under  kno\Mi  circumstances,  and  the  occurrence  thereupon  of  the 
consequent,  that  the  antecedent  was  really  the  condition  on  which,  it 
depended ;  the  uniformity  of  succession  which  was  proved  to  exist 
between  them  might,  for  aught  we  knew,  be  (like  the  succession  of 
day  and  night)  no  case  of  causation  at  all ;  both  antecedent  and  con- 
sequent might  be  successive  stages  of  the  effect  of  an  ulterior  cause. 
Observation,  in  short,  without  experiment  (and  without  any  aid  from 
deduction)  can  ascertain  uniformities,  but  cannot  prove  causation. 

In  order  to  see  these  remarks  verified  by  the  actual  state  of  the 
sciences,  we  have  only  to  think  of  the  condition  of  natural  history.  In 
zoology,  for  example,  thei'e  is  an  immense  number  of  uniformities 
ascertained,  some  of  coexistence,  othei-s  of  succession,  to  many  of 
which,  notwithstanding  considerable  variations  of  the  attendant  circum- 
stances, we  know  not  any  exception :  but  the  antecedents,  for  the 
most  part,  are  such  as  we  cannot  artificially  produce  ;  or,  if  we  can,  it 

*  Unless,  indeed,  the  consequent  was  generated  not  by  the  antecedent,  but  by  the  means 
we  employed  to  produce  the  antecedent.  As,  however,  these  means  are  under  our  power, 
there  is  so  far  a  probability  that  they  are  also  sufficiently  within  our  knowledge,  to  enable 
us  to  judge  whether  that  could  be  the  case  or  not. 


222  INDUCTION. 

is  only  by  setting  in  motion  tlie  exact  process  by  which  nature  pro- 
duces them ;  and  this  being  to  us  a  mysterious  process,  of  which  the 
main  circumstances  are  not  only  unknown  but  unobservable,  the  name 
of  experimentation  would  here  be  completely  misapplied.  Such  are 
the  facts :  and  what  is  the  result  1  That  on  this  vast  subject,  which 
affords  so  much  and  such  varied  scope  for  observation,  we  have  not, 
properly -speaking,  ascertained  a  single  cause,  a  single  unconditional 
uliiformity.  We  know  not,  in  the  case  of  almost  any  of  the  phenom- 
ena that  we  find  conjoined,  which  is  the  condition  of  the  other;  which 
is  cause,  and  which  effect,  or  whether  either  of  them  is  so,  or  they  are 
not  rather  all  of  them"  conjunct  effects  of  causes  yet  to  be  discovered, 
complex  results  of  laws  hitherto  unknown. 

Although  some  of  the  foregoing  observations  may  be,  in  technical 
strictness  of  aiTangement,  premature  in  this  place,  it  seemed  that  a 
few  general  remarks  upon  the  difierence  between  Sciences  of  mere 
Observation  and  Sciences  of  Experimentation,  and  the  extreme  disad- 
vantage under  which  directly  inductive  inquiry  is  necessarily  carried 
on  in  the  former,  were  the  best  preparation  for  discussing  the  methods 
of  direct  induction ;  a  preparation  rendering  superfluous  much  that 
must  otherwise  have  been  introduced,  with  some  inconvenience,  into 
the  heart  of  that  discussion.  To  the  consideration  of  these-  Methods 
we  now  proceed. 


CHAPTER  VIII. 

OF  THE   FOUR  METHODS   OF   EXPERIMENTAL   INaUIRY. 

§  1.  The  simplest  and  most  obvious  modes  of  singling  out  from 
among  the  circumstances  which  precede  or  follow  a  phenomenon, 
those  with  which  it  is  really  connected  by  an  invariable  law,  are  two 
in  number.  One  is,  by  comparing  together  different  instances  in  which 
the  phenomenon  occurs.  The  other  is  by  comparing  instances  in 
which  the  phenomenon  does  occur,  with  instances  in  other  respects 
similar  in  which  it  does  not.  These  two  methods  may  be  respectively 
denominated,  the  Method  of  Agreement,  and  the  Method  of  Difference. 

In  illustrating  these  methods  it  will  be  necessary  to  bear  in  mind 
the  two-fold  character  of  inquiries  into  the  laws  of  phenomena ;  which 
may  be  either  inquiries  into  the  cause  of  a  given  effect,  or  into  the 
eftects  or  properties  of  a  given  c^use.  We  shall  consider  the  methods 
in  their  application  to  either  order  of  investigation,  and  shall  draw  our 
examples  equally  from  both. 

We  shall  denote  antecedents  by  the  large  letters  of  the  alphabet, 
and  the  consequents  con-esponding  to  them  by  the  small.  Let  A, 
then,  be  an  agent  or  cause,  and  let  the  object  of  our  inquiry  be  to 
ascertain  what  are  the  effects  of  this  cause.  If  we  can  either  find,  or 
produce,  the  agent  A  in  such  varieties  of  circumstances,  that  the 
different  cases  have  no  circumstance  in  common  except  A ;  then, 
whatever  effect  we  find  to  be  produced  in  all  our  trials  must,  it  would 
seem,  be  the  effect  of  A.  Suppose,  for  example,  that  A  is  tried  along 
with  B  and  C,  and  that  the  effect  is  abc;   and  suppose  that  A  is  next 


THE  FOUR  EXPERIMENTAL  METHODS.  223 

tried  with  T)  and  E,  but  without  B  and  C,  and  that  the  effect  is  ade. 
Then  wo  may  rouson  thus  :  b  and  c  are  not  effects  of  A,  for  they  were 
not  produced  hy  it  in  the  second  experiment;  nor  are .cZ  and  e,  for  they 
were  not  produced  in  the  first.  Whatever  is  really  the  effect  of  A 
must  have  been  produced  in  both  instances;  now  this  condition  is 
fulfilled  by  no  circumstance  except  a.  The  phenomenon  a  cannot 
have  been  the  effect  of  B  or  C,  since  it  was  produced  where  they 
were  not;  nor  of  D  or  K,  since  it  was  produced  where  they  were  not. 
Therefore  it  is  the  effect  of  A. 

For  example,  let  the  antecedent  A  be  the  contact  of  an  alkaline 
substance  and  an  oil.  This  combination  being  tried  under  several 
varieties  of  circumstance  resembling  each  other  in  nothing  else,  the 
results  agree  in  the  production  of  a  greasy  and  detersive  or  saponaceous 
substance  :  it  is  therefore  coiu'duded  that  the  combination  of  an  oil 
and  an  alkali  causes  the  production  of  a  soap.  It  is  thus  we  inquire, 
by  the  Method  of  Agreement,  into  the  effect  of  a  given  cause. 

In  a  similar  manner  we  may  inquire  into, the  cause  of  a  given  effect. 
Let  a  be  the  effect.  Here,  as  shown  in  the  last  chapter,  ;vve  have  only 
the. resource  of  observation  without  experiment:  we  cannot  take  a 
phenomenon  of  which  we  know  not  the  origin,  and  try  to  find  its  mode 
of  production  by  producing  it ;  if  we  succeeded  in  suqli  a  random  trial 
it  could  only  be  by  accident.  But  if  we  can  observe  a  in  two  different 
combinations,  aic  and  ade;  and  if  we  know,  or  can  discover,  that  the 
antecedent  circumstances  in  these  cases  respectively  were  ABC  and 
ADE;  we  may  conclude  by  a  reasoning  similar  to  that  in  the  pre- 
ceding example,  that  A  is  the  antecedent  connected  with  the  consequent 
(i  by  a  law  of  causation.  B  and  G,  we  may  say,  cannot  be  causes  of  a, 
since  on  its  second  occurrence  they  were  not  present ;  nor  are  D  and  E, 
for  they  were  not  present  on  its  first  occurrence.  A,  alone  of  the 
five  circumstances,  was  found  among  the  antecedents  of  a  in  both 
instances. 

For  example,  let  the  effect  a  be  crystalizatioUi.  We  compare  in- 
stances in  which  bodies  are  known  to  assume  crystaHne  structure,  but 
which  have  no  other  point  of  agreement;  and  we  find  thdm  to  have 
one,  and  as  far  as  we  can  observe,  only  one,  antecedent  in  common  : 
the  deposition  of  a  solid  matter  from  a  liquid  state,  either  a  state  of 
fusion  or  of  solution.  We  conclude,  therefore,  that  the  solidification 
of  a  substance  from  a  liquid  state  is  an  invariable  antecedent  of  its 
crystalization. 

In  this  example  we  may  go  further,  and  say,  it  is  not  only  the 
invariable  antecedent  but  the  cause.  For  in  tliis  case  we  are  able, 
after  detecting  the  antecedent  A,  to  produce  it  artificially,  and  by 
finding  that  a  follows  it,  verify  the  result  of  our  induction.  The 
importance  of  thus  reversing  the  proof  was.  never  more  strikingly- 
manifested  than  when,  by  keeping  a  phial  of  water  charged  with 
siliceous  particles  undisturbed  for  years,  a  chemist  (1  believe  Dr. 
Wollaston)  succeeded  in  obtaining  crystals  of  quartz ;  and  in  the 
equally  interesting  experiment  in  which  Sir  James  Hall  produced 
artificial  marble,  by  the  cooling  of  its  materials  from  fusion  under 
immense  pressure :  two  admirable  examples  of  the  light  which  may 
be  thrown  upon  the  most  secret  processes  of  nature  by  well-contrived 
inten-ogation  of  her. 

But  if  we  cannot  artificially  produce  the  phenomenon  A,  the  con- 


224  INDUCTION. 

elusion  that  it  is  the  cause  of  a  remains  subject  to  very  considerable 
doubt.  Though  an  invai-iable,  it  may  not  be  the  unconditional  ante- 
cedent of  a,  but  may  precede  it  as  day  precedes  night  or  night  day. 
This  uncertainty  arises  from  the  imjjossibility  of  assuring  ourselves  that 
A  is  the  only  immediate  antecedent  common  to  both  the  instances.  If 
we  could  be  certain  of  having  ascertained  all  the  invariable  antece- 
dents, we  might  be  sure  that  the  unconditional  invariable  antecedent, 
or  cause,  mustbe  found  somewhere  among  them.  Unfortunately  it  is 
hardly  ever  possible  to  ascertain  all  the  antecedents,  unless  the  phe- 
nomenon is  one  which  we  can  produce  artificially.  Even  then  the 
difficulty  is  merely  lightened,  not  removed :  men  knew  how  to  raise 
water  in  pumps  long  before  they  adverted  to  what  was  really  the 
operating  circumstance  in  the  means  they  employed,  namely,  the 
pressure  of  the  atmosphere  on  the  open  surface  of  the  water.  It  is, 
however,  much  easier  to  analyze  completely  a  set  of  arrangements 
made  by  ourselves,  than  the  whole  complex  mass  of  the  agencies 
which  nature  happens  to  be  exerting  at  the  moment  when  she  produ- 
ces any  given  phenomenon.  We  may  overlook  some  of  the  material 
circumstances  in  an  experiment  with  an  electrical  machine ;  but  we 
shall,  at  the  worst,  be  better  acquainted  with  them  than  with  those  of 
a  thunder-storm. 

The  mode  of  discovering  and  proving  laws  of  nature,  which  we 
have  now  examined,  proceeds  upon  the  following  axiom :  Whatever 
circumstance  can  be  excluded,  without  prejudice  to  tl>e  phenomenon, 
or  can  be  absent  notwithstanding  it  presence,  is  not  connected  with  it 
in  the  way  of  causation.  The  casual  circumstances  being  thus  elimi- 
nated, if  only  one  remains,  that  one  is  the  catise  which  we  are  in 
search  of:  if  more  than  one,  they  either  are,  or  contain  among  them, 
the  cause  :  and  so,  mutatis  mutandis,  of  the  effect.  As  this  method 
proceeds  by  comparing  different  instances  to  ascertain  in  what  they 
agree,  I  have  termed  it  the  Method  of  Agreement :  and  we  may 
adopt  as  its  regulating  principle  the  following  canon: — 

First  Canon. 

If  two  or  more  instances  of  the  phenomenon  under  investigation  have 
only  one  circumstance  in  common,  the  circumstance  in  which  alone  all 
the  instances  agree,  is  the  cause  (or  effect)  of  the  given  jxhenomenon. 

'•  Quitting  for  the  present  the  Method  of  Agreement,  to  which  we 
shall  almost  immediately  return,  we  proceed  to  a  still  more  potent 
instrument  of  the  investigation  of  nature,  the  Method  of  Difference, 

§  2.  In  the  Method  of  Agreement,  we  endeavored  to  obtain  in- 
stances which  agreed  in  the  given  circumstance  but  differed  in  every 
other :  in  the  present  method  we  require,  on  the  contrary,  two  in- 
stances resembling  one  another  in  every  other  respect,  but  differing  in 
the  presence  or  absence  of  the  phenomenon  we  wish  to  study.  If  our 
object  be  to  discover  the  effects  of  an  agent  A,  we  must  procure  A  in 
some  set  of  ascertained  circumstances,  as  ABC,  and  having  noted  the 
effects  produced,  compare  them  with  the  efiect  of  the  rernaining 
circumstances  B C,  when  A  is  absent.  If  the  effect  of  A B C  is  ahc, 
and  the  effect  of  BC,  he,  it  is  evident  that  the  effect  of  A  is  a.     So 


THE   FOUR  EXPKRI.MENTAL  METHODS.  225 

again,  if  we  begiji  at  the  otUcr  end,  and  desire,  to  investigate  the  gause 
of  an  .ctfect  a,  wo  must  select  an  instance,  as  abc,  in  which  the  effect 
occurs, .and  iiL  which  the  antecedents  were  ABC,  and  we  must  look 
out  for  another  inatance  in  which  the  remaining  circumstances,  he, 
occur  without  a.  If  the  antecedents,  in  that  instance,  are  BC,  we 
know  that  the  cause  of  a  must  be  A :  either  A  alone,  or  A  in  conjunc- 
tion with  some  of  the  other  circumstances  present. 

It  is  scarcely  necessary  to  give  examples  of  a  logical  process  to 
Avhich  we  owe  almost  all  the  inductive  conclusions  we  draw  in  daily 
life.  When  a  man  is  shot  through  the  heart,  it  is  by  this  method  we 
know  that  it  was  the  gun-shot  which  killed  him  :  for  he  was  in  the 
fullness  of  life  immediately  before,  all'  circumstances  being  the  same, 
except  the  wound. 

The  axjoras  which  ai^e  taken  for  gi-anted  in  this  method  are  evidently 
the  following :  Whatever  antecedent  camiot  be  excluded  without  pre- 
venting the  phenomenon,  is  the  cause,  or  a  condition,  of  that  phenom- 
enon ;  Whatever  consequent  can  be  excluded,  with  no  other  differ- 
ence in  the  antecedents  than  the  absence  of  a  particular  one,  is  the 
effect  of  that  one.  Instead  of  comparing  diffei"ent  instances  of  a  jahe- 
nomenon,  to  discover  in  what  they  agree,  this  method  compares  an 
instance  of  its  occurrence  with  an  instance  of  its  non-occuri'ence,  to 
discover  in  what  they  difler.  The  canon  which  is  the  regulating  prin- 
ciple of  the  Method  of  Difference  may  be  expressed  as  follows  : — 

Second  Canon. 

If  an  instance  in  which  the  'phenomenon  under  investigation  occurs, 
and  an  instance  in  which  it  does  not  occur,  have  every  circumstance  save 
ane  i?i  common,  that  one  occurring  only  in  the  former  ;  the  circumstance 
in  which  alone  the  two  instances  differ,  is  the  effect,  or  cause,  or  a  neces- 
sary part  oftflie  caiise,  of  the  phenomenon. 

§  3,  The  two  methods  which  we  have  now  stated  have  many  features 
of  resemblance,  but  there  are  also  many  distinctions  between  them. 
Both  are  methods  of  elimination.  This  tcim  (which  is  enrploycd  in 
the  theory  of  equations  to  denote  the  process  by  which  one  after 
another  of  the  elements  of  a  question  is  excluded,  and  the  solution 
made  to  depend  upon  the  relation  between  the  remaining  elements 
only,)  is  well  suited  to  express  the  operation,  analagous  to  this,  which 
has  been  understood  since  the  time  of  Bacon  to  be  the  foundation  of 
experimental  inquiry  :  namely,  the  successive  exclusion  of  the  various 
circumstances  wliich  are  found  to  accompany  a  phenomenon  in  a  given 
instance,  in  order  to  ascertain  what  are  those  among  them'  which  can 
be  absent  consistently  with  the  existence  of  the  phenomenon.  The 
Method  of  Agreement  stands  on  the  ground  that  whatever  can  be 
eliminated,  is  not  connected  with  the  phenomenon  by  any  law.  The 
Method  of  Difference  has  for  its  foundation,  that  whatever  can  not  be 
eliminated,  is  connected  with  the  phenomenon  by  a  law. 

Of  these  methods,  that  of  Diffc;renco  is  more  particularly  a  method 
of  artificial  experiment ;  while  that  of  Agreement  is  more  especially 
the  resource  we  employ  where  experimentation  is  impossible.  A  few 
reflections  will  prove  the  fact,  and  point  out  the  reason  of  it. 

It  is  inherent  in  the  peculiar  character  of  the  Method  of  Difference, 
Fp 


226  INDUCTION. 

that  the  nature  of  the  combinations  which  it  requires  ns  much  more 
strictly  defined  than  in  the  Method  of  Agi-eement,     The  two  instances 
which  are  to  be  compared  with  one  another  must  be  exactly  similar, 
in  all  circumstances  except  the  one  which  we  are  attemj)ting  to  inves- 
tigate :  they  must  be  in  the  relation  of  ABC  and  BC,  or  of  a Z»c  and 
be.     It  is  true  that  this  similarity  of  circumstances  needs  not  extend 
to  such  as  are  already  known  to  be  immaterial  to  the  result.     And  in 
the  case  of  most  phenomena  we  leani  at  once,  from  the  most  ordinary 
experience,  that  most  of  the   coexistent  phenomena  of  the   universe 
may  be  either  present  or  absent  without  affecting  the  given  phenome- 
non ;   or,  if  present,  are  present  indifferently  when   the  phenomenon' 
does  not  happen,  and  when  it  does.     Still,  even  limiting  the  identity 
which  is  required  between  the  two  instances,  ABC  and  BC,  to  snch 
circumstanceis  as  are  not  already  known  to  be  indifferent ;  it  is  very 
seldom  that  nature  affords  two  instances,  of  which  we  can  be  assured 
that  they  stand  in  this  precise  relation  to  one  another.  '  In  the  spon- 
taneous operations  of  nature  there  is  generally  such  complication  and 
such  obscurity,  they  are  mostly  either  on  so  overwhelmingly  large  or 
on  so  inaccessibly  minute  a  scale,  we  are' so  ignorant  of  a  great  part 
of  the  facts  which  really  take  place,  and  even  those  of  which  we  are 
not  ignorant  are  so  multitudinous,   and  therefore  so  seldom  exactly 
alike  in  any  two  cases,  that  a  spontaneous  experiment,  of  the  kind 
required  by  the  Method  of  Difference,  is  commonly  not  to  be  found. 
AVlaen,  on   the   contrary,    we   obtain   a  phenomenon    by   an   artificial 
experiment,  a  pair  of  instances  such  as  the  method  requires  is  obtained 
almost  as  a  matter  of  course,  j^rovided  the  process  does  not  last  a  long 
time.     A  certain  state  of  sun-ounding  circumstances  existed  before  we 
commenced  the  experiment :  this  is  BC.     We  then  hitroduce  A  ;  say, 
for  instance,  by  merely  bringing  an  object  from  another  part  of  Hie 
room,  before  there  has  been  time  for  any  change  in  the  other  ele- 
ments.    It  is,  in  short  (as  M.  Comte  obsei-\-es),  the  very  nature  of  an 
experiment,  to  introduce  into  the  preexisting  state  of  circumstances  a 
change  perfectly  definite.     We  choose  a  previous  state  of  things  with 
which  we  are  well  acquainted,  so  that  no  unforeseen  alteration  in  that 
state  is  likely  to  pass  unobserved ;    and   into  this  we  introduce,   as 
rapidly  as  possible,  the  phenomenon  which  we  wish  to  study ;  so  that 
we  in  general  are  entitled  to  feel  complete  assurance,  that  the  pre- 
existing state,  and  the  state  which  we  have  prodviced,  differ  in  nothing 
except  in  the  presence  or  absence  of  that  phenomenon.     If  a  bird  is 
taken  from  a  cage,  and  instantly  plunged  into  carbonic  acid  gas,  the 
experimentalist  may  be  fully  assured  (at  ail  events  after  one  or  two 
repetitions)  that  no  circumstance  capable  of  causing  suffocation  had 
supei-vened  in  the  interim,  except  the  change  from  immersion  in  the 
atmosphere  to  immersion  in  carbonic  acid  gas.      There  is  one  doubt, 
indeed,  which  may  remain  in  some   cases  of  this  description ;    the 
effect  may  have  been  produced  not  by  the  change,  but  by  the  means 
we  employed  to  produce  the  change.      The  possibility,  however,  of  this 
last  supposition  generally  admits  of  being  conclusively  tested  by  other 
experiments.  .  It  thus  appears  that  in  the  study  of  the  various  kinds 
of  phenomena  which  we  can,   by  our  vohmtary    agency,  modify  or 
control,  we  can  in  general  satisfy  the  requisitions  of  the  Method  of 
Difference ;  but  that  by  the  spontaneous  operations  of  nature  those 
requisitions  are  seldom  fulfilled. 


THE    FOUR    EXPERIMENTAL    METHODS.  227 

The  reverse  of  this  is  the  case  with  the  Method  of  Agreement. 
We  do  uot  here  require  instances  of  so  special  and  dcterininale  a  kind. 
Any  instances  whatever,  in  which  nature  presents  us  with  a  phenom- 
enon, may  be  examined  for  tlic  purposes  of  this  method ;  and  if  all 
such  instances  agree  ia  anything,  a  conchision  of  considerable  value  is 
already  jittained.  We  can  sekhmi,  indeed,  be  sure  that  this  one  point 
of  agreement  is  the  only  one ;  but  our  ignorance  does  not,  as  irt  the 
Method  of  Difference,  vitiate  the  conclusion ;  the  certainty  of  the 
result,  as  far  as  it  goes,  is  not  affected.  We  have  ascertained  one 
invariable  antecedent  or  consequent,  however  many  other  invariable 
antecedents  or  consequents  may  still  remain  unascertained.  If  ABC, 
ADE,  AFG,  are  all  eqilally  followed  by  a,  then  a  is  an  invariable 
f(':ascqaGntof  A.  If  «ir,  a.'tc,  ({f^,  all  nunibcr  A  iimong  their  ante- 
cedents, then  A  is  connected  as  an  antecedent,  by  some  invariable 
law,  with  a.  But  to  detei-mine  whether  this  invariable  antecedent  is 
a  cause,  or  this  invariable  consequent  an  effect,  we  must  be  able,  in 
addition,  to  produce  the  one  by  means  of  the  other ;  or,  at  least,  to  obtain 
that  which  alone  constitutes  our  assurance  of  having  produced  any- 
thing, namely,  an  instance  in  which  the  effect,  a,  has  come  into  exist- 
ence, with  no  other  change  in  the  preexisting  circumstances  than  the 
addition  of  A.  And  this,  if  we  can  do  it,  is  an  application  of  the 
Method  of  Difference,  not  of  the  Method  of  Agi-eement. 

It  thus  appears  to  be  by  the  Method  of  Difference  alone  that  we  can 
ever,  in  the  way  of  direct  experience,  arrive  with  certainty  at  causes. 
The  Method  of  Agi-eement  leads  only  to  laws  of  phenomena,  as  Mr. 
Whewell  calls  thenx,  but  which  (since  laws  of  causation  are  also  laws 
of  phenomena)  I  prefer  to  designate  as  uniformities  in  which  the  ques- 
tion of  causation  must  for  the  present  remain  undecided.  The  Method 
of  Agreement  is  chiefly  to  be  resorted  to,  as  a  means  of  suggesting 
applications  of  the  Method  of  Difference  (as  in  the  last  example  the  com- 
parison of  ABC,  ADE,  AFQ,  suggested  that  A  was  the  antecedent 
on  which  to  try  the  experiment  ^vhethe^  it  could  produce  a) ;  or,  as  an 
inferior  resource,  in  case  the  Method  of  Difference  is  impracticable  ; 
which,  as  we  before  showed  generally  arises  from  the  impossibility  of 
artificially  producing  the  phenomena.  And  hence  it  is  that  the  Method 
of  Agi-eement,  although  applicable  in  principle  to  either  case,  is  more 
emphatically  the  method  of  investigation  on  those  subjects  where  arti- 
ficial expei-imentation  is  impossible ;  because  on  those  it  is,  generally, 
our  only  resource  of  a  directly  inductive  nature  ;  while,  in  the  phenome- 
na which  we  can  produce  at  pleasure,  the  Method  of  Difference  gene- 
rally affords  a  more  efficacious  process,  which  will  ascertain  causes  as 
well  as  mere  laws. 

§  4.  Our  next  remark  shall  be,  that  there  are  many  cases  in  which, 
although  our  power  of  producing  the  phenomenon  is  complete,  the 
Method  of  Difference  either  cannot  be  made  available  at  all,  or  not 
without  a  previous  employment  of  the  Method  of  Agi-eement.  This 
occurs  when  the  agency  by  which  we  can  produce  the  phenomenon  is 
not  that  of  one  single  antecedent,  but  a  combination  of  antecedents, 
which  we  have  no  power  of  separating  from  each  other  and  exhibiting 
apart.  For  instance,  suppose  the  subject  of  inquiry  to  be  the  cause  of 
the  double  refraction  of  light.  We  can  produce  this  pheijomenoai,,?it^ 
pleasure,  by  employing  any  one  of  the  many  substances  which  ire' 


228  INDUCTION. 

known  to  refract  light  in  tliat  peculiar  manner.  But  if,  taking  one  of 
those  substances,  as  Iceland  spar  for  example,  we  wish  to  detcmiine 
on  which  of  the  properties  of  Iceland  spar  this  remarkable  phenomena 
depends,  we  can  make  no  use,  for  that  purpose;  of  the  Method  of  Dif- 
ference ;  for  we  cannot  find  another  substance  precisely  resembling 
Iceland  spar  except  in  some  one  property.  The  only  mode,  therefore, 
of  prosecuting  this  inquiry  is  that  afforded  by  the  Method  of  Agree- 
ment ;  by  which,  in  fact,  through  a  comparison  of  all  the  known  sub- 
stances Avhich  had  the  property  of  doubly  refracting  light,  it  was  ascer- 
tained that  they  agreed  in  the  single  circumstance  of  being  crystaline 
substances  ;  and  althoiigh  the  converse  does  not  hold,  although  all  crys- 
taline substances  have  not  the  property  of  double  refraction,  it  was 
concluded,  with  reason,  that  there  is  a  real  connexion  between  these 
two  properties  ;  that  either  crystaline  structure,  or  the  cause  which 
gives  rise  to  that  structure,  is  one  of  the  conditions  of  double  refraction. 

Out  of  this  employment  of  the  Method  of  Agi'eement  arises  a  pecu- 
liar modification  of  that  method,.- which  is  sometimes  of  great  avail  in 
the  investigation  of  jiature.  In  cases  similar  to  the  above,  in  which  it 
is  not  possible"  to  obtain  the  precise  pair  of  instances  which  our  second 
canon  requires — instances  agreeing  in  every  antecedent  except  A,  or  in 
every  consequent  except  a  ;  we  may  yet  be  able,  by  a. double  employ- 
ment of  the  Method  of  Agreement,  to  discover  in  what  the  instances 
which  contain  A  or  a,  differ  from  those  which  do  not. 

If  we  compare  various  instances  in  which  a  occurs,  and  find  that 
they  all  have  in  common  the  circumstance  A,  and  (as  far  as  can  be 
observed)  no  other  circumstance,  the  Method  of  Agreement,  so  far  beais 
testimony  to  a  connexion  between  A  and  a.  In  order  to  convert  this 
proof  of  connexion  into  proof  of  causation  by  the  direct' Method  of 
Difference,  we  ought  to  be  able  in  some  one  of  these  instances,  as  for 
example  ABC,  to  leave  out  A,  and  observe  whether  by  doing  so, «  is 
prevented.  Now  supposing  (what  is  often  the  case)  that. we  are  not 
able  to  try  this  decis\\'e  experiment;  yet,  provided  we  can  by  any 
means  discover  what  would  be  its  result  if  we  could  try  it,  the  advan- 
tage will  be  the  same.  Suppose,  then,  that  as  we  previously  examined 
a  variety  of  instances  in  which  a  occuired,  and  found  them  to  agree  in 
containing  A,  so  we  now  observe  a  variety  of  instances  in  which  a  does 
not  occur,  and  find  them  agree  innoi  containing  A;  which  establishes, 
by  the  Method  of  Agi-eeraent,  the  same  connexion  between  the  absence 
of  A  and  the  absence  qf'aj  which  was  before  established  between  their 
presence.  As,  then,  it  had  been  shown  that  whenever  A  is  present  a 
is  present,  so  it  being  now  shown  that  when  A  is  taken  away  a  is  re- 
moved along  with  it,  we  bave  by  the  one  proposition  ABC,  abc,  by 
.the  other  BC,  ic,  the  positive  and  negative  instances  which  the  Method 
of  Difference  requires.  Thus,  if  it  be  true  that  all  animals  which  have 
a  well-developed  respiratory  system,  and  therefore  aerate  the  blood 
perfectly,  agree  in  being  warm-blooded,  while  those  whose  respiratory 
system  is  imperfect  do  not  maintain  a  temperature  much  exceeding 
that  of  the  surrounding  medium,  we  may  argue  fi'om  this  two-fold  expe- 
rience, that  the  change  which  takes  place  in  the  blood  by  respiration 
is  the  cause  of  animal  heat. 

This  method  may  be  called  the  Indirect  Method  of  Difference,  or 
the  Joint  Method  of  Agreement  and  Difference  ;  and  consists  in  a  double 
employment  of  the  Method  of  Agreement,  each  proof  being  indepen- 


THE    POUR    EXrERIMENTAL    METHODS.  229 

tleiit  of  the  otlier,  and  corroborating  it.  But  it  is  not  ecjuivalcnt  to  a 
proof"  by  the  direct  JNIethod  of  Difleroncc.  For  the  requisitions  of  the 
Method  of  Diffcreace  are  not  satisfied,  unless  we  can  be  quite  sure 
either  that  the  instances  affirmative  of  a  agree  in  no  antecedent  what- 
ever but  A,  or  that  the  instances  negative  of  «  agi'ce  in  nothing  but  tlie 
negation  of  A.  Now  if  it  were  possible,  which  it  never  is,  to  have  this 
assurance,  we  should  not  need  the  joint  method;  for  either  of  tke  two 
sets  of  instances  sepaiately  would  then  be  sufficient  to  prove  causation. 
This  indirect  method,  therefore,  can  only  be  viewed  as  a  great  exten- 
sion and  improvement  of  the  Method  of  Agreement,  but  not  as  partici- 
pating in  the  moi'e  cogent  nature  of  the  Method  of  Diflerence.  The 
tbllovving  luay  be  stated  as  its  canon : — 

Third  Canon. 

If-  two  or  more  instances  in  which  -the  phenomenon  occurs  have  only 
one  circumstance  in  common,  while  two  or  more  instances  in  which  it  does 
not  occur  have  nothing  in  common  save  the  absence  of  that  circumstance  ; 
the  circumstance  in  which  alone  the  two  sels  of  instances  differ,  is  the 
effect,  or  cause,  or  a  necessary  ^tart  of  the  cause,  of  the  jihenomenon. 

We  shall  presently  show  that  the  Joint  Method  of  Agreement  and 
Difference  constitutes,  in  another  respect  not  yet  adverted  to,  an  im- 
provement upon  the  common  Method  of  Agreement,  namely,  in  being 
unatfected  by  a  characteristic  imperfection  of  that  method,  tlie  nature 
of  which  still  remains  to  be  pointed  out.  But  as  we  cannot  enter  into 
this  exposition  without  introducing  a  new  element  of  complexity  into 
this  long  and  intricate  discussion,  I  shall  postJ)one  it  to  the  next  chapter, 
and  shall  at  once  proceed  to  the  statement  of  two  other  methods, 
which  -will  complete  the  enumeration  of  the  means  which  mankind 
possess  for  exploring  the  laws  of  nature  by  specific  observation  and 
experience. 

§  5.  The  first  of  these  has  been  aptly  denominated  the  Method  of 
Residues.  Its  pi'inciple  is  very  simple.  Subducting  from  any  given 
phenomenon  all  the  portions  which  by  virtue  of  preceding  inductions, 
can  be  assigned  to  known  causes,  the  remainder  will  be  the  elfeot  of 
the  antecedents  which  liad  been  overlooked,  or  of  which  the  effect  was 
as  yet  an  unknown  quantity. 

Suppose,  as  before,  that  we  have  the  antecedents  ABC,  followed 
by  the  consequents  a  h  c,  and  that  by  previous  inductions,  (founded,  we 
will  suppose,  upon  the  ^Method  of  Dirterence,)  we  have  ascertained  the 
causes  of  some  of  these  effects,  or  the  effects  of  some  of  these  causes ; 
and  are  by  this  means  apprised  that  the  efiect  of  A  is  a,  and  that  the 
effect  of  B  is  b.  Subti-acting  the  sum  of  these  effects  from  the  total 
phenomenon,  there  remains  c,  which  now,  without  any  fresh  experi- 
ment, we  may  know  to  be  the  effect  of  C.  This  Method  of  llesiddes 
is  in  ti-uth  a  peculiar  modification  of  the  Method  of  Difference.  If  the 
instance  ABC,  ahc,  coidd  have  been  compared  with  a  single  instance 
AB,  ab,  we  should  have  proved  C  to  be  the  cause  of  c,  by  the  com- 
mon process  of  the  Method  of  Diffei'ence.  In  the  present  case,  how- 
ever, instead  of  a  single  instance  A  B,  we  have  had  to  study  sejjarately 
the  causes  A  and  B,  and  to  infer  from  the  effects  which  ihey  produce 


230  INDUCTION. 

separately,  what  effect  they  must 'produce  in  the  case  ABC  where 
they  act  together.  Of  the  two  instances,  therefore,  which  the  Method 
of  Difference  requires — the  one  positive,  the  other  negative — the  nega- 
tive one,  or  that  in  which  the  given  phenomenon  is  absent,  is  jiot  the 
direct  result  of  observation  and  experiment,  but  has  been  arrived  at 
by  deduction.  As  one,  of  the  forms  of  the  Method  of  Difference,  the 
Method  of  Residues  partakes  of  its  rigorous  certainty,  provided  the 
previous  inductions,  those  which  gave  the  effects  of  A  and  B,  were  ob- 
tained by  the  same  infallible  method,  and  provided  we  are  certain  that 
C  is  the  only  antecedent  to  which  the  residual  phenom.enon  c-can  be 
refeiTed ;  the  only  agent  of  which  we  had  not  already  calculated  and 
subducted  the  effect.  But  as  we  can  never  be  quite  certain  of  this, 
the  e\Hdence  derived  from  the  Method  of  Resiciues  is  not  complete, 
unless  we  can  obtain  C  ai-tificially  and  try  it  separately,  or  unless  its 
agency,  when  once  suggested,  can  be  accounted  for,  and  proved  de- 
ductively, fi'om  kno^vn  laws. 

Even  with  these  reservations,  the-  Method  of  Residues  is  one  of  the 
most  important  among  our  instruments  of  discovery.  Of  all  the  methods 
of  investigating  laws  of  nature,  this  is  the  most  fertile  in  unexpected 
results  ;  often  infonning  us  of  sequences  in  which  neither  the  cause  nor 
the  effect  were  su^ciently  conspicuous  to  attract  of  themselves  the 
attention  of  observers.  The  agent  C  may  be  an  obscure  circumstance, 
not  likely  to  have  been  perceived  unless  sought  for,  nor  likely  to  have 
been  sought  for  until  attention  had  been  awakened  by  the  insufficiency 
of  the  obvious  causes  to  account  for  the  whole  of  the  effect.  And  c 
may  be  so  disguised  by  its  intermixture  with  a  and  b,  that  it  would 
scarcely  have  presented  itself  spontaneously  as  a  subject  of  separate 
study.  Of  these  uses  of  the  method,  we  shall  presently  cite  some 
remarkable  examples.  The  canon  of  the  Method  of  Residues  is  as 
follows : — 

Fourth  Canox. 

Subduct  from  any  phenomenon  such  part  as  is  hnoicn  by  previous 
inductions  to  be  the  effect  of  certain  antecedents^  aoid  the  residue  of  the 
phenomenon  is  the  effect  of  the  remaining  antecedents. 

§  6.  There  remains  a  class  of  laws  which  it  is  impracticable  to 
ascertain  by  any  of  the  three  methods  which  I  have  attempted  to 
characterize ;  namely,  the  laws  of  those  Permanent  Causes,  or  inde- 
structible natural  agents,  which  it  is  impossible  either  to  exclude  or  to 
isolate  :  which  we  can  neither  hinder  from  being  present,  nor  contrive 
that  they  should  be  present  alone.  It  would  appear  at  first  sight  that 
we  could  by  no  Tneans  sepai-ate  the  effects  of  these  agents  fi-om  the 
effects  of  those  other  phenomena  with  which  they  cannot  be  prevented 
from  coexisting.  In  respect,  indeed,  to  most  of -the  permanent  causes, 
no  such  difficulty  exists;  since,  though  we  cannot  eliminate  them  as 
coexisting  facts,  we  can  eliminate  them  as  influencing  agents,  by 
simply  trying  our  experiment  in  a  local  situation  beyond  the  limits  of 
their  influence.  The  pendulum,  for  example,  has  its  oscillations 
disturbed  by  the  vicinity  of  a  mountain ;  we  remove  the  pendulum  to 
a  sufficient  distance  from  the  mountain,  and  the  disturbance  ceases: 
from  these  data  we  can  determine  by  the  Method  of  Difference,  the 
amount  of  effect  really  due  to  the  mountain;  and  beyond  a  certain 


THE    FOUR    EXrEKIMENTAL    METHODS.  231 

distance  everything  goes  on  precisely  as  it  would  do  if  the  mountain 
exercised  no  influence  whatever,  which^  accordingly,  we,  with  sullicient 
reason,  conclude  to  be  the  tiict.  ' 

The  difliculty,  therefore,  in  applying  the  methods  already  treated  of 
to  determine  the  eflects  of  Permanent  Causes,  is  confined  to  the  cases 
in  which  it  is  impossible  for  us  to  get  out  of  the  local  limits  of  their 
influence.  The  pendulum  can  be  removed  from  the  influence  of  the 
mountain,  but  it  cannot  be  removed  fi-om  the  influence  of  the  eart^h : 
•we  cannot  take  away  the  earth  from  the  ^)endulum,  nor  the  pendulum 
from  the  earth,  to  ascertain  whether  it  would  continue  to  vibrate  if  the 
action  which  the  earth  exerts  upon  it  were  withdrawn.  On  what 
evidfeuce,  then,  do  we  ascribe  its  vibrations  to  the  earth's  influence  1 
Not  on  any  sanctioned  by  the  Method  of  Difference  ;  for  t)ne  of 
the  tAVo  instances,  the  negative  instance,  is  wanting.  Nor  by  the 
Method  of  Agreement ;  for  although  all  j)endulums  agree  in  this,  that 
during  their  oscillations  the  earth  is  always  present,  why  may  we  not 
as  well  ascribe  the  phenomenon  to  the  sun,  which  is  equally  a  co- 
existent fact  in  all  the  experiments  1  It  is  evident  that  to  establish 
even  so  simple  a  fact  of  causation  as  this,  there  was  required  some 
method  over  and  above  those  which  we  have  yet  examined. 

As  another  example,  let  us  take  the  phenomenon  Heat.  Independ- 
ently of  all  hypothesis  as  to  the  real  nature  of  the  agency  so  called, 
this  fact  is  certain,  that  we  are  unable  to  exhaust  any  body  of  the  whole 
of  its  heat.  It  is  equally  certain  that  no  one  ever  perceived  heat  not 
emanating  from  a  body.  Being  unable,  then,  to  separate  Body  and  Heat, 
we  cannot  eflfect  such  a  variation  of  circumstances  as  the  foregoing  three 
methods  require;  we  cannot  ascertain,  by  those  methods,  what  por- 
tions of  the  phenomena  exhibited  by  any  body  are  due  to  the  heat  con- 
tained in  it.  If  we  could  observe  a  bordy  with  its  heat,  and  the  same 
body  entirely  divested  of  heat,  the  Method  of  Difference  would  show 
the  effect  due  to  the  heat,  apart  from  that  due  to  the  body.  If  we 
could  observe  heat  under  circumstances  agreeing  in  nothing  but  heat, 
and  therefore  not  characterized  also  by  the  presence  of  a  body,  we 
could  ascertain  the  effects  of  heat,  from  an  instance  of  heat  with  a  body 
and  an  instance  of  heat  without  a  body,  by  the  Method  of  Agi-eement ; 
or,  if  we  pleased,  we  could  determine  by  the  Method  of  Difference 
what  effect  was  due  to  the  body,  when  the  remainder  which  was  due  to 
the  heat  would  be  given  by  the  Method  of  Residues.  But  we  can  do 
none  of  these  things  ;  and  without  them  the  application  of  any  of  the 
three  methods  to  the  solution  of  this  problem  would  be  illusory.  It 
woidd  be  idle,  for  instance,  to  attempt  to  ascertain  the  effect  of  heat  by 
subtracting  from  the  phenomena  exhibited  by  a  body,  afl  that  is  due  to 
its  other  properties  ;  for  as  we  have  never  been  able  to  observe  any 
bodies  without  a  portion  of  heat  in  them,  the  effects  due  to  that  heat 
may  fonn  a  part  of  the  very  results,  which  we  affect  to  subtract  in  order 
that  the  effect  of  heat  may  be  sliowii  by  the  residue. 

If.  therefore,  there  were  no  other  methods  of  experimental  investi- 
gation than  these  three,  we  should  be  for  ever  unable  to  determine 
the  effects  due  to  heat  as  a  cause.  But  we  have  still  a  resource. 
Though  we  cannot  exclude  an  antecedent  altogether,  we  may  be  able 
to  produce,  or  nature  may  produce  for  us,  some  modification  in  it.  By 
a  modification  is  here  meant,  a  change  in  it,  not  amounting  to  its  total 
removal.     If  some  modification  in  the  antecedent  A  is  always  followed 


232  INDUCTION. 

by  a  change  in  the  consequent  a,  the  other  consequents  h  and  c  re- 
maining the  same ;  or,  vice  versCl,  if  every  change  in  a  is  found  to  have 
been  preceded  by  some  modification  in  A,  none  being  obsersable  in 
any  of  the  other  antecedents  ;  we  may  safely  conclude  that  a  is,  -wholly 
or  in  part,  an  effect  traceable  to  A,  or  at  least  in  some  way  connected 
with  it  through  causation.  For  example,  in  the  case  of  heat,  though 
we  cannot  expel  it  altogether  from  any  body,  we  can  modify  it  in  quan- 
tity, we  can  increase  or  diminish  it ;  and  doing  so,  we  find  by  the  va- 
rious methods  of  experimentation  or  observation  already  treated  of, 
that  such  increase  or  diminution  of  heat  is  followed  by  expansion  or 
conti-action  of  the  body.  In  this  manner  we  aiTive  at  the  conclusion, 
otherwise  unattainable  by  us,  that  one  of  the  effectsof  heat  is  to  enlarge 
the  diiTiensions  of  bodies  ;  or  what  is  the  same  thing  in  other  words,  to 
widen  the  distances  between  their  particles. 

A  change  in  a  thing,  not  amounting  to  its  total  removal,  that  is,  a 
change  which  leaves  it  still  the  same  thing  it  w'as,  must  be  a  change 
either  in  its  quantity,  or  in  some  of  its  relations  to  other  things,  of 
which  relations  the  principal  is  its  position  in  space.  In  the  previous 
example,  the  modification  which  was  produced  in  the  antecedent  was 
an  alteration  in  its  quantity.  Let  us  now  suppose  the  question  to 
be,  what  influence  the  moon  exerts  on  the  surface  of  the  earth.  We 
cannot  try  an  experiment  in  the  absence  of  the  moon,  so  as  to'  observe 
what  teiTestrial  phenomena  her  annihilation  would  put  an  end  to ; 
but  when  we  find  that  all  the  variations  in  the  j)Ositio7i  of  the  moon  are 
followed  by  coiTesponding  variations  in  the  time  and  place  of  high 
water,  the  jilace  being  always  either  on  the  side  of  the  earth  which  is 
nearest  to,  or  on  that  which  is  most  remote  fi'om,  the  moon,  we  have 
ample  evidence  that  the  moon  is,  wholly  or  partially,  the  cause  which 
determines  the  tides.  It  very  commonly  happens,  as  it  does  in  this 
instance,  that  the  variations  of  ah  effect  are  coiTespondent,  or  anal- 
ogous, to  those  of  its  cause ;  as  the  moon  moves  further  towards  the 
east,  the  high  water  point  does  the  same :  but  this  is  not  an  indis- 
pensable condition ;  as  may  be  seen  in  the  same  example,  for  along 
with  that  high  water  point,  there  is  at  the  same  instant  another  high 
water  point  diametrically  opposite  to  it,  and  which,  therefore,  of 
necessity,  moves  towards  the  west  as  the  moon  followed  by  the 
nearer  of  the  tide  waves  advances  towards  the  east :  and  yet  both 
these  motions  are  equally  effects  of  the  moon's  motion. 

That  the  oscillations  of  the  pendulum  are  caused  by  the  earth,  is 
proved  by  similar  evidence.  Those  oscillations  take  place  between 
equidistant  points  on  the  two  sides  of  a  line,  which,  being  pei-pendic- 
ular  to  the  earth,  varies  with  every  variation  in  the  earth's  position, 
either  in  space  or  relatively  to  the  object.  Speaking  accurately,  we 
only  know  by  the  method  now  charactei-ized,  that  all  terrestrial 
bodies  tend  to  the  earth,  and  not  to  some  unkno^vn  fixed  point 
lying  in  the  same  direction.  In  every  twenty-four  hours,  by  the 
earth's  rotation,  the  line  dra\vn  fi'om  the  body  at  right  angles  to  the 
earth  coincides  successively  with  all  the  radii  of  a  circle,  and  in  the 
course  of  six  months  the  place  of  that  circle  varies  by  nearly  tAvo 
hundred  millions  ofm.iles;  yet  in  all  these  changes  of  the  earth's  posi- 
tion, the  line  in  which  bodies  tend  to  fall  continues  to  be  directed  to- 
wards it :  which  proves  that  teiTestrial  gravity  is  directed  to  the  earth, 
and  not,  as  was  once  fancied  by  some,  to  a  fixed  point  of  space. 


run    FOUR    EXPERIMENTAL    METHODS,  233 

The  metliotl  by  whicl'i  tliese  rosults  were  oLtaijied^  may  he  tevmcd 
the  Method  of  Concomitant  Variations  :  it  is  regulated  by  the  I'ollow- 
"  ing  canon  : — 

Fifth  Canon. 

JV/iatcver  inlienoinenon  varies  in  any  manner  wJienever  another 
phenotncnoji  varies  in  some  particu/ar  manner,  is  cither  a  cause  or  an 
effect  of  that  plienomcnon,  or  is  connected  with  it  tJirous^h  some  fact 
of  causation. 

The  last  clause  is  subjoined,  because  it  by  no^means  follows  when 
two  phenomena  accompany  each  other  in  their  variations,  that  the 
one  is  cause  and  the  other  effect.  The  same  thing  may,  atid  indeed 
must  ha^^pen,  supposing  them  to  be  two  diHerent  efi'ects  of  a  common 
cause  :  and  by  this  method  alone  it  would  never  be  possible  to  ascer- 
tain which  of  the  two  suppositions  is  the  true  one.  The  only  way  to 
solve  the  doubt  would  be  that  which  we  have  so  often  adverted  to, 
viz.,  -by  endeavoring  to  ascertain  whether  we  can  produce  the  or;e 
set  of  variations  by  means  of  the  .other.  In  the  case  of  heat,  for 
example,  by  increasing  the  temperature  of  a  body  we  increase  its 
bulk,  but  by  increasing  its  bulk  we  do  not  increase  its  temperature ; 
ou  the  contrary  (as  in  the  rarefaction  of  air  under  the  receiver  of  an 
air-pump),  we  generally  diminish  it :  therefore  heat  is  not  an  effect, 
but  a  cause,  of  increase  of  bulk.  If  we  cannot  ourselves  produce 
the  variations,  \ye  must  endeavor,  though  it  is  an  attempt  which  is 
seldom  successful,  to  find  them  produced  by  nature  in  some  case 
in  which  the  preexisting  circumstances  are  perfectly  known  to  us. 

It  is  scarcely  necessary  to  say,  that  in  order  to  ascertain  the  uniform 
concomitance  of  variations  in  the  effect  Avith  variations  in  the  caiuse,  the 
same  precautions  must  be  used  as  in  any  other  case  of  the  determina- 
tion of  an  invariable  sequence.  We  must  endeavor  to  retain  all  the 
other  antecedents  unclianged,  while  that  particular  one  is  subjected  to 
the  requisite  series  of  variations ;  or  in  other  words,  that  we  may  be 
warranted  in  inferring  causation  from  concomitance  of  variations,  the 
concomitance  itself  must  be  proved  by  the  Method  of  Difference. 

It  might  at  first  appear  that  the  Method  of  Concomitant  Variations 
assumes  a  new  axiom,  or  law  of  causation  in  generp^l,  namely,  that 
every  modification  of  the  cause  is  followed  by  a  change  in  the  effect. 
And  it  docs  usually  happen  that  when  a  phenomenon  A  causes  a  phe- 
nomenon a,  any  variation  in  the  quantity  or  in  the  various  relations  of 
A,  is  unifoi-mly  followed  by  a  variation  in  the  quantity  or  relations  of 
a.  To  take  a  familiar  instance,  that  of  gi-avitation.  The  sun  causes  a 
certain  tendency  to  motion  in  the  earth  ;  here  we  have  cause  and  effect; 
but  that  tendency  is  towards  the  sun,  and  therefore  varies  in  direction 
as  the  sun  varies  in  the  relation  of  position;  and  moreover  the  tendency 
varies  in  intensity,  in  a  certain  numerical  ratio  to  the  sun's  distance 
fi'om  the  earth,  that  is,  according  to  another  relation  of  the  sun. 
Thus  we  see  that  there  is  not  only  an  invariable  connexion  between 
the  sun  and  the  earth's  gi'avitation,  but  that  two  of  the  relations  of  the 
sun,  its  position  with  re,-4pect  to  the  earth  and  its  distance  from  the 
earth,  are  invariably  connected  as  antecedents  with  the  quantity  and 
direction  of  the  earth's  gravitation.  The  cause  of  the  egp-th's  gravita- 
G  G 


234  INDUCTION. 

ting  at  all,  is  simply  tlie  sun;  but  the  cause  of  lier  gravitating  with  a 
given  intensity  and  in  a  given  direction,  is  the  existence  of  the  sun  in 
a  given  direction  and  at  a  given  distance.  It  is  not  strange  that  a  modi- 
fied cause,  which  is  in  truth  a  different  cause,  should  produce  a  differ- 
ent effect.  But  as  the  cause  is  only  different  in  its  quantity,  or  in  some 
of  its  relations,  it  usually  haippens  that  the  effect  also  is  only  changed 
in  its  quantity  or  its  relations. 

Although  it  is  for  the  most  part  true  that  a  modification  of  the  cause 
is  followed  by  a  modification  of  the  effect,  the  Method  of  Concomitant 
Variations  does  not,  however,  presuppose  this  as  an  axiom.  It  only 
requires  the  converse  proposition ;  that  anything  upon  whose  modifica- 
tions, modifications  of  an  effect  are  invariably  consequent,  must  be  the 
cause  {or  connected  with  the  cause)  of  that  effect;  a  proposition,  the 
truth  of  vvhich  is  evident;  for  if  the  thing  itself  had  no  influence  on  the 
effect,  neither  could  the  modifications  of  the  thing  have  any  influence. 
If  the  stars  have  no  power  over  the  fortunes  of  men,  it  is  implied  in  the 
very  terms,  that  the  conjunctions  or  oppositions  of  different  stars  can 
have  no  such  power.        '  ■ 

Although  the  most  striking  applications  of  the  Method  of  Concomi- 
tant Variations  take  place  in  the  cases  in  which  the  Method  of  Differ- 
ence, strictly  so  called,  is  impossible,  its  use  is  not  confined  to  those 
cases  ;  it  may  often  usefully  follow  after  the  Method  of  Diff'erenee,  to 
give  additional  precision  to  a  solution  which  that  has  found.  When 
by  the  Method  of  Difference  it  has  first  been  ascertained  that  a  cer^ 
tain  object  produces  a  certain  effect,  the  Method  of  Concomitant  Va- 
riations may  be  usefully  called  in  to  determine  according  to  what 
law  the  quantity  or  the  different  relations  of  the  effect  follow  those  of 
the  cause. 

§  7.  The  case  in  which  this  method  admits  of  the  most  extensive 
employment,  is  that  in  which  the  variations  of  the  cause  are  variations 
of  quantity.  Of  such  variations  we  may  in  general  afiinn  with  safety, 
that  they  will  be  attended  not  only  with  variations,  but  with  similar 
variations,  of  the  effect:  the  proposition,  that  more  of  the -cause  is 
followed  by  more  of  the  effect,  being  a  coi-ollary  from  the  principle  of 
the  Composition  of  Causes,  which,  as  we  have  seen,  is  the  general 
rule  of  causation;  cases  of  the  opposite  descrijjtion,  in  which  causes 
change  their  properties  on  being  conjoined  with  one  another,  being,  on 
the  contrary,  special  and  exceptional.  Suppose,  then,  that  when  A 
changes  in  quantity,  a  also  changes  in  quantity,  and  in  such  a  manner 
that  we  can  trace  the  numerical  relation  which  the  changes  of  the  one 
bear  to  such  changes  of  the  other  as  take  place  within  our  limits  of 
observation.  We  may  then,  with  certain-  precautions,  safely  conclude 
that  the  same  numerical  relation  will  hold  beyond  those  limits.  If,  for 
instance,  we  find  that  when  A  is  double,  a  is  double ;  that  when  A  is 
treble  or  quadruple,  a  is  treble  or  quadruple  ;  we  may  conclude  that 
if  A  were  a  half  or  a  third,  a  would  be  a  half  or  a  third,  and  finally, 
that  if  A  were  annihilated,  a  would  be  annihilated,  and  that  a  is  wholly 
the  effect  of  A,  or  wholly  the  effect  of  the  same  cause  with  A.  And 
so  with  any  other  numerical  relation  according  to  which  A  and  a  would 
vanish  simultaneously ;  as  for  instance  if  a  were  j^roportional  to  the 
square  of  A.  If,  on  the  other  hand,  a  is  not  wholly  the  effect  o^"  A, 
■  but  yet  varies  when  A  varies,  it  is  probably  (to  use  a  mathematical 


THE    FOUR    EXrEHI.^IENTAL    METHODS.  iioO 

phrase)  a  function  not  of  A  alone  but  of  A  and  something  else :  its 
changes  will  be  such  as  woukl  occur  if  part  of  it  remained  constant, 
or  varied  on  some  o.ber  principle,  and  the  remainder  varied  in  some 
numerical  relation  t,>  the  variations  of  A.  In  that  case,  when  A  dimin- 
ishes, a  will  seem  to  approach  not  towards  zero,  but  towards  vsomc 
other  limit :  and  when  the  series  of  variations  is  siicli  as  to  indicate 
what  that  limit  is,  if  constant,  or  the  law  of  its  vai'iation  if  variable, 
the  limit  will  exactly  measure  how  much  of  a  is  the  effect  of  some 
other  and  independent  cause,  and  the  remainder  will  be  the- effect  of  A 
(or  of  the  cause  of  A).  - 

These  conclusions,"^  however,  must  not  be  drawn,  without  certain 
precautions.  In  the  first  place,  the  possibility  of  drav/ing  them  at  all, 
manifestly  supposes  that  we  are  acquainted  not  only  with  the  variations, 
but  with  the  absolute  quantities,  both  of  A  and  a.  If  we  do  not  know 
the  total  quantities,  we  cannot,  of  course,  detei'mine  the  real  numerical 
relation  according  to  which  those  quantities  vary.  It  is  therefore  an 
error  to  conclude,  as  some  have  concluded,  that  because  increase  of 
heat  expands -bodies,  that  is,  increases  the  distance  between  their 
particles,  therefore  that  distance  is  wholly  the  effect  of  heat,  and  that 
if  we  could  entirely  exhaust  the  body  of  its  heat,  the  particles  would 
be  in  complete  contact.  This  can  never  be  more  than  a  gu6Ss,  and  of 
the  most  hazardous  sort,  not  a  legitimate  induction;  for  since  wc 
neither  know  how  much  heat  there  is  in  any  body,  nor  what  is  the  real 
distance  between  any  two  of  its  particles,  we  Cannot  judge  whether  the 
contraction  of  the  distance  does  or  does  not  follow  the  diminution  of 
the  quantity  of  heat  according  to  such  a  numerical  relation  that  the  two 
quantities  would  vanish  simultaneously.  \ 

In  contrast  with  this,  let  u-s  consider  a  case  in  which  the  absolute 
quantities  are  known;  the  case  contemplated  in  the  first  law  of  motion; 
viz.,  that  all  bodies  in  motion  continue  to  move  in  a  straight  line  with 
uniform  velocity  until  acted  upon  by  some  new  force.  This  assertion 
is  in  open  opposition  to  first  appearances;  all  terrestrial  object^;,  when 
in  motion,  gradually  abate  their  velocity  and  at  last  stop ;  which 
accordingly  the  ancieiits,  with  their  inductio  per  enumerationcm  sim- 
pliccm,  imagined  to  be  the  law.  Every  moving  body,  however, 
encounters  various  obstacles,  as  fi-iction,  the  resistance  of  the  atmos- 
phere, &c.,  which  we  know  by  daily  experience  to  be  causes  capable 
of  destroying  motion.  It  w^as  suggested  tlitit  the  whole  of  the  retard- 
ation might  be  owing  to  these  causes.  How  was  this  inquii*ed  into  ? 
If  the  obstacle^  could  have  been  entirely  retuoved,  the  case  would 
have  been  amenable  to  the  Method  of  Difference.  They  could  not  be 
removed,  they  could  only  be  diminished,  and  the  case,  therefore, 
admitted  only  of  the  Method  of  Concomitant  Variations.  This  accord- 
ingly being  employed,  it  was  found  that  every  diminution  of  the 
obstacles  diminished  the  retardation  of  the  motion  :  and  ina.s'much  as 
in  this  case  (unlike  the  case  of  heat)  the  total  quantitie's  both  of  the 
antecedent  and  of  the  consequent  were  known ;  it  was  practicable  to 
estimate,  with  an  approach  to  accuracy,  both  the  amount  of  the  retard"- 
ation  and  the  amount  of  the  retarding  causes,  or  resistances,  and  to 
judge  how  near  they  both  were  to  being  exhausted ;  and  it  appeared 
that  the  effect  dwindled  as  rapidly ,^  and  at  each  step  was  as  far  on  the 
road  towards  annihilation,  as  the  cause  was.  The  simple  oscillation 
of  a  weight  suspended  fi-om  a  fixed  point,  and  moved  a  little  out  of  the 


238  INDUCTIOiV. 

perpendicular,  wliicli  in  ordinary  circumstances  lasts  but  a  few  minutes, 
was  prolonged  in  Borda's  experiments  to  more  than  thirty  hours,  by 
diminishing  as  much  as  possible  the  friction  at  the  point  of  susjjension, 
and  by  making  the  body  oscillate  in  a  Space  exhausted  as  nearly  as 
possible  of  its  air.  There  could  therefore  be  no  hesitation  in  assign- 
ing the  whole  of  the  retardation  of  motion  to  tbe  influence  of  the 
obstacles ;  and  since,  after  subducting  this  retardation  from  the  total 
phenomenon,  th©  remainder  was  an  uniform  velocity,  the  result  was 
the  proposition  known  as  the  first  law  of  motion. 

There  is  also  another  characteristic  uncertainty  affecting  the  infer- 
ence that  the  law  of  variation  which  the  quantities  observe  within  our 
limits*  of  observation,  will  hold  beyond  those  limits.  There  is  of 
course,  in  the  first  instance,  the  possibility  that  beyond  the  limits,  and 
in  circumstances,  therefore  of  which  we  have  no  direct  experience, 
some  counteracting  cause  might  develop  itself;  either  a  new  agent,  or 
a  new  property  of  the  agents  concerned,  which  lies  dormant  in  the 
circumstances  we  are^  able  to  observe.  This  is  an  element  of  uncer- 
tainty which  enters  largely  into  all  our  predictions  of  effects';  but  it  is 
Jiot  peculiarly  applicable  to  the  Method  of  Concomitc^nt  Variations. 
The  uncertainty,  however,  of  which  I  am  about  to  speak,  is  character- 
istic of  that  method ;  especially  in  the  cases  in  which  the  extreme 
limits,  of  our  observation  are  very  narrow,  in  comparison  with  the 
possible  variations  in  the  quantities  of  the  phenomena.  Any  one  ^^■ho 
has  the  slightest  acquaintance  with  mathematics,  is  aware  that  very 
different  laws  of  variation  may  produce  numerical  results  which  differ 
but  slightly  from  one  another  within  narrow  limits ;  and  it  is  often 
only  when  the  absolute  amounts  of  variation  are  considerable,  that  the 
difference  between  the  results  given  by  one  law  and  by  another,  be- 
comes appreciable.  When,  therefore,  such  variations  in  the  quantity 
of  the  antecedents  as  we  have  the  means  of  observing,  are  but  small  in 
comparison  with  the  total  qua:ntities,  there  is  much  danger  lest  we 
should  mistake  the  numerical  law,  and  be  led  quite  to  miscalculate  the 
variations  which  would  take  place  beyond  the  limits;  a  miscalculation 
which  would  vitiate  any  conclusion  respecting  the  dependence  of  the  effect 
upon  the  cause,  whidi  could  be  founded  upon  those  variations.  Exam- 
ples are  not  wanting  of  such  mistakes.  "The  formulae,"  says  Sir  John 
Herschel,*  "  which  have  been  empirically  deduced  for  the  elasticity  of 
steam  (till  very  recently),  and  those  for  the  resistance  of  fluids,  and 
other  similar  subjects,"  when  relied  on  beyond  the  limits  of  the  obsei-- 
vations  from  which  they  were  deduced,  "  have  almost  invariably  failed 
to  support  the  theoretical  structures  which  have  been  erected  on  them." 

Under  this  uncertainty j  the  conclusion  we  may  draw  froin  the  con- 
comitant variations  of  a  and  A,  to  the  existence  of  an  invariable  and 
exclusive  connexion  between  them,  or  to  the  permanency  of  the  same 
numerical  relation  .between  their  variations  when  the  quantities  are 
much  gi-eater  or  smaller  than  those  whiqh  we  have  had  the  means  of 
observing,  cannot  be  considered  to  rest  upon  a  complete  induction. 
All  that  in  such  a  case  can  be  regarded  as  proved  on  the  subject  of 
causation,  is  that  there  is  some  connexion  between  the  two  phenomena ; 
that  A,  or  something  which  can  influence  A,  must  be  one  of  the  causes 
which  collectively  determine  a.     We  may,  however,  feel  assured  that 

*  Discourse  on  the  Sludy  of  Natural  Philosophy,  p.  179, 


EXAMPLES  OF  THE  TOUR  METHODS.  237 

the  relation  wlilcli  wo  liavo  obsoivotl  to  exist  betweeit  the  variations 
of  A  and  a,  will  hold  true  in  uU  cases  which  fall  between  the  same 
extreme;  limits ;  that  is,  wherever  the  ntnu)st  increase  or  diminution  in 
which  the  result  has  been  found'  by  observation  to  coincide  with  thq 
law,  is  not  exceeded. 

The  four  methods  which  it  has  now.  been  attempted  to  describe,  arc 
tlie  only  possible  modes  of  experimental  inquiry,  of  direct  induction 
d  posteriori,  as  distinguished  from  deduction  :  at  least  I  know  not,  nor 
am  able  to  conceive,  any  others.  And  even  of  these,  the  Method  of 
Residues,  as\ve  have  seen,  is  not  independent  of  deduction;  though,  as 
it  retpures  specific  experience  in  addition,  it  may,  without  impropriety, 
be  included  among  methods  of  direct  observation  and  experiment. 

These,  then,  with  such  assistance  as  can  be  obtained  from  Deduction, 
co;mpose  the  available  resources  of  the  human  mind  for  ascertaining 
the  laws  of  the  succession  of  phenomena.  Before  proceeding  to  point 
out  certain  circumstances,  by  which  the  employment  of  these  methods 
is  subjected  to  an  immense  increase  of  complication  and  of  difficulty, 
it  is  expedient  to  illustrate-  the  use  of  the  methods,  by  suitable 
examples,  drawn  from  actual  physical  investigations.  These,  accord- 
ingly, will  form  the  subject  of  the  succeeding  chapter. 


CHAPTER  IX. 

MISCELLANEOUS   EXAMPLES   OF  THE  FOUR  METHODS. 

•  ■  §  1.  I  SHALL  select,  as  my  first  example,  an  interesting, speculation 
of  one  of  the  most  eminent  theoretical  chemists  of  the  present  or  any 
age,  Dr.  Liebig.  The  object  in  view,  is  to  ascertain  the  immediate 
cause  of  the  death  produced  by  metallic  poisons. 

Arsenious  acid,  and  the  salts  of  lead,  bismuth,  copper,  and  mercury, 
if  introduced  into  the  animal  organism,  except  in  the  smallest  doses, 
destroy  life.  These  facts  have  long  been  known,  as  insulated  truths  of 
the  lowest  order  of  generalization ;  but  it  was  reserved  for  Liebig,  by 
an  apt  employment  of  the  first  two  of  our  methods  of  experimental 
inquiry,  to  connect  these  truths  together  by  a  higher  induction,  point- 
ing out  what  property,  common  to  all  these  deleterious  &ubstances,.  ia 
the  really  operating  cause  of  their  fatal  effect. 

When  solutions  of  these  substances  are  placed  in  sufficiently  close 
contact  with  many  animal  products,  albumen,  milk,  muscular  fibre, 
and  animal  membranes,  the  acid  or  salt  leaves  the  water  in  which 
it  was  dissolved,  and  enters  into  combination  with  the  animal  sub- 
stance ;  which  substance,  after  being  thus  acted  upon,  is  found  to  have 
lost  its  tendency  to  spontaneous  decomposition,  or  putrefaction. 

Observation  also  shows,  in  cases  where  death  has  been  produced  by 
these  poisons,  that  the  parts  of  the  body  with  which  the  poisonous 
substances  have  been  brought  into  contact,  do  not  afterwards  putrefy. 

And,  finally,  when  the  poison  has  been  supplied  in  too  small  a  quan- 
tity to  destroy  life,  eschars  are  produced,  tfiat  is,  certain  superficial 
portions  of  the  tissues  are  destroyed,  which  are  afterwards  thrown  off 
by  the  reparative  process  taking  jjlace  in  the  healthy  parts. 


238  INDUCTION. 

These  three  sets  of  instances  admit  of  being  treated  according  to  the 
Method  of  Agreement.  lu  all  of  them  the  metallic  compounds  are 
broii"-ht  into  contact  with  the  substances  which  compose  the  human  or 
animal  body ;  and  the  instances  do  not  seem  to  agree  in  any  other  cir- 
cumstance. The  remaining  antecedents  are  as  different,  and  even 
opposite,  as  they  could  possibly  be  made ;  for  in  some  the  animal  sub- 
stances exposed  to  the  action  of  the  poisons-  are  in  a  state  of  life,  in 
others  only  in  a  state  of  organization,  in  others  not  even  in  that.  And 
what  is  the  result  which  follows  in  all  the  cases  ?  The  conversion  of 
the  animal  substance  (by  combination  with  the  poison)  into  a  chemical 
compound,  held  togetlier  by  so  powerful  a  force  as  to  resist  the  subse- 
quent action  of  the- ordinary  causes  of  decomposition.  Now  organic 
lif(3  (the  necessary  condition  of  sensitive  life)  consisting  in  a-  contlhiial 
state  of  decomposition  and  recomposition  of  the  different  organs  and 
tissues ;  whatever  incapacitates  them  for  this  decomposition  desti-oys 
life.  And  thus  the  proximate  cause  of  the  death  produced  by  this, 
description  of  poisons,  is  ascertained,  as  far  as  the  Method  of  Agree- 
ment can  ascertain  it. 

Let  us  now  bring  our  conclusion  to  the  test  of  the  Method  of  Differ- 
ence. Setting  out  from  the  cases  already  mentioned,  in  which  the  antece- 
dent is,  the  presence  of  substances  forming  with  the  tissues  a  compound 
incapable  of  putrefaction  (and  u fortiori  incapable  of  the  chemical 
actions  which  constitute  life),  and  the  consequent  is  death,  either  of 
the  whole  organism,  or  of  some  portion  of  it ;  let  us  compare  with  these 
cases  other  cases,  as  much  resembling  them  as  possible,  but  in  which 
that  effect  is  not  produced.  And,  first  of  all,  "  many  insolnble  basic 
salts  of  arsenious  acid  are  known  not  to  be  poisonous.  The  substance 
called  alkargen,  discovered  by  Bunsen,  which  contains  a  veiy  large 
quantity  of  arsenic,  and  approaches  very  closely  in  composition  to  the 
organic  arsenious  compounds  found  in  the  body,  has  not  the  slightest 
injurious  action  upon  the  organism."  Now  when  these  substances  are 
brought  into  contact  with  the  tissues  in  any  way,  they  do  not  combine 
with  them ;  they  do  not  aixest  their  progi'ess  to  decomposition.  As  far, 
therefore,  as  these  instances  go,  it  appears  that  ^^-hen  the  effect  is 
absent,  it  is  by  reason  of  the  absence  of  that  antecedent  which  we  had 
already  good  gi'ound  for  considering  as  the  proximate  cause. 

But  the  rigorous  conditions  of  the  Method  of  Difference  are  not  yet 
satisfied ;  for  we  cannot  be  sure  that  these  unpoisonous  bodies  agree 
with  the  poisonous  substances  in  every  property,  except  the  particular 
one,  of  entering  into  a  difficultly  decomposable  compound  with  the 
animal  tissues.  To  render  the  method  strictly  applicable,  we  need  an 
instance,  not  of  a  different  substance,  but  of  one  of  the  vei-y  same  sub- 
stances, under  cu'cumstances  which  would  prevent  it  from  forming, 
with  the  tissues,  the  sort  of  compound  in  question  ;  and  then,  if  death 
does  not  follow,  our  case  is  made  out.  Now  such  instances  are  afforded 
by  the  antidotes  to  these  poisons.  For  example,  in  case  of  poisoning 
by.  arsenious  acid,  if  hydrated  peroxide  of  iron  is  administered,  the 
destructive  agency  is  instantly  checked.  Now  this  peroxide  is  known 
to  combine  with  the  acid,  and  foi-m  a  compound,  which,  being  in- 
soluble, cannot  act  at  all  on  animal  tissues.  So,  again,  sugar  is 
a  well-known  antidote  to  poisoning  by  salts  of  copper;  and  sugar 
reduces  those  salts  either  into  metallic  copper,  or  into  the  red  sub- 
oxide, neither  of  which  enters  into  combination  with  animal  matter. 


EXAMPLES    OF    TUE    FOUR    METHODS.  239 

The  disease  called  painter's  cqUc/  so  common  in  manufactories  of 
white  lead,  is  unknown  whpre  the  workmen  are  accu&tomed  to  take, 
as  a  preservative,  sulphuric-acid-lemonade  (a  solution  Of  sugar  ren- 
dered acid  by  sulphuric  acid).  Now  diluted  sulphuric  acid  has  the 
property  of  decomposing  all  compounds  of  lead  with  organic  matter,  and 
(of  course)  of  preventing  them  from  being  formed. 

There  is  another -class  of  instances,  of  the  nature  required  by  the 
Method  of  Pifference,  which  seem  at  first  sight  to  conflict  with  the 
theory.  Soluble  salts  of  silver,  such  for  instance  as  the  nitrate,  have 
the  same  stiftcning  antiseptic  effect  on  decomposing  anifnal  substances 
as  corrosive  sublimate  and  the  most  deadly  metallic  poisons  ;  and  when 
applied  to  the  external  parts^of  the  body,  tlie  nitrate  is  a  powerM 
criustic,  depriv.inc"  tho^o  ports  of  rdl  ertivo  vitnlity/nnd  musing  thorn  to 
be  tlu'own  otf  by  the  neighboring  living  structures,  in  the  form  of  an 
eschar.  The  nitrate  and  the  other  salts  of  silver  ought,  then,  it  would 
seem,  if  the  theory  be  correct,  to  be  poisonous;  yet  they  may  b^  ad-  ' 
ministered  "internally  with  perfect  imj)unity.  From  this  apparent 
exception  arises  the  strongest  confirmation  which  this  theory  of  Liebig 
has  yet  received.  Nitrate  of  silver,  in  spite  of  its  chemical  properties, 
does  not  poison  when  introduced  into  the  stomach  ;  but  in  the  stomach, 
as  in  all  animal  liquids,  there  is  common  salt ;  and  in  the  stomach 
there  is  also  free  muriatic  acid.  These  substances  operate  as  natural 
antidotes,  combining  with  the  nitrate,  and  if  its  quantity  is  not  too  great, 
immediately  converting  it  into  chloride  of  silver ;  a  substance  very 
slightly  soluble,  and  therefore  incapable  of  combining  with  the  tissues, 
although  to  the  extent  of  its  solubility  it  has  a  medicinal  influence, 
through  an  entirely  different  class  of  org-anic  actions. 

§  2.  The  preceding  instances  have  afforded  an, induction  of  "a  high 
order  of  conclusiveness,  illustrative  of  the  two  simplest  of  our  four 
methods ;  although  not  rising  to  the  maximum  of  certainty  which  the 
Method  of  Difference,  in  its  most  perfect  exemplification,  is  capable  of 
affording.  For  (let  us  not  forget)  the  positive  instance  and  the  neg- 
ative one  which  the  rigor  of  that  method  requires,  ought  to  differ  only 
in  the  presence  or  absence  of  one  single  circumstance.  Now,  in  the 
preceding  argument,  tliey  differ  in  the  presence  or  absence  not  of  a  sin- 
gle circumstance,  but  of  a  single  substance :  and  as  every  substance  has 
innumerable  properties,,  there  is  no  knowing  what  number  of  real  dif- 
ferences are  involved  in  what  is  nominally  and  apparently  only  one 
difference.  It  is  conceivable  that  the  antidote,  the  peroxide  of  iron  for 
example,  may  counteract  the  poison  through  some  other  of  its  proper- 
ties than  that  of  forming  an  insoluble  compound  with  it ;  and  if  so,  the 
theory  would  fall  to  the  ground,  so  far  as  it  is  supported  by  that  in- 
stance. This  source  of  uncertainty,  which  is  a  serious  hindrance  to 
all  extensive  generalizations  in  chemistry,  is  however  reduced  in  tho 
present  case  to  almost  the  lowest  degree  possible,  when  we  find  that 
not  only  one  substance,  but  many  substances,  possess  the  capacity  of 
acting  as  antidotes  to  metallic  poisons,  and  that  all  these  agree  in  the 
property  of  forming  insoluble  compounds  with  the  poisons,  while  they 
cannot  be  ascertained  to  agree  in  any  other  property  whatsoever.  We 
have  thus,  in  favor  of  the  theory,  all  the  evidence  which  can  be  ob- 
tained by  what  we  termed  the  Indirect  Method  of  Difference,  or  the 
Joint  Method  of  Agreement  and  Difference ;  the  evidence  of  which, 


240  IXDUCTION. 

though  it. never  can  amount  to  that  of  the  Method  of  Diffevence  prop- 
erly so  called,  may  approach  indefifiitely  near  to  it. 

No  similar  defect  of  completeness  in  proof  will  be  found  i'n  the 
following  Original  investigation,  for  which  I  am  indebted  to  ISIr.  Alex- 
ander "Bain,  at  present  Lecturer  on  Moral  Philosophy  in  Marischal 
CoUeo^e,  Aberdeen ;  one  of  the  men  from  whom  science  and  philoso- 
phy have  most  to  hope,  and  Avho  has  permitted  me  to  lay  his  extensive 
knowledgeof  every  department  of  physical  inquiry  freely  under  con- 
tribution, for  the  purpose  of  exemplifying  and  illustrating  the  doctrines 
ofthis  work..^ 

§■  3.  Let  the  object  be  to  ascertain  the  law  of  what  is  termed  hiduccd 
electricity  ;  to  find  under  what  conditions  any  electrified  body,  whether 
positively  or  negatively  electrified,  gives  rise  to  a  contrary  electric 
state  in  some  other  body  adjacent  to  it. 

The  most  familial-  exemplification  oPthe  phenomenon  to  be  investi- 
gated, is  the  following.  Around  the  prime  conductors  of  an  electrical 
machine,  the  atmosphere  to  some  distance,  or  any  conducting  surface 
suspended  in.  that  atmosj)here,  is  ibund  to  be  in  an  electric  condition 
opposite  to  that  of  the  prime  conductoi-  itself  Near  and  around  the 
positive  prime  conductor  there  is  a  negative  electricity,  and  near  and 
around  the  negative-  prime  conductor  there  is  positive  electricity. 
When  pith  balls  are  brought  near  to  either  of  the  conductors,  they 
become  electiified  with  the  opposite  electricity  to  it ;  either  receiving 
a  share  from  the  alrfeady  electrified  atmosphere  by  conduction,  or 
acted  upon  by  the  direct  inductive  influence  of,  the  conductor  itself: 
they  are  then  attracted  by  the  conductor  to  which  they  are  in  opposi- 
tion; or,  if  withdrawn  in  their  electrified  state,  they  will  be  attracted 
by  any  other  oppositely  dafarged  body.  In  like  Inanner  the  hand,  if 
brought  near  enough  to  the  coiiductor,  receives  or  gives  an  electric 
discharge  ;  now  we  have  no  evidence  that  a  charged  conductor  can  be 
suddenly  discharged  unless  by  the  approach  of  a  body  oppositely  elec- 
trified. In  the  case,  therefore,  of  the  electrical'  machine,  it  apj^ears 
that  the  accumulation  of  electricity  in  an  insulated  conductor  is  always 
accompanied  by  the- excitement  of , the  contrary  electricity  in  the  sur- 
rounding atmosphere,  and  in  exery  conductor  placed  near  the  former 
conductor.  It  does  not  seem  possible,  in  this  case,  to  produce  one 
electricity  by  itself 

Let  us  now  examine  all  the  other  instances  which  we  can  obtain, 
resembling  this  instance  in  the  given  consequent,  namely,  the  evolution 
of  an  opposite  electricity  in  the  neighborhood  of  an  electi'ified  body. 
As  one  remai'kable  instance  we  have  the  Leyden  jar ;  and  after  the 
splendid  experiments  of  Faraday  in  complete  and  final  establishment 
of  the  substantial  identity  of  magnetism  and  electricity,  we  may  cite 
the  magnet,  both  the  natural  and  the  electro-magnet,  in  neither  of 
which  is  it  possible  to  produce  one  kind  of  electricity  by  itself,  or  to 
chai"*e  one  pole  without  charging  an  opposite  pole  with  the  contrary 
electricity  at  the  same  time;  We  cannot  have  a  magnet  with  one 
pole  :  if  we  break  a  natural  loadstone  into  a  thoasand  pieces,  each 
piece  will  have  its  two  oppositely  electrified  poles  complete  within 
itself  In  the  voltaic  circuit,  again,  we  cannot  have  one  cunent  with- 
out its  opposite.  In  the  ordinary  electric  anachine,  the  glass  cylinder 
or  plate,  aild  the  rubber,  acquire  opposite  electricities. 


EXAMPLES    OF    THE    FOUR    METHODS.    "  241 

From  all  these  instancesj  treated  by  the  Method  of  Agreement,  a  - 
general  law  appears  to  result.  The  instances  -embrace  all  tlie  known 
modes  in  whicli  a  body  can  become  charged  with  electricity ;  and  in 
all  of"  thi'm  tlicre  is  tbund,  as  a  concx)mitant  or  consequent,  the  excite- 
ment ot*  the  opposite  electric  state  in  some  other  body  or  bodies.  It 
seems  to  follow  that  the  two  facts  are  invariably  connected,  and  that 
the  excitement  of  electricity  in  any  body  has  for  one  of  its  necessary 
conditions  the  possibility  of  a  simultaneous  excitement  of  the  opposite 
electricity  in  some  neighboring  body. 

As  the  two  contrary  electricities  can  only  be  produced  together,  so 
they  can  only  cease  together.  Tliis  may  be  sho\vn  by  an  application 
of  the  Method  of  Difference  to  the  example  of  the  Leyden  jar.  It 
needs  scai'cely  be  here  remarked  that  in  the  Leyden  jar,  electricity 
can  be  accumulated  and  n^taincd  in  considerable  quantity,  by  the  con- 
trivance of  having  two  conducting  surfaces  of  equal  extent,  and  parallel 
to  each  other  through  the  whole  of  that  extent,  with  a  non-conducting 
substance  such  as  glass  between  them.  When  one  side  of  the  jar  is 
charged  positively,  the  other  is  charged  negatively,  and  it  was  by  virtue 
of  this  fact  that  the  Leyden  jar  served  just  now  as  an  instance  in  our 
employment  of  the  Method  of  Agreement.  Now  it  is  impossible  to 
discharge  one  of  the  coatings  unless  the  other  can  be  discharged  at 
the  same  time.  A  conductor  held  to  the  positive  side  cannot  convey 
away  any  electricity  unless  an  equal  quantity  be  allowed  to  pass  from 
the  negative  side  :  if  one  coating  be  perfectly  insulated,  the  charge 
is  safe.  The  dissipation  of  one  must  proceed  pari  passu  with  the 
other. 

The  law  thus  strongly  indicated  admits  of  corroboration  by  the 
Method  of  Concomitant  Variations.  The  Leyden  jar  is  capable  of 
receiving  a  much  higher  charge  than  can  ordinarily  be  given  to  the 
conductor  of  an  electrical  machine.  Now  in  the  case  of  the  Leyden 
jar,  the  metallic  surface  which  receives  the  induced  electricity  is  a 
conductor  exactly  similar  to  that  which  receives  the  primary  charge, 
and  is  therefore  as  susceptible  of  receiving  and  retaining  the  one  elec- 
tricity, as  the  opposite  surface  of  receiving  and  retaining  the  other : 
but  in  the  machine,  the  neighboring  body  which  is  to  be  oppositely 
electrified  is  the  surrounding  atmosphere,  or  any  body  casually  brought 
near  to  the  conductor ;  and  as  these  are  generally  much  inferior  in 
their  capacity  of  becoming  elcctrifiiMl,  to  the  conductor  itself,  their  lim- 
ited power  imposes  a  corresponding  limit  to  the  capacity  of  the  con- 
ductor for  being  charged.  As  the  capacity  of  the  neighboring  body 
for  supporting  the  opposition  increases,  a  higher  charge  becomes  pos- 
sible :  and  to  this  appears  to  be  owing  the  great  superiority  of  the 
Leyden  jar. 

A  further  aiul  most  decisive  confirmation  by  the  Method  of  Differ- 
ence, is  to  be  found  in  out;  of  Faraday's  experiments  in  the  course  of 
his  researches  on  the  subject  f)f  induced  electricity. 

Since  common  or  machine  electricity,  and  voltaic  electricity,  may 
be  considered  for  the  present  pui-pose  to  be  identical,  Faraday  wished 
to  know  whether,  as  the  prime  conductor  develops  opposite  electri- 
city upon  a  conductor  in  its  \icinity,  so  a  voltaic  cuiTent  miming 
along  a  wire  would  induce  an  opposite  current  upon  another  wire  laid 
parallel  to  it  at  a  short  distance.  Now  this  case  is  similar  to  the  cases 
previously  examined,  in  every  cii'cumstance  except  the  one  to  which 
Hh 


242  INDUCTION. 

we  have  ascribed  the  effect.  We  found  in  the  former  instances  that 
whenever  electricity  of  one  kind  was  excited  in  one  body,  electricity 
of  the  opposite  kind  must  be  excited  in  a  neighboring  body ;  and  the 
interpretation  of  this,  in  the  language  of  cause  and  effect,  is,  that  all 
causes  which  can  excite  the  one  kind  of  electricity,  have  the  property 
of  simultaneously  exciting  an  equal  amount  of  the  other.  But  in 
Faraday's  experiment  this  indispensable  opposition  exists  within  the 
wire  itself  From  the  nature  of  a  voltaic  charge,  the  two  opposite' 
currents  necessary  to  the  existence  of  each  other  are  both  accommo- 
dated in  one  wire ;  and  there  is  no  need  of  another  wire  placed  be- 
side it  to  contain  one  of  them,  in  the  same  way  as  the  Leyden  jar 
must  have  a  positive  and  a  negative  surface.  The  exciting  cause  can 
and  does  produce  all  the  effect  which  its  laws  require,  independently 
of  any  electric  excitement  of  a  neighboring  body.  Now  the  result 
of  Faraday's  experiment  with  the  second  wire,  was  that  no  opposite 
current  was  produced.  There  was  an  instantaneous  effect  at  the 
closing  and  breaking  of  the  voltaic  circuit;  electric  inductions  ap- 
peared when  the  two  wires  were  moved  to  and  from  one  another ; 
but  these  are  phenomena  of  a  different  class.  There  was  no  in- 
duced electi-icity  in  the  sense  in  which  this  is  predicated  of  the 
Leyden  jar;  there  was  no  sustained  current  running  up  the  one  wire 
while  an  opposite  cuiTent  ran  down  the  neighboring  wire;  and  this 
alone  would  have  been  a  true  parallel  case  to  the  other. 

It  thus  appears  by  the  combined  evidence  of  the  Method  of  Agree- 
ment, the  Method  of  Concomitant  Variations,  and  the  most  rigorous 
form  of  the  Method  of  Difference,  that  neither  of  the  two  kinds  of 
electricity  can  be  excited  without  an  equal  excitement  of  the  other 
and  opposite  kind :  that  both  are  effects  of  the  same  cause,  that  the 
possibility  of  the  one  is  a  condition  of  the  possibility  of  the  other,  and' 
the  quantity  of  the  one  an  impassable  limit  to  the  quantity  of  the  other. 
A  scientific  result  of  considerable  interest  in  itself,  and  illustrating 
those  three  methods  in  a  maimer  both  characteristic  and  easily  in- 
,  telligible. 

§  4.  Our  third  example  shall  be  extracted  from  Sir  John  Herschel's 
Discourse  on  the  Study  of  Natural  Phil osopJiy,  ViVfork  Te^lete  v/'ith. 
admirably  selected  exemplifications  of  inductive  processes  fi'om  almost 
every  department  of  physical  science,  and  in  which  alone,  of  all  books 
which  I  have  met  with,  the  four  methods  of  induction  are  recognized, 
although  not  characterized  and  defined  nor  their  correlation  shown,  so 
distinctly  as  has  appeared  to  me  desirable.  The  present  example  is 
justly  described  by  Sir  John  Herschel  as  "  one  of  the  most  beautiful 
specimens"  which  can  be  cited  ."of  inductive  experimental  inquiry 
lying  within  a  moderate  compass ;"  the  theory  of  dew,  first  promul- 
gated by  the  late  Dr.  Wells,  and  now  universally  adopted  by  scien- 
tific men. 

The  passages  in  inverted  commas  are  extracted  verbatim  fi-om  Sir 
John  Herschel,  *  but  to  those  who  possess  his  work  I  would  strongly 
recommend  to  read  the  entire  passage  in  the  original,  and  fully  pos- 
sess themselves  of  the  purport  of  the  speculation  as  a  whole,  before 
applying  themselves,  with  me,  to  the  logical  analysis  of  the  different 
steps  of  the  argument. 

*  Discourse,  pp.  ISO — 162. 


EXAJIPLES  OF  TUK   FOUR   AIimiODS.  243 

■ "  Suppose  dew  were  tlie  phenomenon  proposed,  w-liosc  cause  we 
woulJ  know.  In  the  first  phice"  we  must  determine  precisely  what 
we  nicun  by  dew ;  what  the  fact  really  is,  whose  cause  we  desire  to 
investigate.  "  We  "must  separate  dew  from  rain,  and  the  moisture  of 
fogs,  and  limit  the  application  of  the  term  to  what  is  really  meant, 
which  is,  the  spontaneous  appearance  of  moisture  on  substances 
exposed  in  the  open  air  when  no  rain  or  risible  wet  is  falling."  This 
answers  to  a  preliminary  operation  which  will  be  characterized  in  the 
ensuing  book,  treating  of  operations  subsidiary  to  induction.*  The 
state  of  the  question  being  iixed,  we  come  to  the  solution. 

"  Now,  here  we  have  analogous  phenomena  in  the  moisture  which 
bedews  a  cold  metal  or  stone  when  wO  breathe  upon  it ;  that  which 
appears  on  a  glass  of  water  fresh  from  the  well  in  hot  waather ;  that 
which  appears  oil  tlie  inside  of  windows  when  sudden  rain  or  hail 
chills  the  ext-ernal  air;  that  which  runs  down  our  walls  when,  after  a 
long. frost,  a  warm  moist  thaw  comes  on."  Comparing  these  cases,  we 
find  that  they  all  contain  the  phenomenon  which  was  proposed  as  the 
subject  of  investigation.  Now  "  all  these  instances  agree  in  one  point, 
the  coldness  of  the  object  dewed,  in  comparison  with  the  air  in  contact 
with  it."  But  there  still  remains  the  most  important  case  of  all,  that 
of  nocturnal  dew  :  does  the  same  circumstance  exist  in  this  case  1  "  Is 
it  a  fact  that  the  object  dewed  is  colder  than  the  air  1  Certainly  not, 
one  would  at  first  be  inclined  to  say;  for  what  is  to  make  it  so  1  But .... 
the  experiment  is  easy  ;  we  have  only  to  lay  a  thermometer  in  contact 
with  the  dewed  substance,  and  hang  one  at  a  little  distance  above  it, 
out  of  reach  of  its  influence.  The  experiment  has  been  therefore 
made;  the  question  has  been  asked,  and  the  answer  has  been  inva- 
riably in  the  affirmative.  Whenever  an  object  contracts  dew,  it  is 
colder  than  the  air." 

Here  then  is  a  complete  application  of  the  Method  of  Agreement, 
establishing  the  fact  of  an,  invariable  connexion  between  the  deposition 
of  dew  on  a  surface,  and  die  coldness  of  that  surface  compared  with  the 
external  air.  But  which  of  these  is  cause  and  which  effect;  or  are  they 
both  effects  of  something  else?  On  this  subject  the  Method  of  Agree- 
ment can  afford  us  no  light:  we  must  call  in  a  moi'e  potent  method. 

"  That  dews  are  accompanied  with  a  chill  is  a  common  remark;  but 
vulgar  prejudice  would  make  the  cold  the  effect  rather  than  the  cause. 
We  must  therefore  collect  more  facts,  or  which  come&  to  the  same  thing, 
vary  tlie  circumstances  ;  since  every  instance  in  which  the  circum- 
stances differ  is  a  fresh  fact;  and  especially,  we  must  note  the  contrary 
or  negative  cases,  i.  e.,  where  no  dew  is  produced :"  for  vyO  are  aware 
that  a  comparison  between  instances  of  dew,  and  instances  of  no  dew, 
is  the  condition  necessary  to  bring  the  Method  of  Difference  into  play. 

"  Now,  first,  no  dew  is  produced  on  the  surface  of  polished  metals, 
but  it  is  very  copiously  on  glass,  both  exposed  with  their  faces 
upwards,  and  in  some  cases  the  under  side  of  a  horizontal  plate  of 
glass  is  also  dewed."t     Here  is  an  instance  in  which  the  effect  is  pro- 

*  Vide  infra,  book  iv.,  chap.  ii.  On  Abstraction, 

+  This  last  circumstance  (adds  Sir  John  Herschel)  "  cxchides  the  fall  of  moisture  from 
the  sivy  in  an  invisible  form,  which  would  naturally  suggest  itself  as  a  cause."  I  have 
omitted  this  passage  in  the  text,  as  not  pertinent  to  the  pilrpose  in  hand,  the  argument 
which  it  contains  being  deductive  and  h  priori.  The  fall  of  moisture  is  rejected  as  a  cause, 
because  from  its  laws  previously  known,  we  inXer  that  it  could  not  have  produced  the  par- 
ticular phenomenon  last  mentioned 


244  INDUCTION. 

duced,  and  another  instance  in  which  it  is  not  produced  ;  but  we  cannot 
yet  pronounce,  as  the  canon  of  the  Method  of  Difference  requires, 
that  the  latter  instance  agrees  with  the  former  in  all  its  circumstancea 
except  one ;  for  the  differences  between  glass  and  polished  metals  are 
manifold,  and  the  only  thing  we  can  as  yet  be  sure  of  is^  that  the 
cause  of  dew  will  be  found  among  the  circumstances  by  which  the 
former  substance  is  distinguished  from  the  latter.  But  if  we  could  be 
sure  that  glass,  and  the  various  other  substances  on  which  dew  is 
deposited,  have  only  one  quality  in  common,  and  that  polished  metals 
and  the  other  substances  on  which  dew  is  not  deposited  have  also 
nothing  in  common  but  the  one  circumstance,  of  not  having  the  one 
quality  which  the  others  have ;  the  requisitions  of  the  Method  of 
Difference  would  be  completely  satisfied,  and  we  should  recognize,  in 
that  quality  of  the  substances,  the  cause  of  dew.  This,  accordingly, 
is  the  path  of  inquiry  which  is  next  to  be  pursued. 

"In  the  cases  of  polished  metal  and  polished  glass,  the  contrast 
shows  evidently  that  the  substance  has  much  to  do  with  the  phenome- 
non;  therefore  let  the  substance  alone  be  diversified  as  much  as 
possible,  by  exposing  polished  surfaces  of  various  kinds.  This  done, 
a  scale  of  intensity  becomes  obNaous.  Those  polished  substances  are 
found  to  be  most  strongly  dewed  which  conduct  heat  worst ;  while 
those  which  conduct  well,  resist  dew  most  effectually."  The  compli- 
cation increases  ;  here  is  the  Method  of  Concomitant  Variations  called 
to  our  assistance ;  and  no  other  metliod  was  practicable  upon  this 
occasion ;  for  the  quality  of  conducting  heat  could  not  be  excluded, 
since  all  substances  conduct  heat  in  some  degree.  The  conclusion 
obtained  is,  that  cceteris  jjaribus  the  deposition  of  dew  is  in  some 
proportion  to  the  power  which  the  body  possesses  of  resisting  the 
passage  of  heat ;  and  that  this,  therefore,  (or  something  connected  with 
this,)  must  be  at  least  one  ef  the  causes  which  assist  in  producing  the 
deposition  of  dew  upon  the  surface. 

"  But  if  we  expose  rough  surfaces  instead  of  polished,  we  some- 
times find  this  law  interfered  with.  Thus,  roughened  iron,  especially 
if  painted  over  or  blackened,  becomes  dewed  sooner  tlian  varaished 
paper:  the  kind  of  surface,  therefore,  has  a  great  influence;  Expose, 
then,  the  same  material  in  very  diversified  states  as  to  surface,"  (that 
is,  employ  the  Method  of  Difference  to  ascertain  concomitance  of 
variations,)  "and  another  scale  of  intensity  becomes  at  once  apparent; 
those  stirfaccs  which  jiart  with  their  heat  most  readily  by  radiation,  are 
found  to  contract  dew  most  copiously."  Here,  therefore,  are  the 
requisites  for  a  second  employment  of  the  Method  of  Concomitant 
Variations ;  which  in  this  case  also  is  the  only  method  available,  since 
all  substances  radiate  heat  in  some  degree  or  other.  The  conclusion 
obtained  by  this  new  application  of  the  method  is,  that  ca.teris  paribus 
the  deposition  of  dew  is  also  in  some  proportion  to  the  power  of 
radiating  heat ;  and  that  the  quality  of  doing  this  abundantly  (or  some 
cause  on  which  that  quality  depends)  is  another  of  the  causes  which 
promote  the  deposition  of  dew  upon  the  substance. 

"  Again,  the  influence  ascertained  to  exist  of  substance  and  surface 
leads  us  to  consider  that  of  texture  :  and  here,  again,  we  are  presented 
on  trial  with  remarkable  differences,  and  with  a  third  scale  of  intensity, 
pointing  out  substances  of  a  close  finn  textui-e,  such  as  stones,  metals, 
&c.,  as  unfavorable,  but  those  of  a  loose  one,  as  cloth,  wool,  velvet,  eider- 


EXAMPLES    OF    THE     FOUR     METHODS.  245 

down,  cotton,  &(•.,  as  eminently  favorable  to  the  contraction  of  dew." 
The  Method  of  Concomitant  Variations  is  here,  for  the  third  time,  had 
recourse  to ;  and,  as  before,  from  necessity,  since  the  texture  of  no 
substance  is  absolutely  Hrm  or  absolutely  loose.  Looseness  of  texture, 
therefore,  or  something  which  is  tho  cause  of  that  quality,  is  another 
circumstance  which  promotes  the  deposition  of  dew ;  but  this  third 
cause  resolves  itself  into  the,  first,  viz.,  the  quality  of  resisting  the 
passage  of  heat :  for  substances  of  loose  texture  "  are  precisely  those 
which  are  best  adapted  for  clothing,  or  for  impeding  the  free  passage 
of  heat  from  the  skin  into  the  air,  so  as  to  allow  their  outer  surfaces  to 
be  very  cold  while  they  remain  warm  within  ;"  and  this  last  is,  there- 
fore, an  induction  (from  fresh  instances)  simply  curruhorative  of  a 
former  induction. 

It  thus  appears  that  the  instances  in  which  much  dew  is  deposited, 
which  are  very  various,  agree  in  this,  and,  so  far  as  we  are  able  to 
observe,  in  this  only,  that  they  either  radiate  heat  rajjidly  or  conduct 
it  slowly  :  qualities  between  which  there  is  no  other  circumstance  of 
agreement,  than  that  by  virtue  of  either,  the  body  tends  to  lose  heat 
fi-om  the  surface  more  rapidly  than  it  can  be  restored  from  within. 
The  instances,  on  the  contrai-y,  in  which  no  dew,  or  but  a  small 
quantity  of  it,  is  formed,  and  which  are  also  extremely  various,  agree 
(so  far  as  we  can  observe)  in  nothing  except  in  not  having  this  same 
property.  We  seem,  therefore,  to  have  detected  the  sole  difl'erence 
between  the  substances  on  which  dew  is  produced,  and  those  on  which 
it  is  not  produced.  And  thus  have  been  realized  the  requisitions  of 
what  we  have  termed  the  Indirect  Method  of  Difference,  or  the  Joint 
Method  of  Agreement  and  Difference.  The  example  aflibrded  of  this 
indirect  method,  and  of  the  manner  in  which  the  data  are  prepared 
for  it  by  the  INIetliods  of  Agreement  and  of  Concomitant  Variations, 
is  the  most  important  of  all  the  illustrations  of  induction  afforded  by 
this  most  interesting  speculation. 

We  might  now  consider  the  question,  upon  what  the  deposition  of 
dew  depends,  to  be  completely  solved,  if  we  could  be  (juite  sure  that 
the  substances  on  which  dew  is  produced  differ  from  those  on  which  it 
i?  not,  in  nothing  but  in  the  property  of  losing  heat  fi-om  the  surface 
faster  than  the  loss  can  be  repaired  from  within.  And,  although  we 
never  can  have  that  complete  certainty,  this  is  not  of  so  much  import- 
ance as  might  at  first  be  supposed ;  for  we  have,  at  all  events,  ascer- 
tained that  even  if  there  be  any  other  quality  hitherto  unobserved 
which  is  present  in  all  tlie  substances  which  contract  dew,  and  absent 
in  those  which  do  not,  this  other  pr(»perty  must  be  one  which,  in  all 
that  great  number  of  substances,  is  present  or  absent  exactly  where  the 
property  of  being  a  better  radiat(;r  than  conductor  is  present  or  absent ; 
an  extent  of  coincidence  which  af!brds  the  strongest  presumption  of  a 
community  of  cause,  and  a  consequent  invariable  coexistence  between 
the  two  properties  ;  so  that  the  property  of  being  a  better  radiator 
than  conductor,  if  not  itself  the  cause,  almost  certainly  always  accom- 
panies the  cause,  and  for  purposes  of  prediction,  no  ciTor  will  bje 
committed  by  treating  it  as  if  it  were  really  such. 

Reverting  now  to  an  earlier  stage  of  the  inquiry,  let  us  remember 
that  wo  had  ascertained  that,  in  every  instance  where  dew  is  formed, 
there  is  actual  coldness  of  the  surface  below  the  temperature  of  the 
fiurrounding  air;  but  we  vieve  not  sure  whether  this  coldness  was  the 


246  INDUCTION. 

cause  of  dew,  or  its  effect.  This  doubt  we  are  now  able  to  resolve. 
We  have  found  that,  in  every  such  instance,  the  substance  must  be  one 
which,  by  its  own  properties  or  laws,  would,  if  exposed  in  the  night, 
become  colder  than  the  siairounding  air.  But  if  the  dew  were  the 
cause  of  the  coldness,  that  effect  would  be  produced  in  other  substances, 
and  not  solely  in  those  whose  own  laws  suffice  to  produce  it  whether 
there  were  dew  or  no.  That  supposition,  therefore,  is  repelled.  But 
there  were  only  three  suppositions  possible ;  the  dew  is  the  cause  of 
the  coldness ;  both  are  caused  by  some  third  circumstance ;  or  the 
coldness  is  the  cause  of  the  dew\  The  first  is  refuted.  The  second  is 
inapplicable :  the  cause  of  the  coldness  is  a  known  cause ;  a  radiation 
from  the  surface  greater  than  can  be  supplied  by  conduction :  now  this, 
by  its  known  laws,  can  produce  no  direct  effect  except  coldness.  There 
remains  only  the  third  supposition,  that  the  coldness  is  the  cause  of  the 
dew :  which,  therefore,  may  be  considered  as  completely  made  out. 

This  law  of  causation,  already  so  amply  established,  admits,  how- 
ever, of  most  efficient  additional  corroboration  in  no  less  than  three 
vvays.  First,  by  deduction  from  the  known  laws  of  aqueous  vapor 
when  diffused  through  air  or  any  other  gas ;  and  although  we  have 
not  yet  come  to  the  Deductive  Method,  we  will  not  omit  what  is  neces- 
sary to  render  this  speculation  complete.  It  is  known  by  direct  exper- 
iment that  only  a  limited  quantity  of  water  can  remain  suspended  in 
the  state  of  vapor  at  each  degi-ee  of  temperature,  and  that  this  maxi- 
mum grows  less  and  less  as  the  temperature  diminishes.  From  this  it 
follows,  deductively,  that  if  there  is  already  as  much  vapor  suspended 
as  the  air  will  contain  at  its  existing  temperature,  any  lowering  of  that 
temperature  will  cause  a  portion  of  the  vapor  to  be  condensed  and 
become  water.  But,  again,  we  know  deductively,  from  the  laws  of 
beat,  that  the  contact  of  the  air  with  a  body  colder  than  itself,  will 
necessarily  lower  the  temperature  of  the  stratum  of  air  immediately 
applied  to  its  surface  ;  and  will  therefore  cause  it  to  part  with  a  portion 
of  its  water,  which  accordingly  will,  by  the  ordinary  laws  of  gravita- 
tion or  cohesion,  attach  itself  to  the  surface  of  the  body,  thereby  con- 
stituting dew.  This  deductive  proof,  it  will  have  been  seen,  has  the 
advantage  of  proving  at  once,  causation  as  well  as  coexistence;'  and  it 
has  the  additional  advantage  that  it  also  accounts  for  the  cxcejytions  to 
the  occurrence  of  the  phenomenon,  the  cases  in  which,  although  the 
body  is  colder  than  the  air,  yet  no  dew  is  deposited;  by  showing  that 
this  will  necessarily  be  the  case  when  the  air  is  so  imdersupplied  with 
aqueous  vapor,  comparatively  to  its  temperature,  that  even  when  some- 
what cooled  by  the  contact  of  the  colder  body,  it  can  still  continue  to 
hold  in  suspension  all  the  vapor  which  was  previously  suspended  in  it: 
thus  in  a  very  dry  summer  there  are  no  dews,  in  a  very  dry  winter  no 
hoar  frost.  Here,  therefore,  is  an  additional  condition  of  the  produc- 
tion of  dew,  which  the  methods  we  previously  made  use  of  failed  to 
detect,  and  which  might  have  remained  still  undetec*ted,  if  recourse  had 
not  been  had  to  the  plan  of  deducing  the  effect  from  the  ascertained 
properties  of  the  agents  known  to  be  present. 

The  second  corroboration  of  the  theory  is  by  direct  experiment, 
accoi-ding  to  the  canon  of  the  Method  of  Difference.  We  can,  by 
cooling  the  surface  of  anybody,  find  in  all  cases  some  temperature 
(more  or  less  inferior  to  that  of  the  surrounding  air,  according  to  its 
hygrometric    condition,)  at   which   dew  will  begin  to  be  ^deposited. 


EXAMPLES  OF  THE  FOUR  METHODS.  247 

Here,  too,  therefore,  the  causation  is  directly  proved.  We  can,  it  is 
true,  accomplish  this  only  on  a  small  scale  ;  hut  we  have  ample  I'eason 
to  conclude  that  the  same  operation,  if  conducted  iu  JSTature's  great 
laboratory,  would  equally  produce  the  elVect. 

And,  finally,  even  on  that  great  scale  we  are  able  to  verify  the  result. 
The  case  is  one  of  those  (rare  cases,  as  we  have  shown  them  to  be)  in 
which  Nature  works  the  experiment  for  us  in  the  same  manner  in 
which  we  ourselves  perform  it;  introducing  ji^to  the. previous  state  of 
things  a  single  and  pcrfec;tly  definite  new  circumstance,  and  manifest- 
ing the  ett'ect  so  rapidly  that  there  is  not  time  for  any  other  material 
change  in  the  preexisthig  circumstances.  Let  us  quote  again  Sir  John 
Horschel : — "  It  is  observed  that  dew  is  never  copiously  deposited  in 
situations  much  screened  from  the  open  sky,  and  not  at  all  in  a  cloudy 
night;  but  \f  the  clouds  ivithdraiv  even  for  afow  viiinitea,  and  have  a 
clear  opening,  a  deposition  of  dew  presently  begins,  and  goes  on  increas- 
ing  Dew  formed  in  clear  intervals  will  often  even  evaporate  again 

when  the  sky  becomes  thickly  overcast."  The  proof,  therefore,  is 
complete,  that  the  presence  or  absence  of  an  uninterrupted  communi- 
cation with  the  sky  causes  the  deposition  or  non-deposition  of  dew. 
Now,  since  a  clear  sky  is  nothing  but  the  absence  of  clouds,  and  it  is  a 
known  property  of  clouds,  as  of  all  other  bodies  between  which  and 
any  given  object  nothing  intervenes  but  an  elastic  iluid,  tliat  they 
tend  to  raise  or  keep  up  the  superficial  temperature  of  the  object  by 
radiating  heat  to  it,  we  see  at  once  that  the  disappearance  of  clouds 
will  cause  the  surface  to  cool ;  so  that  Nature,  in  this  case,  produces  a 
change  in  the  antecedent  by  definite  and  known  means,  and  the  con- 
sequent follows  accordingly  :  a  natural  experiment  which  satisfies  the. 
requisitions  of  the  Method  of  Difference.* 

The  accumulated  proof  of  which  the  Theory  of  Dew  has  been  found 
susceptible,  is  a  striking  example  of  the  fullness  of  assurance  which  the 
inductive  evidence  of  laws  of  causation  may  attain,  in  cases  in  which 
the  invariable  sequence  is  by  no  means  obvious  to  a  superficial  view. 
It  is  unnecessary  to  subjoin  Sir  John  Herschel's  summary  of  the  result, 
as  it  does  not  contain  all  the  ])roofs  which  I  have  given,  and  our  more 
detailed  analysis  of  each  step  of  the  process  renders  such  a  recapitula- 
tion unnecessary. 

§  5.  This  admirable  example  will  have  conveyed  to  any  one  by 
whom  it  has  been  duly  followed,  so  clear  a  conception  of  the  use  and 
practical  management  of  three  of  the  four  methods  of  experimental 

*  I  must,  however,  remark,  that  this  example,  which  seems  to  militate  against  the  asser- 
tion we  made  of  the  comparative  inapplicabihty  of  the  Method  of  Difference  to  cases  of 
pure  observation,  is  really  one  of  those  exceptions  which,  according  to  a  proverbial  expres- 
sion, prove  the  general  rule.  For,  be  it  observed,  in  this  case  in  which  Nature,  in  her 
experiment,  seems  to  have  imitated  the  type  of  the  experiments  made  by  man,  she  has  only 
succeeded  in  producing  the  likeness  of  man's  most  imperfect  experiments,  namely,  those 
in  which,  though  he  succeeds  in  producing  the  jihenomcnon,  lie  does  so  by  employing  com- 
plex means,  which  he  is  unable  (lerfectly  to  analyze,  and  can  form,  therefore,  no  sutlicient 
judgment  what  portion  of  the  ctlects  may  be  due,  not  to  the  supposed  cause,  but  to  some 
unknown  agency  of  the  means  by  which  that  cause  was  produced.  In  the  natural  experi- 
ment which  we  are  speaking  of,  the  means  used  was  the  clearing  off  a  canopy  of  clouds; 
and  we  certainly  do  not  know  sufficiently  in  what  this  process  consists,  or  upon  what  it 
depends,  to  be  certain  a  priori  that  it  might  not  operate  upon  the  deposition  of  dew  inde- 
pendently of  any  thermometric  effect  at  the  earth's  surface.  Fhen,  therefore,  in  a  case  so 
fkvorable  as  this  to  Nature's  experimental  talents,  her  experiment  is  of  little  value  except 
ia  corroboration  of  a  conclusion  already  attained  through  other  means. 


248  INDUCTION. 

inquiry,  as  to  supersede  the  necessity  of  any  further  exemphfication 
of  them.  The  remaining  method,  that  of  Residues,  not  having  found 
any  place  either  in  this  or  in  the  two  preceding  investigations,  I  shall 
extract  from  Sir  John  Herschel  some  examples  of  that  method,  with 
the  remarks  by  which  they  are  introduced. 

"  It  is  by  this  process,  in  fact,  that  science,  in  its  present  advanced 
state,  is  chiefly  promoted.  Most  of  the  phenomena  which  Nature 
presents  are  very  complicated;  and  when  the  eflects  of  all  known 
causes  are  estimated  with  exactness,  and  subducted,  the  residual  facts 
are  constantly  appearing  in  the  form  of  phenomena  altogether  new, 
and  leading  to  the  most  important  conclusions. 

"For  example:  the  return  of  the  comet  predicted  by  Professor 
Encke,  a  great  many  times  in  succession,  and  the  general  good  agree- 
ment of  its  calculated  with  its  obsei-ved  place  during  any  one  of  its 
periods  of  visibility,  would  lead  us  to  say  that  its  gravitation  towards 
the  sun  and  planets  is  the  sole  and  suflficient  cause  of  all  the  phenom- 
ena of  its  orbitual  motion  :  but  when  the  effect  of  this  cause  is  strictly 
calculated  and  subducted  from  the  obsei'ved  motion,  there  is  found  to 
remain  behind  a  residual  phenomenon,  which  would  never  have  been 
otherwise  ascertained  to  exist,  which  is  a  small  anticipation  of  the 
time  of  its  reappearance,  or  a  diminution  of  its  periodic  time,  which 
cannot  be  accounted  for  by  gravity,  and  whose  cause,  is  therefore  to  be 
inquired  into.  Such  an  anticipation  would  be  caused  by  the  resistance 
of  a  medium  disseminated  through  the  celestial  regions;  and  as  there 
are  other  good  reasons  for  believing  this  to  be  a  vera  causa,""  (an 
actiially  existing  antecedent,)  "it  has  therefore  been  ascribed  to  such 
a  resistance, 

"  M.  Arago,  having  suspended  a  magnetic  needle  by  a  silk  thread, 
and  set  it  in  vibration,  observed,  that  it  came  much  sooner  to  a  state 
of  rest  when  suspended  over  a  plate  of  copper,  than  when  no  such 
plate  was  beneath  it.  Now,  in  both  cases  there  were  two  Terce  causm''^ 
(antecedents  known  to  exist)  "  why  it  sJiould  come  at  length  to  rest, 
viz.,  the  resistance  of  the  air,  which  opposes,  and  at  length  destroys, 
all  motions  performed  in  it;  and  the  want  of  perfect  mobility  in  the 
fiilk  thread.  But  the  effect  of  these  causes  being  exactly  known  by 
the  observation  made  in  the  absence  of  the  copper,  and  behig  thus 
allowed  for  and  subducted,  a  residual  phenomenon  appeared,  in  the 
fact  that  a  retarding  influence  was  exerted  by  the  copper  itself;  and 
this  fact,  once  ascertained,  speedily,  led  to  the  knowledge  of  an  entirely 
new  and  unexpected  class  of  relations."  This  example  belongs,  how- 
ever, not  to  the  Method  of  Residues  but  to  the  Method  of  Difference, 
the  law  being  ascertained  by  a  direct  comparison  of  the  results  of  two 
experiments,  which  differed  in  nothing  but  the  presence  or  absence  of 
the  plate  of  coj^per.  To  have  made  it  exemplify  the  Method  of  Res- 
idues, the  effect  of  the  resistance  of  the  air  and  that  of  the  rigidii^,  of 
the  silk  should  have  been  calculated  d  jjriori,  fi-om  the  laws  obtained 
by  separate  and  fcu'egone  experiments. 

"  Unexpected  and  peculiarly  striking  confirmations  of  inductive 
laws  frequently  occm-  in  the  form  of  residual  phenomena,  in  the  course 
of  investigations  of  a  widely  different  nature  from  those  which  gave  rise 
to  the  inductions  themselves.  A  very  elegant  example  may  be  cited 
in  the  unexpected  confirmation  of  the  law  of  the  development  of  heat 
in  elastic  fluids  by  compression,  which  is  afforded  by  the  phenomena 


KXAMTLES  OF  THE  FOUR  METHODS.  249 

of  souiul.  Tlu'  iiKjuirv  into  tlio  cause  of  soiiiul  had  led  to  coiielusioiis 
respecting  its  mode  of  propagation,  from  which  its  vehxity  in  the  aix* 
couhl  he  precisely  calculatecl.  The  c^dculations  were  performed; 
but,  when  compared  with  fact,  though  the  agreement  was  quite  suffi- 
cient to  show  the  general  cttrrectuess  of  the  cause  and  mode  of  propa- 
gation assigned,  yet  the  loholc  velocity  could  not  be  shown  to  arise 
from  this  theory.  There  was  still  a  residuid  velocity  to  be  accounted 
for,  which  placed  dynamical  philosophers  for  a  long  time  in  a  great 
dilemma.  At  length  Laplace  struck  on  the  happy  idea,  that  this 
might  arise  from  the  heat  developed  in  the  act  of  that  condensa- 
tion which  necessarily  takes  place  at  every  vibration  by  which  sound 
is  conveyed.  The  matter  was  subjected  to  e.xact  calculation,  and 
the  result  was  at  once  the  complete  explanation  of  the  residual  phe- 
nomenon, and  a  striking  confirmation  of  the  general  law  of  the  devel- 
opment of  heat  by  compression,  under  circumstances  beyond  artificial 
imitation." 

"  Many  of  the  new  elements  of  chemistry  have  been  detected  in  the 
investigation  of  residual  phenomena.  Thus  Arfwedson  discovered 
lithia  by  perceiving  an  excess  of  weight  in  the  sulphate  j)roduced  from 
a  small  portion  of  what  he  considered  as  magnesia  present  in  a  mineral 
he  had  analyzed.  It  is  on  this  principle,  too,  that  the  small  concen- 
trated residues  of  great  operations  in  the  arts  are  almost  sure  to  be  the 
lurking  places  of  now  chemical  ingredients :  witness  iodine,  brome, 
selenium,  and  the  new  metals  accompanying  platina  in  the  expeiu- 
ments  of  Wollaston  and  Tennant.  It  was  a  happy  thought  of  Glauber 
to  examine  what  everybody  else  threw  away."* 

The  disturbing  effects  mutually  produced  by  the  earth  and  planets 
upon  each  other's  motions  were  first  brought  to  light  as  residual  phe- 
nomena, by  the  ditference  which  appeared  between  the  observed 
places  of  those  bodies,  and  the  places  calculated  on  a  consideration 
solely  of  their  gravitation  towards  the  sun.'  It  was  this  which  deter- 
mined philosophers  to  consider  the  law  of  gravitation  as  obtaining  be- 
tween all  bodies  whatever,  and  therefore  between  all  particles  of 
matter  ;  their  first  tendency  having  been  to  regard  it  as  a  force  acting 
only  between  each  planet  or  satellite  and  the  central  body  to  Vvhose 
system  it  belonged.  Again,  the  catastrophists,  in  geology,  be  their 
opinion  light  or  wrong,  support  it  upon  the  plea,  that  after  the  effect 
of  all  causes  now  in  operation  has  been  allowed  for,  there  remains  in 
the  existing  constitution  of  the  earth  a  large  residue  of  facts,  proving 
the  existence  at  former  periods  either  of  other  forces,  or  of  the  same 
forces  in  a  much  greater  degree;  of  intensity.  To  add  one  more 
example  :  if  it  be  possible  to  establish,  what  is  generally  rather  as- 
sumed than  proved,  that  there  is  in  one  human  individual,  one  sex,  or 
one  race  of  mankind  over  another,  an  inherent  and  inexplicable  supe- 
riority in  mental  faculties,  this  must  bo  proved  by  subtractingfrom  the 
differences  of  intellect  which  we  in  fact  see,  all  that  can  be  traced  by 
known  laws  either  to  the  ascertained  differences  of  physical  organiza- 
tion, or  to  the  differences  whi<;h  have  existed  in  the  outward  circum- 
stances in  which  the  subjects  of  the  comparison  have  hitherto  been 
placed.  Wliat  these  causes  might  fail  to  account  for,  would  constitute 
a  residual  phenomenon,  which  and  which  alone  would  be  evidence  of 

*  HERsCHEr.,  ul  supra,  pp.  78-9,  and  86. 
I  I 


250  INDUCTION. 

an  ulterior  original  distinction,  and  the  measure  of  its  amount.  But 
the  strongest  assertors  of-  such  supposed  differences  have  hitherto  been 
very  negligent  of  providing  themselves  with  these  necessary  logical 
Conditions  of  the  establishment  of  their  doctrine. 

The  spirit  of  the  Method  of  Residues  being,  it  is  hoped,  sufficiently 
intelligible  from  these  examples,  and  the  other  three  methods  having 
been  so  aptly  exemplified  in  the  inductive  processes  which  produced 
the  Theory  of  Dew,  we  may  here  close  our  exposition  of  the  four 
methods,  considered  as  employed  in  the  investigation  of  the  simpler 
and  more  elementary  order  of  the  combinations  of  phenomena. 


CHAPTER  X. 

OF   PLURALITV   OF  CAUSES;   AND  OF  THE   INTERMIXTURE  OF   EFFECTS. 

§  1.  In  the  preceding  exposition  of  the  four  methods  of  observation 
and  experiment,  by  which  we  contrive  to  distinguish  among  a  mass  of 
coexistent  phenomena  the  particular  effect  due  to  a  given  cause,  or  the 
particular  cause  which  gave  birth  to  a  given  effect ;  it  has  been  neces- 
sary to  suppose,  in  the  first  instance,  for  the  sake  of  simplification,  that 
this  analytical  operation  is  encumbered  by  no  other  difficulties  than 
what  are  essentially  inherent  in  its  nature;  and  to  represent  to  our- 
selves, therefore,  every  effect,  on  the  one  hand  as  connected  exclu- 
sively with  a  single  cause,  and  On  the  other  hand  as  incapable  of  being 
mixed  and  confounded  with  any  other  coexistent  effect.  We  have  re- 
garded ahcdc,  the  aggregate  of  the  phenomena  existing  at  any  mo- 
ment, as  consisting  of  tlissimilar  facts,  a,  b,c,d,  and  e,  for  each  of  which 
one,  and  only  one,  cause  needs  be  sought ;  the  difficulty  being  only  that 
of  singling  out  this  one  cause  fi-om  the  multitude  of  antecedent  circum- 
stances, A,B,  C,  D,  and  E. 

If  such  were  the  fact,  it  would  be  comparatively  an  easy  task  to  in- 
vestigate the  laws  of  nature.  But  the  supposition  does  not  hold,  in 
either  of  its  parts.  In  the  first  place,  it  is  not  true  that  the  same  phe- 
nomenon is  always  produced  by  the  same  cause  :  the  effect  a  may 
sometimes  arise  from  A,  sometimes  from  B.  And,  secondly,  the  effects 
of  different  causes  are  often  not  dissimilar,  but  hornogeneous,  and 
marked  out  by  no  assignable  boundaries  fi-om  one  another :  A  and  B 
may  produce  not  a  and  h,  but  different  portions  of  an  effect  a.  The 
obscurity  and  difficulty  of  the  investigation  of  the  laws  of  phenomena 
is  singularly  increased  by  the  necessity  of  adverting  to  these  two  cir- 
cumstances ;  Intermixture  of  Effects,  and  Plurality  of  Causes.  To  the 
latter,  being  the  simpler  of  the  two  considerations,  we  shall  first  direct 
our  attention. 

It  is  not  ti'ue,  then,  that  one  effect  must  be  connected  with  only  one 
cause,  or  assemblage  of  conditions  ;  that  each  phenomenon  can  be  pro- 
duced only  in  one  way.  There  are  often  several  independent  modes 
in  which  the  same  phenomenon  could  have  originated.  One  fact  may 
be  the  consequent  in  several  invariable  sequences;  it  may  follow,  with 
equal  uniformity,  any  one  of  several  antecedents,  or  collections  of  ante- 
cedents.    Many  causes  may  produce  motion ;  many  causes  may  pro- 


PLURALITY   OF    CAUSES,  251 

duce  some  kinds  of  sensation  :  many  causos  may  produce  death.  A 
given  effect  may  really  be  produced  by  a  certain  cause,  and  yet  be 
perfectly  capable  of  being  produced  without  it. 

§  2.  One  of  the  principal  consequences  of  this  fact  of  Plurality  of 
Causes  is,  to  render  the  tirst  of  our  inductive  riiethods,  that  of  Agree- 
ment, uncertain.  To  illustrate  that  method,  we  supposed  two  instances. 
A  B  C  followoil  by  a  h  r,  and  A  J)  1^]  followed  by  (?  d  c.  From  these  in- 
stances it  miirht  be  concluded  that  A  is  an  invariable  antecedent  of  o; 
and  even  that  it  is  the  unconditional  invariable  antecedent  or  cause,  if 
we  could  be  sure  that  there  is  no  other  antecedent  common  to  the  two 
cases.  That  this  difficulty  may  not  staml  in  the  way,  let  us  suppose 
the  two  cases  positively  ascertained  to  have  no  antecedent  in  common 
except  A.  The  moment,  however,  that  we  let  in  tin*  possibility  of  a  plu- 
rality of  causes,  the  conclusion  fails.  For  it  involves  a  tacit  suppo- 
sition that  a  must  have  been  produced  in  both  instances  by  the  same 
cause.  If  there  can  possibly  have  been  two  causes,  those  two  may,  for 
example,  be  C  and  E  :  the  one  may  have  been  the  cause  of  a  in  the 
former  of  the  instances,'  the  other  in  the  latter,  A  ha\'ing  no  influence 
in  either  case. 

Suppose,  for  example,  that  two  great  artists,  or  great  philosophers, 
that  two  extremely  selfish,  or  extremely  generous  charactei-s,  were 
compared  together  as  to  the  circumstances  of  ;their  education  and  his- 
tory, and  the  two  cases  were  found  to  agree  only  in  one  circumstance": 
would  it  follow  that  this  one  circuriistance  was  the  cause  of  the  quality 
which  characterized  both  those  individuals  ?  Not  at  all ;  for  the 
causes  at  work  to  produce  any  given  type  of  character  are  innumer- 
able ;  and  the  two  persons  might  equally  have  agreed  in  their  char- 
acter, although  there  had  been  no  manner  of  reserabhmce  in  their 
previous  history. 

This,  therefore,  is  a  characteristic  imperfection  of  the  INIethod  of 
Agreement ;  from  which  imperfeciion  the  Method  of  Difference  is  fre^. 
For  if  we  have  two  instances,  ABC  and  BC,  of  which  BC  gives  be, 
and  A  being  added  converts  it  into  a  he,  it  is  certain  that  in  this  instance 
at  least  A  was  either  the  cause  of  a,  or  an  indispensable  portion  of  its 
cause,  even  thoui^h  the  cause  which  produces  it  in  other  instances  may 
be  altogether  different.  Plurality  of  Causes,  therefore,  not  only  does 
nf»t  diminish  the  reliance  due  to  the  Method  of  Difference,  but  does  not 
even  render  a  greater  number  of  obstjrvations  or  experiments  necessary  : 
two  instances,  the  one  positive  and  the  other  negative,  are  still  suffi- 
cient for  the  most  complete  and  rigorous  induction.  Not  so,  however, 
with  the  Method  of  Agreement.  The  conclusions  which  that  yields, 
when  the  number  of  instances  compared  is  small,  are  of  no  real  value, 
except  as,  in  the  character  of  suggestione,  they  may  lead  either  to 
experiments  bringing  them  to  the  test  of  the  Method  of  Difference,  or 
to  reasonings  which  may  explain  and  verify  them  deductively. 

It  is  only  when  the  instances,  being  indefinitely  multiplied  and  varied, 
continue  to  suggest  the  same  result,  that  this  result  accpiires  any  high 
degree  of  independent  value.  If  there  are  but  two  instances,  ABC 
and  ADE,  although  the-se  instances  have  no  antecedent  in  common 
except  A,  yet  as  the  effect  may  possibly  have  been  produced  in  the 
two- cases  by  different  causes,  the  result  is  at  most  only  a  slight  proba- 
bility in  favor  of  A  ,•  there  may  be  causation,  but  it  is  almost  equally 


252  INDUCTION. 

probable  that  there  was  only,  as  the  expression  is,  a  coincidence.  But 
the  oftener  we  repeat  the  observation,  varying  the  circumstances,  the 
more  we  advance  towards  a  solution  of  this  doubt.  For  if  we  try 
AFG,  AHK,  &c.,  all  entirely  unlike  one  another  except  in  containing 
the  circumstance  A,  and  if  we  find  the  effect  a  entering  into  the  result 
in  all  these  cases,  we  must  suppose  one  of  two  things,  either  that  it  is 
caused  by  A,  or  that  it  has  as  many  different  causes  as  there  are  in- 
stances. With  each  addition,  therefore,  to  the  number  of  instances, 
the  presumption  is  strengthened  in  favor  oi  A.  The  inquirer,  of  course, 
will  not  neglect,  if  an  opportunity  present  itself,  to  exclude  A  from 
some  one  of  these  combinations,  from  AHK  for  instance,  and  by  trying 
H  K  separately,  appeal  to  the  Method  of  Difference  in  aid  of  the  Method 
of  Agreement.  By  the  former  method  alone  can  it  be  ascertained  that 
A  is  the  cause  of  a;  but  that  it  is  either  the  cause  or  another  effect  of 
the  same  cause,  may  be  placed  beyond  any  reasonable  doubt  by  the 
Method  of  Agreement,  provided  the  instances  are  very  numerous,  as 
well  as  sufficiently  various. 

After  how  gi-eat  a  multiplication,  then,  of  varied  instances,  all  agree- 
ing in  no  other  antecedent  ex<;ept  A,  is  the  supposition  of  a  plurality 
of  causes  sufficiently  rebutted,  and  the  conclusion  that  a  is  the  effect  of 
A  divested  of  the  characteristic  imperfection  and  reduced  to  a  virtual 
certainty  %  This  is  a  question  which  we  cannot  be  exempted  from 
answering ;  but  the  consideration  of  it  belongs  to  what  is  called  the 
Theory  of  Probability,  which  will  form  the  subject  of  a  chapter  here- 
after. It  is  seen,  however,  at  once,  that  the  conclusion  does  amount  to 
a  practical  certainty  after  a  sufficient  number  of  instances,  and  that  the 
method,  therefore,  is  not  radically  vitiated  by  the  characteristic  imperfec- 
tion. The  result  of  these  considerations  is  only,  in  the  first  place,  to 
point  out  a  new  source  of  inferiority  in  the  Method  of  Agreement  as 
compared  with  other  modes  of  investigation,  and  new  reasons  for  never 
resthig  contented  with  the  results  obtained  by  it,  without  attempting  to 
confirm  tliem  either  by  the  Method  of  Difference,  or  by  coimecting 
them  deductively  with  some  law  or  laws  already  ascertained  by  that 
superior  method.  And,  in  the  second  place,  we  leaj-n  from  this,  the 
true  theory  of  the  value  of  mere  number  of  instances  in  inductive 
inquiry.  The  tendency  of  unscientific  inquiries  is  to  rely  too  much 
upon  number,  without  analyzing  the  instances  ;  without  looking  closely 
enough  into  their  nature,  to  ascertain  what  circumstar^ces  are  or  are  not 
eliminated  by  means  of  them.  Most  people  hold  their  conclusions 
with  a  degree  of  assurance  proportioned  to  the  mere  mass  of  the  expe- 
rience on  which  they  appear  to  rest :  not  considering  that  by  the  addi- 
tion of  instances  to  instances,  all  of  the  same  kind,  that  is,  differing  from, 
one  another  only  in  points  already  recognized  as  immaterial,  nothing 
whatever  is  added  to  the  evidence  of  the  conclusion.  A  single  instance 
eliminating  some  antecedent  which  existed  in  all  the  other  cases,  is  of 
more  value  than  the  greatest  multitude  of  instances  which  are  reckoned 
by  their  number  alone.  It  is  necessary,  no  doubt,  to  assure  ourselves, 
by  a  repetition  of  the  observation  or  experiment,  that  no  error  has 
been  committed  concerning  the  individual  facts  observed;  and  until  we 
have  assured  ourselves  of  this,  instead  of  varying  the  circumstances,  we 
cannot  too  scrupulously  repeat  the  same  experiment  or  observation 
without  any  change.  But  when  once  this  assurance  has  been  obtained, 
the  multiplication  of  instances  which  do  not  exclude  any  more  cir- 


PLURALITY    OF   CAUSES.  253 

cumstanccs  would  be  entirely  useless,  were  it  not  for  the  Plurality 
of  Causes. 

It  is  of  importance  to  remark,  that  the  peculiar  modification  of  the 
Method  of  AE^recmcnt  which,  as  partaking  in  some  degree  of  the  na- 
ture of  the  Method  of  Diff'ercnce,  1  have  called  the  Joint  Method  of 
Agi'eement  and  Dift'ei-ence,  is  not  afi'ected  by  the  characteristic  imper- 
fection now  pointed  out.  For,  in  the  joint  method,  it  is  supposed  not 
only  that  the  instances  in  which  a  is,  agree  only  in  containing  A,  but 
also  that  the  instaTices  in  which  a  is  not,  agi-ee  oidy  in  not  contain- 
ing A.  Now,  if  this  be  so,  A  must  be  not  only  the  cause  of  a,  but  the 
only  possible  cause  :  for  if  there  were  another,  as  for  example  B, 
then  in  the  instances  in  which  a  is  not,  B  must  have  been  absent  as 
well  as  A,  and  it  would  not  be  true  that  these  instances  agree  only 
in  not  containing  A.  This,  therefore,  constitutes  an  immense  advan- 
tage of  the  joint  method  over  the  simple  Method  of  Agreement.  It 
may  seem,  indeed,  that  the  advantage  does  not  belong  so  much  to  the 
joint  method,  as  to  one  of  its  two  premisses  (if  they  may  be  so 
called),  the  negative  premiss.  The  Method  of  Agreement,  when 
applied  to  negative  instances,  or  those  in  which  a  phenomenon  does 
not  take  place,  is  certainly  fi-ee  from  the  characteristic  imperfection 
which  affects  it  in  the  affirmative  case.  The  negative  premiss,  it 
might  therefore  be  supposed,  could  be  worked  as  a  simple  case  of 
the  Method  of  Agreement,  without  requiring  an  affirmative  premiss  to 
be  joined  witli  it.  But  although  this  is  true  in  principle,  it  is  gen- 
erally altogether  impossible  to  work  the  Method  of  Agreement  by 
negative  instances  without  positive  ones :  it  is  so  much  more  diffi- 
cult to  exhaust  the  field  of  negation  than  that  of  affirmation.  For 
instance,  let  the  question  be,  what  is  the  cause  of  the  transparency  of 
bodies  :  with  what  prospect  of  success  could  we  set  ourselves  to 
inquire  directly  in  what  the  multifarious  substances  which  are  not 
transparent,  agree  1  But  we  might  hope  much  sooner  to  seize  some 
point  of  resemblance  among  the  comparatively  few  and  definite 
species  of  objects  which  arc  transparent ;  and  this  being  attained, 
we  should  quite  naturally  be  put  upon  examining  whetlKU-  the  ab- 
sence of  this  one  circumstance  be  not  precisely  the  point  in  which 
all  opaque  substances  will  be  found  to  resemble. 

The  Joint  Method  of  Agreement  and  Diffijrence,  therefore,  or,  as 
I  have  otherwise  called  it,  the  Indirect  Method  of  Difference  (be- 
cause, like  the  Method  of  Difference  properly  so  called,  it  proceeds  by 
a.scertaining  how  and  in  what  the  cases  where  the  phenomenon  is 
present,  difter  from  those  in  which  it  is  absent)  is,  after  the  direct 
Method  of  Difference,  the  most  powerful  of  the  remaining  instru- 
ments of  inductive  investigation  •  and  in  the  sciences  which  depend 
on  pure  obscr\-ation,  with  little  or  no  aid  from  experiment,  this 
method,  so  well  exemplified  in  the  beautiful  speculation  on  tin;  cause 
of  dew,  is  the  primary  resource,  so  far  as  direct  appeals  to  experi- 
ence are  concerned. 

§  3.  We  have  thus  far  treated  Plurality  of  Causes  only  as  a  possible 
supposition,  which,  until  nnnoved,  renders  our  inductiolis  uncertain, 
and  have  only  considered  by  what  means,  where  the  plurality  does  not 
really  exist,  we  may  be  enabled  to  disprove  it.  But  we  must  also  con- 
sider it  as  a  case  actually  occurring  in  nature,  and  which,  as  often  as 


254  INDUCTION. 

it  does  occur,  our  methods  of  induction  ought  to  be  capable  of  ascer- 
taining and  establishing.  For  this,  however,  there  is  required  no 
peculiar  method.  When  an  effect  is  really  producible  by  two  or  more 
causes,  the  process  for  detecting  them  is  in  no  way  different  from  that 
by  which  we  discover  single  causes.  They  may  (first)  be  discovered 
as  separate  sequences,  by  separate  sets  of  instances.  One  set  of  ob- 
Bervationfj  or  experiments  shows  that  the  sun  is  a  cause  of  heat,  another 
that  friction  is  a  source  of  it,  another  tliat  percussion,  another  that  elec- 
tricity, another  that  chemical  action  is  such  a  source.  Or  (secondly) 
the  plurality  may  come  to  light  in  the  course  of  collating  a  number  of 
instances,  when  we  attempt  to  find  some  cu-cumstance  in  which  they 
all  agi'ee,  and  fail  in  doing  so.  We  find  it  impossible  to  trace,  in  all 
the  cases  in  which  the  effect  is  met  with,  any  common  circiuustance. 
We  find  that  we  can  eliminate  all  the  antecedents  ;  that  no  one  of  them 
is  present  in  all  the  instances,  no  one  of  them  indispensable  to  the 
effect.  On  closer  scrutiny,  however,  it  appears,  that  though  no  one  is 
always  present,  one  or  other  of  several  always  is.  If,  on  further  anal- 
ysis, we  can  detect  in  these  any  common  element,  we  may  be  able  to 
ascend  from  them  to  some  one  cause  which  is  the  really  operative  cir- 
cumstance in  them  all.  Thus  it  might,  andperhaps  will  be,  discovered, 
that  in  the  production  of  heat  by  friction,  percussion,  chemical  action,  &c., 
the  ultimate  source  is  one  and  the  same.  But  if  (as  continually  hap- 
pens) we  cannot  take  this  ulterior  step,  the  different  antecedents  must  be 
set  down  as  distinct  causes,  each  sufficient  of  itself  to  produce  the  effect. 
We  may  here  close  our  remarks  on  the  Plurality  of  Causes,  and  pro- 
ceed to  the  still  more  peculiar  and  more  complex  case  of  the  Intermix- 
ture of  Effects,  and  the  interference  of  causes  with  one  another:  a 
case  constituting  the  principal  part  of  the  complication  and  difficulty  of 
the  study  of  nature ;  and  with  which  the  four  only  possible  methods 
of  directly  inductive  investigation  by  observation  and  experiment,  are 
for  tJre  most  pait,  as  will  appear  presently,  quite  unequal  to  cope. 
The  instrument  of  Deduction  alone  is  adequate  to  unravel  the  com- 
plexities proceeding  from  this  source  ;  and  the  foiu'  methods  have  httle 
more  in  their  power  than  t©  supply  premisses  for  our  deductions. 

§  4.  A  concuiTence  of  two  or  more  causes,  not  separately  producing 
each  its  own  effect,  but  intei^fering  with  or  modifying  the  effects  of  one 
another,  takes  place,  as  has  already  been  explained,  in  two  different 
ways.  In  the  one  case,  which  is  exemplified  by  the  joint  operation  of 
different  forces  in  mechanics,  the  separate  effects  of  all  the  causes  con- 
tinue to  be  produced,  but  are  compounded  with  one  another,  and  dis- 
apfjear  in  one  total, '  In  the  other  case,  illustrated  by  the  case  of  chem- 
ical action,  the  separate  effects  cease  entirely,  and  are  succeeded  by 
phenomena  altogether  different,  and  governed  by  different  laws. 

Of  these  cases  the  former  is  by  far  the  more  frequent,  and  this  case 
it  is  which,  for  the  most  part,  eludes  the  grasp  of  our  experimental 
methods.  The  other  and  exceptional  case  is  essentially  amenable  to 
them.  When  the  laws  of  the  original  agents  cease  entirely,  and  a 
phenomenon  makes  its  appearance,  which,  with  reference  to  those 
laws,  is  quite  heterogeneous ;  when,  for  example,  two  gaseous  sub- 
stances, hydrogen  and  oxygen,  on  being  brought  together,  throw  off 
their  peculiar  properties,  and  produjce  the  substance  called  water ;  in 
such  cases  the  new  fact  may  be  subjected  to  experimental  inquiry,  like 


INTERMIXTURE    OF    EFFECTS.  255 

any  other  phenomenon  ;  and  the  elements  which  arc  said  to  compose 
it  may  be  considered  as  the  mere  agents  of  its  production  ;  the  condi- 
tions on  which  it  depends,  tlie  facts  which  make  up  its  cause. 

Tlie  ejects  of  th(>  new  phenomenon,  the  j^rojfertics  of  water,  for  in- 
stance, are  as  ^easily  found  by  experiment  as  the  effects  of  any  other 
cause.  But  to  discover  the  cause  of  it,  tliat  is,  the  particular  conjunc- 
tion of  agents  from  which  it  resuUs,  is  often  difficult  enough.  In  the 
first  place,  the  origin,  and  actual  production  of  the  phenomenon,  is 
most  freqdently  inaccessible  to  our  ol)servation.  If  we  could  not  have 
learned  the  composition  of  water  until  we  found  instances  in  which  it 
was  actually  produced  from  oxygen  and  hydrogen,  we  should  have 
been  forced  to  wait  until  the  casual  thought  struck  some  one  of  passing 
an  electric  spark  through  a  mixture  of  the  two  gases,  or  inserting  a 
lighted  taper  into  it,  merely  to  try  what'would  happen.  Further,  even 
if  we  could  have  ascertained  by  the  Method  of  Agreement,  that  oxygen 
and  hydrogen  were  both  present  when  water  is  produced,  no  experi- 
mentation on  oxygen  ^nd  hydrogen  separately,  no  knowledge  of  their 
laws,  could  have  enabled  us  deductively  to  infer  that  they  would  pro- 
duce water.     We  require  a  specific  experiment  on  the  two  combined. 

Under  these  difficulties,  we  should  generally  have  been  indebted  for 
our  knowledge  of  the  causes  of  this  class  of  effects,  not  to  any  incjuiry 
directed  specifically  towards  that  end,  but  either  to  accident,  or  to  tho 
gi'adual  progress  of  experimentation  on  the  different  combinations  ot 
which  the  producing  agents  are  susceptible  ;  if  it  were  not  for  a  pecu- 
liarity belonging  to  effects  of  this  description,  tliat  they  often^,  under 
some  particular  combination  of  circumstances,  reproduce  their  causes. 
If  water  results  from  the  juxtaposition  of  hydrogen  and  oxygen  when- 
ever this  can  be  made  sufficiently  close  and  intimate,  so,  on  the  other 
hand,  if  water  itself  be  placed  in  certain  situations,  hydrogen  and  oxy- 
gen are  repi'oduced  from  it :  an  abrupt  termhiation  is  put  to  the  n6w 
laws,  and  the  agents  reappear  separately  with  their  own  properties  as 
at  first.  AVliat  is  called  chemital  analysis  is  the  process  of  searching 
for  the  causes  of  a  phenomenon  among  its  effects,  or  rather  among  the 
effects  produced  by  the  action  of  some  other  causes  upon  it. 

Lavoisier,  by  heating  mercury  to  a  high  temperature  in  a  close  vessel 
containing  air,  found  that  the  mercury  increased  in  weight  and  became 
what  was  then  called  Ted  precipitate,  while  the  au:,  on  being  examined 
after  the  experiment,  proved  to  haye  lost  weight,  and  to  have  become 
incapable  of  supporting  life  or  combustion.  -When  red  precipitate  was 
exposed  to  a  still  greater  heat,  it  became  mercury  again,  and  gave  off 
a  gas  which  did  support  life  and  flame.  Thus  the  agents  which  by 
theit  combination  produced  red  precipitate,  namely,  the  mercury  and 
the  gas,  reappear  as  effects  resulting  from  that  precipitate  when  acted 
upon  by  heat.  So,  if  we  decompose  water  by  means  of  irou  filings, 
we  produce  two  effects,  rust  and  hydrogen  :  now  rust  is  already  known 
by  experiments  upon  the  component  substances,  to  be  an  effect  of  the 
union  of  iron  and  oxygen:  tho  iron  we  ourselves  supplied,  but  the 
oxygen  must  have  been  produced  from  the  water.  The  result  there- 
fore is  that  the  water  has  disappeared,  and  hydrogen  and  oxygen  have 
appeared  in  its  stead  :  or  in  other  words,  the  original  laws  of  these 
gaseous  agents,  which  had  been  suspended  by  the  superinduption  of 
the  new-laws  called  the  properties  of  water,  have  again  started  iijto 
existence,  and  the  causes  of  water  are  found  among  its  effects. 


256  INDUCTION. 

Where  tvvo  plienomena,  between  the  laws  or  properties  of  which 
considered  in  themselves  no  connexion  can  be  traced,  are  thus  recipro- 
cally cause  and  effect,  each  capable  in  its  turn  of  being  produced  from 
the  other,  and  each,  when  it  produces  the  other,  ceasing  itself  to  exist 
(■as  water  is  produced  fi-ora  oxygen  and  hydrogen,  and  oxygen  and 
hydrogen  are  reproduced  from  water);  this  causation  of  the  two 
pbenonlena  by  one  another,  each  of  them  being  generated  by  the 
.other's  destruction,  is  properly  ti-ansfonnation.  The  idea  of  chemical 
composition  is  an  idea  of  transfomiation,  but  of  a  transfonnation  which 
is  incomplete ;  since  we  consider  the  oxygen  and  hydrogen  to  be 
present  in  the  water  as  oxygen  and  hydrogen,  and- capable  of, being 
discx)vered  in  it  if  our  senses  were  sufficiently  keen  :  a  supposition  (for 
it  is  no  more)  grounded  solely  upon  the  fact,  that  the  weight  of  the 
water  is  the  sum  of  the  separate  weights  of  the  two  ingredients.  If 
there  had  not  been  this  exception  to  the  entire  disappearance,  in  the 
compound,  of  the  laws  of  the  separate  ingredients ;  if  the  combined 
agents  had  not,  in  this  one  particular  of  weight,. preserved  their  own 
laws,  and  produced  a  joint  result  equal  to  the  sum  of  their  separate 
results ;  we  should  never,  probably,  have  had  the  notion  now  implied 
by  the  words  chemical  composition :  and,  in  the  fact  of  water  produced 
fi-om  hydrogen  and  oxygen  and  hydrogen  and  oxygen  produced  from 
water,  as  the  transformation  would  have  been  complete,  we  should 
have  seen  only  a  transformation.  • 

In  these  cases,  then,  when  the  heteropathic  effect  (as  we  called  it  in 
a  former  chapter)  is  but  a  transformation  of  its  cause,  or  in  other 
words,  when  the  effect  and  its  cause  are  reciprocally  such,  and 
mutually  convertible  into  each  other;  the  problem  of  finding  the  cause 
resolves  itself  into  the  -far  easier  one  of  finding  an  effect,  which  is  the 
kind  of  inquiry  that  admits  of  being  prosecuted  by  direct  experiment. 
But  there  are  other  cases  of  heteropathic  effects  to  which  this  mode  of 
investigation  is  not  ajiplicable.  Take,  for  instance,  the  heteropathic 
laws  of  mind ;  that  portion  of  the  phenomena  of  our  mental  nature 
which  are  analogous  to  chemical  rather  than  to  dynamical  phenomena; 
as  when  a  complex  passion  is  formed  by  the  coalition  of  several 
elementary  impulses,  or  a  complex  emotion  by  several  simple  pleasures 
or  pains,  of  which  it  is  the  result,  without  being  the  aggregate,  or  in 
any  respect  homogeneous  with  them.  The  product,  in  these  cases,  is 
generated  by  its  various  factors ;  but  the  factors  cannot  be  reproduced 
from  the  product :  just  as  a  youth  can  gi'ow  into  an  old  man,  but  an 
old  man  cannot  grow  into  a  youth.  We  cannot  ascertain  from  what 
simple  feelings  any  of  our  complex  states  of  mind  are  ^eiierated,  as 
we  ascertain  the  ingredients  of  a  chemical  compound,  by  making  it, 
in  its  turn,  generate  them.  We  can  only,  therefore,  discover  these 
laws  by  the  slow  process  of  studying  the  simple  feelings  themselves, 
and  ascertaining  synthetically,  by  experimenting  on  the  various  com- 
binations of  which  they  are  susceptible,  what  they,  by  their  mutual 
action  upon  one  another,  are  capable  of  generating. 

§  5.  It  might  have  been  supposed  that  the  other,  and  apparently 
simpler  variety  of  the  mutual  interference  of  causes,  where  each  cause 
continues  to  produce  its  own  proper  effect  according  to  the  same  laws 
to  which  it  confonns  in  its  separate  state,  would  have  presented  fewer 
difficulties  to  the  inductive  inquirer  than  that  of  which  we  have  just 


INTERMIXTURE    OF    EFFECTS.  257 

fiiiislieJ  the  consideration.  It  presents,  however,  so  far  as  direct  in- 
duction apart  from  deduction  is  concerned,  iniinitoly  grtiater  diillc id- 
ties.  Wlien  a  concurrence  of  causes  f^ives  rise  to  a  new  effect  bearing 
no  relatioa  to  the  separate  effects  of  tliosc  causes,  the  resulting  phe- 
nomenon at  least  stands  forth  undisguised,  inviting  attention  to  its 
peculia^'ity,  and  presenting  no  obstacle  to  (»ur  recognizing  its  pi'esence 
or  absence  among  any  number  of  surrounding  phenomena.  It  admits 
therefore  of  being  easily  brought  under  the  canons  of  induction,  pro- 
\ided  instances  can  be  obtained  such  as  those  canons  require :  and  the 
non-occurrence  of  such  instances,  or  the  want  of  means  to  produce 
them  artificially,  is  the  real  and  only  difficulty  in  such  investigations ; 
a  difficulty  not  logical,  but  in  some  sort  physical..  It  is  otherwise  with 
cases  of  what,  in  a  preceding  chapter,  has  been  denominated  the 
Composition  of  Causes.  There,  the  effects  of  the  separate  causes  do 
not  terminate  and  give  place  to  others,  thereby  ceasing  to  form  any 
part  of  the  phenomenon  to  be  investigated  ;  on  the  contrary  they  still 
take  place,  but  are  intermingled  with,  and  disguised  by,  the  homoge- 
neous and  closely-allied  effects  of  other  causes.  They  are  no  longer 
a,  b,  c,  d,  e,  existing  side  by  side,  and  continuing  to  be  separately  dis- 
cernible;  they  are  -\-  a,  —  a,  ^  b,  —  b,  2  b,  Sec,  some  of  which  cancel 
one  another,  while  many  others  do  not  .appear  distinguishably  but 
merge  in  one  sum  :  forming  altogether  a  result,  between  which  and 
the  causes  whereby  it  was  produced  there  is  often  an  insurmountable 
difficulty  in  tracing  by  observation  any  lixeil  relation  whatever. 

The  general  idea  of  the  Composition  of  Causes  has  been  seen  to  be, 
that  although  two  or  more  laws  interfere  with  one  another,  and  appa- 
rently frustrate  or  modify  one  another's  operation,  yet  in  reality  all 
are  fulfilled,  the  collective  effect  being  the  exact  sum  total  of  the 
effects  of  the  causes  taken  separately.  A  familiar  instance  is  that  of  a 
body  kept  in  equilibrium  by  two  equal  and  contrary  foixes.  One  of 
the  forces  if  acting  alone  would  carry  it  so  far  to  the  west,  the  other  if 
acting  alone  would  carry  it  exactly  as  far  towards  the  cast :  and  the 
result  is  the  same  as  if  it  had  been  first  carried  to  the  west  as  far  as 
the  one  force  would  carry  it,  and  then  back  towards  the  east  as  far  as 
the  other  would  caiTy  it,  that  is,  precisely  the  same  distance ;  being 
ultimately  left  where  it  was  found  at  first. 

All  laws  of  causation  are  liable  to  be  in  this  manner  counteracted, 
and  seemingly  frustrated,  by  coming  into  conflict  with  other  laws,  the 
separate  result  of  which  is  cjpposite  to  theirs,  or  more  or  less  incon- 
sistent with  it.  And  hence,  with  almost  every  law,  many  instances  in 
which  it  really  is  entirely  fulfilled,  do  not,  at  first  siglit,  appear  to  be 
cases  of  its  operation  at  all.  It  is  so  in  the  example  just  adduced  :  a 
force,  in  mechanics,  means  neither  more  nor  less  than  a  cause  of 
motion,  yet  the  sum  ofthe  effects  of  two  causes  of  motion  may  be  rest. 
Again,  a  bcjdy  solicited  by  two  forces  in  directions  making  an  angle 
with  one  another,  moves  in  the  diagonal;  and  it  seems  a  paradox  to 
say  that  motion  in  the  diagonal  is  flhe  sum  of  two  motions  in  two  other 
lines.  Motion,  however,  is  but  changes  of  place,  and  at  every  instant 
the  body  is  in  the  exact  place  it  would  have  been  in  if  the  forces  liad 
acted  during  alternate  instants  instead  of  acting  in  the  same  instant; 
(saving  that  if  we'  suppose  two  forces  to  act  successively  which  are  in 
truth  simultaneous,  we  must  of  course  allow  them  double  the  time.) 
It  is  evident,  therefore,  that  each  force  has  had,  during  eaeh  uistant, 
Kk 


258'  INDUCTION. 

all  the  effect  which  belonged  to  it ;  and  that  the  modifying  influence 
which  one  of  two  concurrent  causes  is  said  to  exercise  with  respect  to 
the-  other,  may  be  considered  as  exerted  not  over  the  action  of  the 
cause  itself,  but  over  the  effect  after  it  is  completed.  For' all  purposes 
of  predicting,  calculating,  or  explaining  their  joint  result,  causes  which 
compoimd  their  effects  may  be  treated  as  if  they  produced  simultane- 
ously each  of  them  its  own  effect,  and  all  these  effects  coexisted  visibly. 
Since  the  laws  of  causes  are  as  really  fulfilled  when  the  causes  are 
said  to  be  counteracted  by  opposing  causes,  as  when  they  are  left  to 
their  own  undisturbed  action,  we  must  be  cautious  not  to  express  the 
laws  in  such  terms  as  would  render  the  assertion  of  their  being  fulfilled 
in  those  cases  a  contradiction.  If,  for  instance,  it  were  stated  as  a  law 
of  nature  that  a  body  to  which  a  force  is  applied  moves  in  the  direction 
of  the  force,  with  a  velocity  pi'oportioned  to  the  force  directly,  and  to 
its  o^vn  mass  inversely  ;  when  in  point  of  fact  some  bodies  to  which  a 
force  is  applied  do  not  move  at  all,  and  those  which  do  move  are,  fi-om 
the  very  first,  retarded  by  the  action  of  gravity  and  other  resisting 
forces,  and  at  last  stopped  altogether ;  it  is  clear  that  the  general  propo- 
sition, although  it  would  be  true  imder  a  certain  hypothesis,  would  not 
express  the  facts  as  they  actually  occur.  To  accommodate  the  expres- 
sion of  the  law  to  the  real  phenomena,  we  must  say,  not  that  the  object 
moves,  but  that  it  tends  to  move  in  the  direction  and  with  the  velocity 
specified.  We  might,  indeed,  guard  our  expression  in  a  different  mode, 
by  saying  that  the  body  moves  in  that  manner  unless  prevented,  or  except 
in  so  far  as  prevented  by  some  counteracting  cause.  ,  But  the  body 
does  not  only  move  in  that  manner  unless  counteracted;  it  tends  to 
move  in  that  manner  even  when  counteracted  ;  it  still  exerts,  in  the 
original  direction,  the  same  energy  of  movement  as  if  its  first  impulse 
had  been  undisturbed,  and  produces,  by  that  energy,  an  exactly  equiva- 
lent quantity  of  effect.  This  is  true  even  when '  the  force  leaves  the 
body  as  it  found  it,  in  a  state  of  absolute  rest ;  as  when  we  attempt  to 
raise  a  body  of  three  tons  weight  with  a  force  equal  to.  one  ton.  For 
if,  while  we  are  applying  this  force,  the  wind  or  water  or  any  other 
agent  supplies  an  additional  force  just  exceeding  two  tons,  the  body 
will  be  raised ;  thus  proving  that  the  force  we  applied  exerted  its  full 
effect,  by  neutralizing  an  equivalent  portion  of  the  weight  which  it  was 
insufficient  altogether  to  overcome.  And  if)  while  we  are  exerting 
this  force  of  one  ton  upon  the  object  in  a  direction  contrary  to  that  of 
gravity,  it  be  put  into  a'scale  and  weighed,  it  will  be  fbund  to  have 
lost  a  ton  of  its  weight,  or,  in  other  words, '  to  press  downwards  with 
a  force  only  equal  to  the  difference  of  the  two  forces. 

These  facts  are  coiTectly  indicated  by  the  expression  tentlcncy.  All 
laws  of  causation,,  in  consequence  of  their  liability  to  be  counteracted, 
require  to  be  stated  in  words  affirmative  of  tendencies  only,  and  not  of 
actual  results.  In  those  sciences  of  causation  which  have  an  accurate 
nomenclature,  there  are  special  w'or'ds  which  signify  a  tendency  to  the 
,  particular  effect  with  which  the  science  is 'conversant ;  thus  j)resst/rc,  in 
mechanics,  is  synonymous  with  tendency  to  motion,  and  forces  are  not 
reasoned  upon  as  causing  actual  motion,  but  as  exerting  pressure.  A 
similar  improvement  in  terminology  would  be  very  salutary  in  many 
other  branches  of  science. 

Tlie  habit  of  neglecting  this  necessary  element  in  the  precise  ex- 
pression of  the  laws  of  nature,  has  given  birth  to  the  popular  prejudice 


INTERMIXTURE    OF    EFFECTS.  259 

that  all  general  truths  have  exceptions ;  and  much  unmerited  distrust 
has  thence  accrued  to  the  conclusions  of  philosophy,  when  they  have 
been  submitted  to. the  judgment  of  persons  who  wei-.e  not  philosophers. 
The  rough  generalizations  suggested  by  common  observation  usually 
have  exceptions  ;  but  the  principles  of  science,  or  in  other  words,  the 
laws  of  causation,  have  not.  "  What  is  thought  to  be  a,n  exception  to 
a  princi})le,"  (tii  quote  words  used  on  a  difterent  occasion,)  "  is  always 
some  other  and  distuict  principle  cutting  into  the  former ;  some  other 
force  which  impinges  against  the  first  force,  and  deflects  it  from  its 
direction.  Therd  are  not  a  law  and  an  exception  to  that  l,aw,  the  Itivv 
acting  in  ninety-nine  cases  and  the  exception  in  one..  There  are  two 
laws,  each  possibly  acting  in  the  whole  hundi'cd  cases,  ai\d  bringing 
about  a  common  effect  by  their  conjunct  oj)ei'ation.  If  tl>c  foixc  which, 
being  the  less  conspicuous  of  the  two,  is  called  the  dhturhing  force, 
prevails  sufficiently  over  the  other  force  in  some  one  case,  to  constitute 
that  case  what  is  commonly  called  an  exception,  the  same  disturbing 
force  prqbably  acts  as  a  modifying  cause  in  many  other  cases  which  no 
one  will  call  exceptions.  . 

"  Thus  if  it  wei'e  stated  to  be  a  law  of  nature  that  all  heavy  bodies  , 
fall  to  the  ground,  it  wx)uld  probably  be  said  "that  the  resistance  of  the 
atmosphere,  which  prevents  a  balloon  from  falling,  constitutes  the 
balloon  an  exception  to  that  pretended  law  of  nature.  But  the  real 
law  is,  that  all  heavy  bodies  tend  to  fall ;  and  to  this  there  is  no  excep- 
tion, not  even  the  sun  and  moon  ;  for  even  they,  as  every  astronomer 
knows,  tend  towards  the  earth,  with  a  force  exactly  equal  to  that  with 
which  the  earth  tends  towards  them.  The  resistance  of  the  atmosphere 
might,  in  the  particular  case  of  the  balloon,  from  a  misapprehension  of 
what  the  law  of  gravita,tion  is",  be  said  to  prevail  over  the  law ;  but  its 
disturbing  effect  is  quite  as  real  in  evej-y  other  case,  since,  though  it 
does  not  prevent,  it  retards  th6  fall  of  all  bodies  whatever.  The  rule, 
and  the  so-called  exception,  do  not  divide  the  cases  between  them ; 
each  of  thern  is  a  comprehensive  rule  extending  to  all  cases.  To  call 
one  of  these  c(»ncurrent  principles  an  exception  to  the  other,  is  super- 
ficial, and  contrary  to  the  correct  principles  of  nomenclature  and 
arrangement.-  An  effect  of  precisely  the  same  kind,  and  arising  from 
the  same  cause,  ought  not  to  be  placed  in  two  different  categories, 
merely  as  there  does  or  docs  not  exist  another  cause  preponderating 
over  it." 

§  G.  We  have  now  to  consider  according  to  what  method  these 
complex  effects,  compounded  of  the  effects  of  many  causes,  are  to  be 
studied  ;  how  we  are  enabled  to  trace  each  eflect  to  the  concurrence 
of  causes  in  which  it  originated,  and  ascertain  the  conditions  of  its 
recurrence,  the  circumstances  in  which  it  may  be  expected  again  to 
occur.  The  conditions  of  a  phenomenon  \vhich  arises  from  a  com- 
position of  causes,  may  be  investigated '.  either  deductively  or  experi- 
mentally. 

The  case,  it  is  evident,  is  naturally  susceptible  of  the  deductive 
mode  of  investigation.  The  law  of  an  effect  of  this  description  is  a 
result  of  the  laws  of  the  separate  causes  on  the  combination  of  which 
it  depends,  and  is  therefore  in  itself  capable  of  being  deduced  from 
these  laws.  This  is  called  the  method  a  priori.  The  other,  or  a 
vosteriori  method,  professes  to  proceed  according  to  the  canons  of 


•260  INDUCTION. 

experimental  inquiry.  Considering  the  whole  assemblage  of  con- 
cun-ent  causes  which  produced  the  phenomenon,  as  one  single  cause, 
it  attempts  to  ascertain  that  cause  in  the  ordinary  manner,  by  a  com- 
parison of  instances.  This  second  method  subdivides  itself  into  two 
different  varieties.  If  it  merely  collates  instances  of  the  effect,  it  is  a 
method  of  pure  observation.  If  it  operates  upon  the  causes,  and  tries 
different  combinations  of  them  in  hopes  of  ultimately  hitting  the 
precise  combination  which  will  produce  the  given  total  effect,  it  is  a 
noiethod  of  experiment. 

In  order  more  completely  to  clear  up  the  nature  of  each  of  these 
three  methods,  and  determine  which  of  them  deserves  the  preference, 
it  will  be  expedient  (conformably  to  a  favorite  maxim  of  Lord  Chan- 
cellor Eldon,  to  which,  though  it  has  often  incurred  philosophical 
ridicule,  a  deeper  philosophy  will  not  refuse  its  sanction),  to  "clothe 
them  in  circumstances."  We  shall  select  for  this  purpose  a  case 
which  a,s  yet  furnishes  no  very  brilliant  example  of  the  success  of  any 
of  the  three  methods,  but  which  is  all  the  more  suited  to  illustrate  the 
difficulties  inherent  in  them.  Let  the  subject  of  inquiry  be,  the  condi- 
tions of  health  and  disease  in  the  human  body ;  or  (for  greater  simpli- 
city), the  conditions  of  recovery  fi-om  a  given  disease  ;  and  in  order 
to  nan-ow  the  question  still  more,  let  it  be  limited,  in  the  first  instance, 
to  this  one  inquiry:  Is,  or  is  not  some  particular  medicament  (mer- 
cury, for  instance),  a  remedy  for  that  disease. 

Now,  the  deductive  method  would  set  out  from  known  properties 
of  mercury,  and  known  laws  of  the  human  body,  and  by  reasoning 
from  these,  would  attempt  to  discover  whether  mercury  will  act  upon 
the  body  when  in  the  morbid  condition  supposed,  in  such  a  manner  as 
to  restore  health.  The  experimental  method  would  simply  administer 
mercury  in  as  many  cases  as  possible,  noting  the  age,,  sex,  tempera- 
ment, and  other  peculiarities  of  bodily  constitution,  the  particular  form 
or  variety  of  the  disease,  the  particular  stage  of  its  progi'css,  &c.,  re- 
marking in  which  of  these  cases  it  produced  a  salutary  effect,  and  with 
what  circumstances  it  was  on  those  occasions  combined.  The  method 
of  simple  observation  would  compare  instances  of  recovery,  to  find 
whether  they  agreed  in  having  been  preceded  by  the  administration  of 
mercury;  or  would  compare  instances  of  recovery  with  instances  of 
failure,  to  find  cases  which,  agreeing  in  all  other  respects,  differed  only 
in  the  fact  that  mercury  had  been  administered,  or  that  it  h^d  hot. 

§  7.  That  the  last  of  these  three  modes  of  investigation  is  applicable 
to  the  case,  no  one  has  ever  seriously  contended.  No  conclusions  of' 
value,  on  a  subject  of  such  intricacy,  ever  were  obtained  in  that  way. 
The  utmost  that  could  result  would  be  a  vague  general  impression  for 
or  against  the  efficacy  of  mercury,  of  no  real  avail  for  guidance  unless 
confirmed  by  one  of  the  other  two  methods.  Not  that  the  results, 
which  this  method  strives  to  obtain,  would  not  be  of  the  utmost  possi- 
ble value  if  they  could  be  obtained.  If  all  the  cases  of  recovery  which 
presented  themselves,  in  an  examination  extending  to  a  great  number 
of  instances,  were  cases  in  which  mercury  had  been  administered,  we 
might  generalize  with  confidence  from  this  experience,  and  should 
have  obtained  a  conclusion  of  real  value.  But  no  such  basis  for  gene- 
ralization can  we,  in  a  case  of  this  desci'iption,  hope  to  obtain.  The 
reason  is  that  which  we  have  so  often  spoken  of  as  constituting  the 


INTERMIXTURE    OF    EFFECTS.  261 

characteristic  imperfection  of  the  Method  of  Agreement ;  Plurality  of 
Causes.  Supposing  even  that  mercury  does  tend  to  cure  the  disease, 
so  many  other  causes,  both  natural  and  artificial,  also  teqd  to  cure  it, 
that  there  are  sure  to  be  abundant  instances  of  recovery  in  which 
mercury  lias  not  been  administered  :  unless,  indeed,  the  practice  be  to 
administer  it  in  all  cases;  on  which  supposition  it  will  equally  be 
found   in   the   cases  of  iuilure. 

When  an  effect  results  from  the  union  of  many  causes,  the  Bhare 
which  each  has  in  the  determination  of  the  •effect  cannot  in  general  be 
great :  and  the  effect  is  not  likely,  even  in  its  presence  or  absence, 
still  less  in  its  variations,  to  follow  very  exactly  any  onp.  of  the  causes. 
Recovery  from  a  disease  is  an  event  to  which,  in  every  case,  many  inffu- 
ences  must  concur.  Mercury  may  be  one  such  influence  ;  but,  from 
the  Very  fact  t^iat  there  are  many  other  such,  it  will- necessarily  happen 
that  although  mercury  is  administered,  the  patient,  for  want  of  other 
concurring  influences,  will  oft(>n  not  recover,  and  that  he  often  will 
recover  when  it  is  not  administcu'ed,  the  other  favorable  influences 
being  sufficiently  powerful  v/ithout  it.  Neither,  therefore,  will  the 
instances  of  recovery  agree  in  the  adtainistration  of  mercury,  nor  will 
the  instances  of  failure  agree  in  the  non-administration  of  it.  It  is 
much  if,  by  multijilied  and  accurate  returns  from  hospitals  and  the  like, 
we  can  collect  that  there  are  rather  more  recoveries  and  rather  fewer 
failures  when  mercury  is  administered  than  when  it  is  not ;  a  result  of 
very  secondary  value  even  as  a  guide  to  practice,  and  almost  worthless 
as  a  contribution  to  the  tlueory  of  the  subject. 

§  8.  The  inapplicability  of  the  m.ethod  of  simple  observation  to 
ascertain  the  conditions  of  effects  dependent  on  many  concurring  causes, 
being  thus  recognized  ;  we  .shall  next  hiquire  whether  any  greater 
benefit  can  bo  expected  from  the  other  branch  of  the  a  posteriori 
method,  that  which  proceeds  by  directly  trying  different  combinations 
of  causes,  either  artificially  produced  or  found  in  nature,  and  taking 
notice  what  is  their  qffect :  as,  for  example,  by  actually  trying  the  effect 
of  ^mercury,  in  as  many  different  circumstances  as  possible.  This 
method  differs  from  the  one  which  we  have  just  examined,  in  turning 
our  attention  directly  to  the  causes  or  agents,  instead  of  turning  it  to 
the  effect,  recovery  fi-om  the  disease.  And  since,  as  a  general  rule, 
the  effects  of  causes  are  far  more  accessible  to  our  study  than  the  causes 
of  effects,  it  is  natural  to  think  that  this  method  may  be  successful 
although  the  former  must  necessarily  fail. 

The  method  now  under  consideration  is  called  the  Empirical  Method ; 
and  in  order  to  estimate  it  fairly,  we  must  suppose  it  to  be  completely, 
not  incompletely,  empirical.  We  must  exclude  from  it  (sverything 
which  partakes  of  the  nature  not  of  an  experimental  but  of  a  deductive 
operation.  If  for  instance  we  try  experiments  with  mercury  upon  a 
person  in  health,  in  order  to  as(jcrtain  the  general  laws  of  its-  action 
upon  the  human  body,  an<l  then  reason  from  these  laws  to  determine 
how  it  will  act  upon  persons  afft-ctod  with  a  particular  disease,  this 
may  be  a  really  effectual  method,  but  this  is  Reduction.  The  experi- 
mental method  does  not  derive  the  law  of  a  complex  case  from  the 
simpler  laws  which  conspire  to  produce  it,  but  makes  its  experiments 
directly  upon  the  complex  case.  Wo  must  make  entire  abstraction  of 
all  knowledge  of  the  simpler  tendencies,  the  modi  oj)erandi  of  mercury 


262  INDUCTION. 

in  de.tail ;  our  experimentation  must  aim  at  obtaining  a  direct  answer 
to  the  specific  question,  Does  or  does  not  mercuiy  tend  to  cure  the 
particular  disease  1      '      ■ 

Let  us  see,  therefore,  how  far  this  case  admits  of  the  ohsen-ance  of 
those  rules  of  experimentation,  which  it  is  found  necessary  to  observe 
"in  other  (iases.  When  we  devise  an  experiment  to  ascertain  the  effect 
of  a  given  agent,  there  are  certain  precautions  which  we  never,  if  we 
can  help  it,  omit.  In  the  first  place,  we  introduce  the  agent  into  the 
midst  of  a  set  of  circumstances  which  we  have  exactly  ascertained.  It 
needs  hardly  be  remarked  how  far  this  condition  is  from  being  realized 
in  any  case  connected' with  the  phenomena  of  life  ;  how  far  we  are 
fi-om  knowing  what  are  all  the  citcumstances  which  preexist  in  any 
instance  in  which  mercury  is  administered  to  a  living  being.  This 
difficulty,  however,  though  insuperable  in  most  cases,  may.  not  be  so 
in' all ;  there  are  sometimes  (though  I  should  think  never  in  physiology) 
concurrences  of  many  causes,  in  which  we  yet  know  accurately  what 
the  causes  are.  But  when  w;e  have  got  clear  of  this  obstacle  we  en- 
counter another  still  more  serious.  In  other  cases,  when  we  intend  to 
try  an  experiment,  we  do  not  reckon  it  enovigh  that  there  be  no  cir- 
cumstance in  the  case,  the  presence  of  which  is  unknown  to  us.  We 
require  also  that  none  of  the  ciixumstances  which  we  do  know  of,  shall 
have  effects  susceptible  of  being  confounded  with  those  of  the  agent 
whose  properties  we  wish  to  study.  We  take  the  utmost  pains  to 
exclude  all  causes  capable  of  composition  with  the  given  cause  ;  or  if 
forced  to  let  in  any  such  causes,  we  take  care  to  make  them  such,  thdt 
we  can  compute  and  allow  for  their  influence,  so  that  the  effect  of  the 
given  cause  may,  after  the  subduction  of  those  other  effects,  be  appa- 
rent as  a  residual  phenomenon, 

These  precautions  are  inapplicable  to  such  cases  as  we  are  now  con- 
sidering. The  mercury  of  our  experiment  being  tried  with  an  unknown 
multitude  (or  even  let  it  be  a  known  multitude)  of  other  influencing 
circumstances,  the  mere  fact  of  their  being  influencing  circumstances 
implies  that  they  disguise  the  effect  of  the  mercury,  and  preclude  us 
from  knowing  whether  it  has  any  effect  or  no.  Unless  we  already  knew 
what  and  how  much  is  owing  to  every  other  circumstance  (that  is,  un- 
less we  suppose  the  very  problem  solved  which  we  are  considering  the 
means  of  solving),  we  cannot  tell  that  those  other  circumstances  may 
not  have  produced  the  whole  of  the  effect,  independently  or  even  in 
spite  of  the  mercury.  The  Method  of  Difference,  in  the  ordinary  mode 
of  its  use,  namely,  by  comparing  the  state  of  things  following  the  ex- 
periment with  the  state  which  preceded  it,  is  thus,  in  the  case  of  inter- 
mixture of  effects,  entirely  unavailing ;  because  other  causes  than  that 
whose  effect  we  are  seeking  to  determine,  have  been  operating  during 
the  transition.  As  for  the  other  mode  of  employing  the  Method  of 
Difference,  namely,  by  comparing,  not  the  same  case  at  two  different 
periods,  but  different  cases,  this  in  the  present  instance  is  quite  chi- 
merical. In  phenomena  so  compliccfted  it  is  questionable  if  two  cases 
similar  in  all  respects  but  one  ever  occuiTed  ;  and  were  they  to  occur, 
we  could  not  possibly  know  that  they  were  so  exactly  similar. 

Anything  like  a  scientific  use  of  the  method  of  experiment,  in  these 
complicated  cases,  is  therefore  out  of  the  question.  We  can  in  the 
most  favorable  cases  only  discover,  by  a  succession  of  trials,  that  a  cer- 
tain cause  is  very  often  followed  by  a  certain  effect.     For,  in  one  of 


INTERMIXTURE    OF    EFFECTS.  2G3 

these  conjunct  effects,  the  portion  which  is  dctcrmiucJ  by  any  one  of 
the  influencing  agents,  is  generally,  as  we  before  remarked,  but  small; 
and  it  must  be  a  more  potent  cause-  than  most,  if  even  the  tendency 
whicli  it  really  exerts  is  nut  tluvarted  by  other  tendencies  in  nearly  as 
many  cases  as  it  is  fulfilled. 

If  so  littlb  can  be  done  by  the  experimental  nietliod  to  dotermine  the 
conditions  oi'  an  effect  of  many  combined  causes,  in  the  case  of  medical 
science,  still  less  is  this  method  applicable  to  a  class  of  phenomena 
more  complicated  than  even  tliosc  of  pliy.siology,  the  phenomena  of 
politics^nd  iiistory.  There,  Plurality  of  Causes  exists  ui  almost  bound- 
less excess,  and  the  effects  are,  for  the  most  part,  inextricably  inter- 
woven with  one  another.  To  adct  to  the  embariassmeut,  most  of  the 
inquiries  in  political  science  relate  to  the  ])ro(luction  of  effects  of  a 
most  compreliensive  description,  such  as  the  jjublic  wealth,  public 
security,  j'l^iblic  morality,  and  the  like:  results, liable  to  be  affected 
directly  or  indirectly  either  in  jjIus  or  in  mitius  by  nearly  every  fact 
which  exists,  or  event  which  occurs,  in  human  society.  The  vulgar 
notion,  that  the  safe  methods  on  poUtical  subjects  are  those  of  Baconian 
induction,  that  the  true  guide  is  not  general  reasoning  but  specific 
experience,  will  one  day  be  quoted  as  among  the  most  unecjui vocal 
marks  of  a  low  state  of  the  speculative  faculties  in  any  age  in  which  it 
is  accredited.  What  can  be  more  ludicrous  than  the  sort  of  parodies 
on  experimental  reasoning  which  one  is  accustomed  to  meet  with,  not 
in  popular  discussion  only,  but  in  grave  treatises  when  the  affairs  of 
nations  are  the  theme.  "  How,"  it  is  asked,  "  can  an  institution  be 
bad,  when  the  country  has  prospered  under  it '{"  "  How  c&,n  such  or 
such  causes,  have  contributed  to  the  prosperity  of  one  country,  when 
another  has  prospered  without  them  V  Whoever  makes  use  of  an 
argument  of  this  kind,  not  intending  to  deceive,  should  be  sent  back 
to  learn  the  elements  of  some  one  of  the  n>ore  easy  physical  sciences. 
Such  rensoners  ignore  the  fact  of  Plurality  of  Causes  in  the  very  case 
which  aff'ords  the  most  signal  eiiample  of  it.  So  little  could  be  con- 
cluded, in  such  a  case,  from  any  possible  collation  of  individual  instances, 
that  even  the  impossibility,  in  social  phenomena,  of  making  artificial 
experiments,  a  circumstance  otherwise  so  prejudicial  to  directly  induc- 
tive inquiry,  hardly  affords,  in  this  case,  additional  reason  of  regret. 
For  even  if  we  could  try  experiments  upon  a  nation,  or  upon  the 
human  race,  with  as  little  scruple  as  M.  Majendie  tries  them  upon  dogs 
or  rabbits,  we  should  never  succeed  in  making  two  instances  identical 
in  every  respect  except  the  presence  or  absence  of  some  one  definite 
circumstance.  The  nearest  approach  to  an  experiment,  in  the  philo- 
soj)hical  sense,  which  takes  place  in  politics,  is  the  introduction  of  a 
new  operative  element  into  national  affairs  by  some  special  and  assign- 
able measure  of  government,  such  as  the  enactment  or  repeal  of  a 
particular  law.  But,  where  there  are  S(j  m^ny  influences  at  wol-k,  it 
requires  some  time  for  the  influence  of  any  new  cause  upon  national 
phenomena  to  become  apparent ;  and  as  the  causes  operating  in  so 
extensive  a  sphere  are  not  only  infinitely  numerous,  but  in  a  state  of 
perpetual  alteration,  it  is  always  certain  that  Ix^fore  the  cjffect  of  a  new 
cause  becomes  conspicuous  enough  to  bo  a  subject  of  induction,  so 
many  of  the  other  influencing  circumstance^  will  have  changed  as  to 
vitiate  the  experiment. 

Two,  therefore,  of  the  three  possible  methods  for  the  study  of  phe- 


264  INDUCTION. 

notnena  resulting  from  the  composition  of  many  causes,  being  from  the 
very  nature  of  the  case,  inefficient  and  ilkisory ;  there  remains  only 
the  third — that  which  considers  the  causes  separately,  atid  computes 
the  effect  from  the  balance  of ^  the  different  tendencies  which  produce 
it :  in  short,  the  deductive,  or  a  priori  method.  The  more  particular 
consideration  of  this  intellectual  process  requires  a  chapter  to  it8el£ 


CHAPTER  XI. 

OF  THE  DEDUCTIVE   METHOD. 


§  1.  The  mode  of  investigation  which,  from  the  proved  inapplicability 
of  direct  methods  of  observation  ahd  experiment,  remains  to  us  as  the 
mahi  source  of  the  knowledge  we  possess,  or  can  acquire,  respecting 
the  conditions,  and  laws  of  recuiTence,  of  the  more  complex  phenom- 
ena, is  called  in  its  most  general  expression,  the  Deductive  Method; 
and  consists  of  three  operations  :  the  first,  one  of  direct  induction  ;  the 
second,  of  ratiocination  ;  and  the  third,  of  verification. 

I  call  the  first  step  in  the  process  an, inductive  operation,  because 
there  must  be  a  direct  induction  as  the  basis  of  the  whole  ;  although 
in  many  particular  investigations  the  place  of  the  induction  may  be 
supplied  by  a  prior  deduction ;  but  the  premisses  of  this  prior  deduc- 
tion must  have  been  derived  from  induction. 

The  problem  of  the  Deductive  Method  is,  to  find  the  law  of  an  effect 
from  the  laws  of  the  different  tendencies  of  which  it  is  the  joint  result. 
The  first  requisite,  therefore,  is  to  know  the  laws  of  those  tendencies ; 
the  law  of  each  of  the  concurrent  causes  :  and  this  supposes  a  previous' 
process  of  observation  or  experiment  upon  each  cause  separately ;  or 
else  a  previous  deduction,  which  also  must  depend  for  its  ultimate 
premisses  upon  observation  or  experiment.  Thus,  if  the  subject  be 
social,  or  historical  phenomena,  the  premisses  of  the  Deductive  Method 
must  be  the  laws  of  the  causes  which  determine  that  class  of  phenom- 
ena ;  and  those  causes  are  human  actions,  together  with  the  general 
outward  circumstances  under  the  dominion  of  which  mankind  are 
placed,  and  which  constitute  man's  position  in  this,  world.  The -De- 
ductive Method,  applied  to  social  phenomena,  must  begin,  therefore, 
by  investigating,  or  must  suppose  to  have  been  already  investigated, 
the  laws  of  human  action,  and  those  properties  of  outward  things  by 
which  the  actions  of  human  beings  in  society  are  determined.  Some 
of  these  general  truths  will  naturally  be  obtained  by  observation  and 
experiment,  others  by  deduction :  the  more  complex  laws  of  human 
action,  for  example,  may  be  deduced  from  the  simpler  ones ;  but  the 
simple  or  elementary  laws  will  a,lways,  and  necessarily  have  been  ob- 
tained by  a  directly  inductive  process. 

To  ascertain,  then,  the  laws  of  each  separate  cause  which  takes  a 
share  in  producing  the  effect,  is  the  first  desideratum  of  the  Deductive 
Method.  To  know  what  the  causes  are,  which  must  be  subjected  te 
this  process  of  study,  may  or  may  not  be  difficult.  In  the  case  last 
mentioned,  this  first  condition  is  of  easy  fulfilment.  That  social  ph&. 
nomena  depended  upon  the  acts  and  mental  impressions  of  humaij 


THE    DEDUCTIVE    METHOD,  2G5 

beings,  never  could  have  been  a  matter  of  any  doubt,  however  imper- 
fe<'tly  it  may  have  been  known  either  by  what  laWs  those  impressions 
and  actions  are  governed,  or  to  what  social  consi;quences  their  laws 
naturally  lead.  Neither,  again,  after  physical  science  had  attained  a 
certain  development,  coidd  there  be  any  real  doubt  where  to  look  for 
the  laws  on  which  the  phenomena  of  life  dejiend,  since  they  must  be 
the  mechanical  and  chemical  laws  of  the  solid  and  fluid  sul>stances 
composing  the  orgaiiized  body  and  the  medium  in  which  it  subsists, 
together  with  the  peculiar  vital  laws  of  the  diflcrent  tissues  constituting 
the  organic  structure.  In  other  cases,  really  ftir  more  simple  than 
these,  it  was  much  less. obvious  in  what  quarter  the  causes  were  to  be 
lookfd  for :  as  in  the  great  case  of  the  celestial  phenomena.  Until, 
by  comi)ining  the  laws  of  certain  causes,  it  ^vtl3  found  that  those  laws 
explained  all  the  facts  which  experience  had  proved  concerning  the 
heavenly  motions,,  and  led  to  predictions  which  it  always  verified, 
mankind  never  knew  that  those  7ccrc  the  causes.  But  whether  we 
are  able  to  put  the  question  before  or  not  until  after  we  have  become 
capable  of  answering  it,  in  either  case  it  must  be  answered  ;  the  laws 
of  the  different  causes  must  be  ascertained,  before  we  can  proceed  to 
deduce  from  them  tjic  conditions  of  the  effect. 

The  mode  of  ascertaining  these  laws  neither  is,  nor  can  be,  any 
other  than  the  fourfold  method  of  experimental  inquiry,  already  dis- 
cussed. A  few  remarks  on  the  application  of  that  method  to  cases  of 
the  Composition  of  Causes,  are  all  that  is  requisite. 

It  is  obvious  that  we  cannot  expect  to  find  the  law  of  a  tendency, 
by  an  induction  from  cases  in  which  the  tendency  is  counteracted. 
The  laws  of  motion  could  never  have  been  brought  to  light  from  the 
observation  of  bodies  kept  at  rest  by  the  equilibrium  of  opposing 
fotces.  Even  where  the  tendency  is  not,  in  the  ordinary  sense  of  the 
word,  counteracted,  but  only  modified,  by  having  its  effects  comjiounded 
with  the  effects  arising  from  some  other  tendency  or  tendencies,  we 
are  still  in  an  imfavorable  position  for  tracing  by  means  of  such  cases, 
the  law -of  the  tendency  itself  It  would  have  been  difficult  to  dis- 
cover the  law  that  every  body  in  motion  tends  to  continue  moving  in  a 
straight  line,  by  an  induction  from  instances  in  which  the  motion  is 
deflected  into  a  curve,  by  being  compounded  with  the  effect  of  an 
accelerating  force.  Notwithstanding  the  resources  aftbrded  in  this 
description  of  cases  by  the  Method  of  Concomitant  Variations,  the 
principles  of  a  judicious  experimentation  prescribe  that  the  law  of  each 
of  the  tendencies  should  be  studied,  if  possible,  in  cases  in  which  that 
tendency  operates  alone,  or  in  combination  with  no  agencies  but  those 
of  which  the  effect  can,  from  previous  knowledge,  be  calculated  and 
allowed  fbr. 

AccordinglyT^n  the  cases,  unhappily  very  numerous  and  important, 
in  which  the  caiises  do  not  suffin-  themselves  to  be  separated  and 
observed  apart,  there  is  much  difficulty  in  laying  down,  with  due 
certainty,  the  inductive  foundation  necessary  to  support  the  deductive 
method.  This  difficulty  is  most  conspicuous  in  the  case  of  physiological 
phenomena ;  it  being  impossible  to  separate  the  different  agencies 
which  collectively  compose  an  organized  body,  without  destroying  the 
very  phenomena  which  it  is  our  object  to  investigate : 

following  life,  in  creatures  we  dissect, 

We  lose  it,  in  the  nioment  we  detect. 


266  INDUCTION. 

And  for  this  reason  I  am  not  quite  prepared  to  agree  with  M.Cornte, 
in  deeming  the  scienpe  of  society  and  government  intrinsically  a  more 
difficult  study  than  the  science  of  organic  and  animal  life.  I  cannot 
but  incline  to  the  opinion,  that  physiology  is  embarrassed  by  gi-eater 
natural  difficulties,  and  is  probably  susceptible  of  a  less  degree  of 
ultimate  perfectipn,  than  the  social  science;  'inasmuch  as  it  is  possible 
to  study  the  laws  of  one  man's  mind  and  actions  apart  from  otlier  men, 
much  less  imperfectly  than  we  can  study  the  laws  of  one  organ  or 
tissue  df  the  human  body  apart  from  the  other  organs  or  tissues. 

It  is  profoundly  remarked  by  M.  Comte,  that  pathological  facts,  or, 
to  speak  in  common  language,  diseases  in  their  different  forms  and 
degrees,  afford  in  the  case,  of  physiological  investigation  the  nearest 
equivalent  to  experimentatipn  properly  so  called;  inasmuch  as  they 
often  exhibit  to  us  a  definite  disturbance  in  some  one  organ  or  organic 
function,  the  remaining  organs  and  functions  being,  in  the  first  instance 
at  least,  unaffected.  It  is  true  that  from  the  perpetual  actions  and 
reactions  which  are  going  on  among  all  the  parts  of  the  organic 
economy,  there  can  be  no  prolonged  disturbance  in  any  one  fimction 
without  ultimately  involving  many  of  the  others ;  and  when  once  it  has 
done'  so,  the  experirnent  for  the  most  part  loses  its  scientific  value.  All 
■depends  upon  observing  the  early  stages  of  the  derangement;  which, 
unfortunately,  are  of  necessity  the  least  marked,  Ifj  however,  the 
organs  and  functions  not  disturbed  in  the  first  instance,  become  affected 
in  a  fixed  order  of  succession,  some  light  is  thereby  thrown  upon  the 
action  which  one  organ  exercises  over  another ;  and  we  occasionally 
obtain  a  series  of  effects,  which  we  can  refer  with  some  confidence  to 
the  original  local  derangement ;  but  for  this  it  is  necessary  that  we 
should  know  that  the  original  derangement  tvas  local.  -  If  it  was  what 
is  termed  constitutional,  that  is,  if  we  do  not  know  in  what  part  of  the 
animal  economy  it  took  its  rise,  or  the  precise  nature  of  the  disturbance 
which  took  place  in  that  part,  we  are  unable  to  determine  wliich  of  the 
various  derangements  was  cause  and  which  effect;  which  of  them 
were  produced  by  one  another,  and  which  by  the  direct,  though 
perhaps  tardy,  action  of  the  original  Qause. 

Besides  natural  pathological  facts,  we  can  produce  pathological  facts 
artificially ;  we  can  try  experiments,  even  in  the  popular  sense  of  the 
term,  by  subjecting  the  living,  being  to  some  external  agent,  such  as 
the  mercury  of  our  former  example.  As  this  experimentation  is  not 
intended  to  obtain  a  direct  solution  of  any  practical  question,  but  to 
discover  general  laws,  from  which  afterwards  the  conditions  of  any 
particular  effect  may  be  obtained  by  deduction  ;  the  best  cases  to  select 
are  those  of  which  the  circumstances  can  be  best  ascertained  :  and 
such  are  generally  not  those  in  which  there  is  any  practical  object  in 
view.  The  exjjeriments  are  best  tried,  not  in  a  state  iSf  disease,  which 
is  essentially  a  changeable  state,  but  in  the  condition  of.  health,  coxa- 
paratively  a  fixed  state.  In  the  one,  unusual  agencies  are  at  work, 
the  results  of  which  we  have  no  means  of  predicting ;  in  the  otlier, 
the  course  of  the  accustomed  physiological  phenomena  would,  it  may 
generally  be  presumed,  remain  undisturbed,  were  it  not  for  the  dis- 
turbing cause  vvhich  we  introduce. 

Such,  with  the  occasional  aid  of  the  method  of  Concomitant  Varia- 
tions (the  latter  not  less  encumbered  than  the  more  elementary 
methods,  by  the  peculiar  difficulties  of  the  subject),  are  our  indue- 


THE    DEDUCTIVE    METHOD.  207 

live,  resources  for  ascertaiuing  the  laws  of  the  causes  considered  sepa- 
rately, when  we  have  it  not  in  our  power  to  make  trial  of  them  in  a 
state  of  actual  separation.  The  insufficiency  of  these  resources  is  so 
glaring  that  no  one  can  be  surprised  at  the  backward- state  of  the 
science  of  physiology  ;  in  which  indeed  our  knowledge  of  causes  is  so 
imperfect,  that  we  can  neither  ex])lain,  nor  could,  without  specilic 
experience,  have  predicted  many  of  the  facts  which  are  certified  to  us 
by  the  most  ordinary  observation.  Fortunately,  wc  are  much  better 
informed  as  to  the  empirical  laws  of  the  phenomena,  that  is,  the 
unifonnities  respecting  which  we  cannot  yet  decide  whether  they  are 
■^cases  of  causation  or  mere  results  of  it.  Not  oidy  has  the  order  iij 
■which  the  facts  of  organization  and  life  successively  manifest  them- 
selves, from  the  first  genu  of  existence  to  death,  been  found  to  be  uni- 
foiTn,  and  veiy  accurately  ascertainable ;  but,  moreover,  by  a  great 
application  of  the  Method  of  Concomitant  Variations  to  the  entire 
facts  of  comparative  anatomy  and  physiology,  the  conditions  of  or- 
ganic structure  corresponding  to  each  class  of  functions  have  been 
determined  with  considerable  precisiori.*  Whether  these  organic 
conditions  are  the  whole  of  the  conditions,  and  whether  they  be  con- 
ditions at  all,  or  mere  collateral  effects  of  some  common  cause,  we  are 
quite  ignorant :  nor  are  we  ever  likely  to  know,  unless  we  could  con- 
struct an  organized  body,  and  Irj  whether  it  would  live. 

Under  §uch  disadvantages  do  we,  in  cases  of  this  description,  at- 
tempt the  initial,  or  inductive  step,  in  the  application  of  the  Deductive 
Method  to  complex  phenomena.  But  such,  fortunately,  is  not  the 
common^  case.  In  general,  the  laws  of  the  causes  on  which  the  effect 
depends  may  be  obtained  by  an  induction  from  comparatively  simple 
instances,  or,  at  the  worst,  by  deduction  from  the  laws  of  simpler 
causes  so  obtained.  By  simple  instances  are  meant,  of  course,  those 
in  which  the  action  of  each  calise  was  not  intermixed  or  interfered 
with,  or  not  to  any  gieat  extent,  by  other  causes  whose  laws  wcie 
unknown.  And  only  when  the  induction  which  furnished  the  prem- 
isses to  the  Deductive  Method  rested  upon  such  instances,  has  the 
application  of  such  a  method  to  the  ascertainment  of  the  laws  of  a 
complex  effect,  been  attended  with  brilliant  results. 

§  2.  ^Vhen  the  lavvs  of  the  causes  have  been  -ascertained,  and  the 
first  stage  of  the  gi-eat  logical  operation  now  under  discussion  satis- 
factorily accompKshcd,  the  second  parj,  follows;  that  of  determining, 
from  the  laws  of  the  causes,  what  eflect  any  given  combination  of  those 
causes  will  prod'uce.  This  is  a  process  of  calculation,  in  the  wider 
sense  of  the  term  ;  and  very  often  involves  processes  of  calculation  in 
the  narrowest  sense.  It  is  a  ratiocination ;  and  when  our  knowledge 
of  the  causes  is  so  perfect,  as  to  extend  to  the  exact  numerical  laws 
which  they  observe  in  producing  their  effects,  the  ratiocination  may 
reckon  among  its  premisses  the  theorems  of  the  science  of  number,  in 
the  whole  immense  extent  of  that  science.  Not  only  are  the  highest 
truths  of  mathematics  often  required  to  enable  us  to  compute  an  effect, 
the  numerical  law  of  which  we  already  know  ;  but,  even  by  the  aid 
of  those  highest  truths,  we  can  go  but  a  little  way.  In  so  simple  a 
case  as  the  celebrated  problem  of  throe  bodies  gravitating  towards  one 

♦  This  great  philosophical  operation' has  been  admirably  characterized  in  the  third  vol- 
ume of  M.  Comte's  truly  encyclopedical  work. 


268  tNDUCTION. 

another,  witli  a  force  directly  as  their  mass  and  inversely  as  the  square 
of  the  distance,  all  the  resources  of  the  calculus  have  not  hitherto 
sufficed  to  obtain  anything  more  than  an  approximate  general  solution. 
In  a  case  a  little  more  complex,  but  still  one  of  the  simplest  w^hich 
arise  in  practice,  thajt  of  the  motion  of  a  projectile,  the  causes  which 
affect  tlie  velocity  and  range  (for  example)  of  a  cannon-ball  may  be  all 
known  and  estimated ;  the  force  of  the  gunpowder,  the  angle  of  eleva- 
tion, the  density  of  ..the  air,  the  strength  and  direction  of  the  sound; 
but  it  is  one  of  the  most  difficult  of  all  mathematical  problems  to 
combine  all  these,  so  as  to  determine  the  effect  resulting  from  their 
collective  action.  i 

Besides  the  theorems  of  nvimber,  those  of  geometry  also  come  in  as 
premisses,  where  the  effects  take  place  in  space,  and  involve  motion 
and' extension,  as  in  mechanics,  optics,  acoustics,  astronomy.  But 
when  the  complication  increases,  and  the  effects  are  under  the  influ- 
ence of  so  many  and  such  shifting  causes  as  to  give  no  room  either  for 
fijXed  numbers,  or  for  straight  lines  and  regular  curves,  as  -in  the  case 
of  .physiological,  to  say  nothing  of  mental  and  social  phenomena,  the 
laws  of  number  and  extension  are  applicable,  if  at  all,  only  on  that 
large  scale  on  which  precision  of  details  becomes  unimportant ;  and 
although  these  laws  play  a  conspicuous  part  in  the  most  striking 
examples  of  the  investigation  of  nature  by  the  Deductive  Method,  as 
for  example  in. the  Newtonian  theory  of  the  celestial  motions,  they  are 
by,  no  means  an  indispensable  part  of  every  such  process.  All  that  is 
essential  in  it  is  the  ratiocination  from  a  general  law  to  a  particular 
case,  that  is,  the  determination,  by  means  of  the  particular  circum- 
stances of  that  case,  what  result  is  required  in  that  instance  to  fulfill  the 
law.  Thus,  in  the  Torricellian  experiment,  if  the  fact  that  air  had 
weight  had  been  previously  kno^yn,  it  would  have  been  easy,  without 
any  numerical  data,  to  deduce  from  the  general  law  of  equilibrium, 
that  the  .mercury  W^ould  stand  in  the  tube  at  such  a'height  that  the 
column  of  mercury  would  exactly  balance  a  column  of  the  atmosphere 
of  equal  diameter;  because  otherwise,  eqiiilibrium  would  not  exist. 

-By  such  ratiocinations  from  the  separate  laws  of  the  causes,  we  may, 
to  a  certain  extent,  succeed  in  answering  either  of  the  following  ques- 
tions:  Given  a  certain  combination  of  causes,  what  effect  will  follow] 
and,  What  combinatioTn  of  causes,  if  it  existed,  would  produce  a  given 
effect  ]  Tti  the  one  case,  we  determine  the  effect  to  be  exj>ected  in 
any  complex  circumstances  of  which  the  different  elements  are  known : 
in  the  other  case  we  learn,  according  to  what  law — -under  what  ante- 
cedent conditions — a  given  complex  effect  will  recur. 

§  3.  But  (it  may  here  be  asked)  are  not  the  same  arguments  by 
which  the -methods  of  direct  observation  and  experiment  were  set 
aside  as  illusory  when  applied  to  the  laws  of  complex  phenomena, 
applicable  with  equal  force  against  the  Method  of  Deduction  1  When 
in  every  single  instance  a  multitude,  often  an  unknown  multitude,  of 
ag'encies,  are  clashing  and  combining,  what  security  have  we  that  in 
our  computation  a  priori  we  have  taken  all  these  into  our  reckoning  ? 
How  many  must  we  not  generally  be  ignorant  of?  Among  those 
which  we  know,  how  probable  that  some  have  been  overlooked ;  and 
even  were  all  included,  how  vain  the  pretence  of  summing  up  the 
effects  of  many  causes,  unless  we  know  accurately  the  numerical  law 


THE  DEDUCTIVE  METHOD.  269 

of  each, — a  condition  in  most  cases  not  to  be  fulfilled  ;  and  even  when 
fulfilled,  to  niaki;  the  calculation  transcends,  in  any  but  very  simple 
cases,  the  utmost  power  of  mathematical  science  with  its  most  modem 
improvements. 

lliese  objections  truly  have  much  weight,  and  would  be  altogether 
unansweiable,  if  there  were  no  test  by  which,  when  we  employ  the 
Deductive  Metlunl,  we  might  judge  whether  an  error  of  any  of  the 
abt)ve  di'scriptious  had  been  committed  or  no.  Such  a  test,  however, 
there  is:  and  its  application  forms,  under  the  name  of  Verification, 
the  third  essential  component  part  of  the  Deductive  Method ;  without 
which  all  the  results  it  can  give  have  little  other  value  than  that  of 
guess-work.  To  warrant  reliance  upon  the  general  conclusions  arrived 
at  by'  deduction,  these  conclusions  must  be  found,  on  a  careful  com- 
parison, to  accord  with  the  results  of  direct  observation  wherever  it 
can  be  had.  If,  when  we  have  experience  to  compare  with  them,  this 
experience  confirms  them,  we  may  safely  ti-ust  to  them  in  other  cases 
of  which  our  specific  experience  is  yet  to  come.  But  if  our  deductions 
have  led  to  the  conclusion  that  from  a  particular  combination  of  causes 
a  given  effect  would  result,  then  in  all  known  cases  where  that  combi- 
nation can  be  shown  to  have  existed,  and  where  the  effect  has  not 
followed,  we  must  be  able  to  show  (or  at  least  to  make  a  probable 
surmise)  what  frustrated  it :  if  we  cannot,  the  theory  is  imperfect,  and 
not  yet  to  be  relied  upon.  Nor  is  the  verification  complete,  unless 
some  of  the  cases  in  which  the  theory  is  borne  out  by  the  observed 
result,  are  of  at  least  equal  complexity  with  any  other  cases  in  which 
its  application  could  be  called  for. 

It  needs  scarcely  be  observed,  that  if  direct  observation  and  collation 
of  instances  have  furnished  us  with  any  empirical  laws  of  the  effect, 
whether  true  in  all  observed  cases  or  only  true  for  the  most  part,  the 
most  effectual  verification  of  which  the  theory  could  be  susceptible 
would  be,  that  it  led  deductively  to  those  empirical  la^vs  :  that  the 
uniformities,  whether  complete  or  incomplete,  which,  were  observed  to 
exist  among  the  phenomena,  were  accounted  for  by  the  laws  of  the 
causes,  were  such  as  could  not  hut  c^\6t  if  those  be  really  the  causes 
by  which  the  phenomena  are  produced.  Thus  it  was  very  reasonably 
deemed  an  essential  requisite  of  any  true  theory  pf  the  causes  of  the 
celestial  motions,  that  it  should  lead  by  deduction  to  Kepler's  laws: 
which,  accordingly,  the  Newtcniian  theory  did. 

In  order,  therefore,  to  facilitate  the  verification  of  theories  obtained 
by  deduction,  it  is  important  that  as  many  as  possible  of  th^  empirical 
laws  of  the  phenomena  should  be  ascertained,  by  a  comparison  of  in- 
stances, conformably  to  the  Method  of  Agreement :  as  well  as  (it  must 
be  added)  that  the  phenomima  themselves  should  be.  described,  in  the 
most  comprehensive  as  well  as  accurate  manner  possible ;  by  collect- 
ing from  the  observation  of  parts,  the  simplest  possible  correct  expres- 
sion for  the  corresponding  wholes:  as  when  the  series  of  the  observed 
places  of  a  planet  was  first  expressed  by  a  system  of  epicycles,  and 
subsequently  by  an  ellipse. 

,  It  is  worth  remarking,  that  complex  instances  which  would  have 
been  of  no  use  for  the  discovery  of  the  simple  laws  into  which  we 
ultimately  analyze  their  phenomena,  nevertheless,  when  they  have 
served  to  verify  the  analysis,  become  additional  evidence  of  the  laws 
themselves.     Although  we  could  not  have  got  at  the  I3.W  from  com- 


270  INDUCTION. 

plex  cases,  still  when  the  law,  got  at  otherwise,  is  found  to  be  In 
accordance  with  the  result  of  a  complex  case,  that  case  becomes  a 
new  experiment  on  the  law,  and  helps  to  confirm  what  it  did  not 
assist  us  to  discover.  It  is  a  new  trial  of  the  principle  in  a  different 
set  of  circumstances ;  and  occasionally  serves  to  eliminate  some  cir- 
cumstance not  previously  excluded,  and  to  effect  the  exclusion  of 
which,  might  require  an  experiment  impossible  to  be  executed.  This 
was  strikingly  conspicuous  in  the  example  formei'ly  quoted,  in  which 
the  difference  between  the  observed  and  the  calculated  velocity  of 
sound  was  ascertained  to  result  from  the  heat  extricated  by  the  con- 
densation which  takes  place  in  each  sonorous  vibration.  This  was  a 
trial,  in  new  circumstances,  of  the  law  of  the  development  of  heat  by 
compression ;  and  it  certainly  added  materially  to  the  proof  of  the  uni- 
versality of  that  law.  Accordingly  any  law  of  nature  is  deemed  to 
have  gained  in  point  of  certainty,  by  being,  found  to  explain  some 
complex  case  which  had  not  previously  been  thought  of  in  connexion 
with  it ;  and  this  indeed  is  a  consideration  to  which  it  is  the  habit  of 
scientific  men  to  attach  rather  too  much  value  than  too  little. 

To  the  Dedvictive  Method,  thus  characterized  in  its  three  constituent 
parts.  Induction,  Ratiocination,  and  Verification,  the  human  mind  is 
indebted  for  its  most  glorious  triumphs  in  the  investigation  of  nature.. 
To  it  we  owe  all  the  theories  by  which  vast  and  complicated  phenomena 
are  embraced  under  a  iew  simple  laws,  which,  considered  as  the  laws, 
of  those  gz-eat  phenomena,  could  never  have  been  detected  by  their 
direct  study.  We  may  form  some  conception  of  what  the  method  has 
done  for  us,  from  the  case  of  the  celestial  motions ;  one  of  the  simplest 
among  the  greater  instances  of  the  Composition  of  Causes,  since  (ex- 
cept in  a  few  cases  not  of  primary  importance)  each  of  the  heavenly 
bodies  may  be  considered,  without  material  inaccuracy,  to  be  never  at 
one  time  influenced  by  the  attraction  of  more  than  two  bodies,  the 
sun  and  one  other  planet  or  satellite,  making,  with  the  reaction  of  the 
body  itself,  and  the  tangential  force,  only  four  different  agents  on  the 
concurrence  of  which  the  motion's  of  that  body  depend  ;  a  much  smaller 
number,  no  doubt,  than  that  by  which  any  other  of  the  gi'eat  phenom- 
ena of  nature  are  determined  or  modified.  Yet  how  could  we  ever 
ha,ve  ascertained  the  combination  of  forces  upon  which  the  motions  of 
the  earth  and  planets  are  dependent,  by  merely  comparing  the  orbits, 
or  velocities,  of  different  planets,  or  the  different  velocities  or  positions 
of  the  same  planet  ?  Notwithstanding  the  regularity  which  manifests 
itself  in  those  motions,  in  a  degree  so  rare  among  the  effects  of  a  con- 
currence of  causes  ;  although  the  periodical  recurrence  of  exactly  the 
same  effect,  affords  positive  proof  that  all  the  combinations  of  causes 
which  occin-  at  all,  recur  periodically ;  we  -should  never  have  known 
what  the  causes  were,  if  the  existence  of  agencies  precisely  similar  on 
our  own  earth  had  not,  fortunately,  brought  the  causes  themselves 
within  the  reach  of  experimentation  under  simple  circumstances.  As 
we  shall  have  occasion  to  analyze,  further  on,  this  great  example  of 
the  Method  of  Deduction,  we  shall  not  occupy  any  time  with  it  here, 
but  shall  proceed  to  that  secondary  application  of  the  Deductive 
Method,  the  result  of  which  is  not  to  prove  laws  of  phenomena  but 
to  explain  them. 


EXPLANATION    OP    LAWS.  271 


CHAPTER  XII. 

OF   THE    EXPLANATION   OF   LAWS  OF  NATUR6. 

§  1.  The  Jetluctive  operation,  by  which  we  derive  the  law  of  an  effect 
from  the  laws  of  the  causes  of  which  the  concurrence  gives  rise  to  it, 
may  he  undertaken  either  for  the  purpose  of  discovering  the  law,  or 
of  explaining  a  law  already  discovered.  The  word  es-planat'ion  occurs 
so  continually,  and  holds  so  important  a  place  in  philosophy,  that  a 
little  time  spent  in  fixing  the  meaning  of  it  will  he  profitably  em- 
ployed. 

An  individual  fact  is  said  to  be  explained,  by  pointing  out  its  cause, 
that  is,  by  stating  the  law  or  laws  of  causation,  of  which  its  production 
is  an  instance.  Thus,  a  conflagration  is  explained, -when  it  is  proved 
to  have  arisen  from  a  spark  falling  into  the  midst  of  aheap  of  combus- 
tibles. And  in  a  similar  manner,  a  law  or  uniforrnity  in  nature  is  said 
to  be  explained,  when  another  law  or  laws  are  pointed  out,  of  which 
that  law  itself  is  but  a  case,  and  from  which  it  could  be  deduced. 

§  2.  There  are  three  distinguishable  sets  of  circumstances  in  which 
a  law  of  acusation  may  be  explained  from,  or,  as  it  also  is  often  ex- 
pressed, resolved  into,  other  laws. 

The  first  is  the  case  already  so  fully  considered ;  an  intermixture  of 
laws,  producing  a  joint  effect  equal  to  the  sum  of  the  effects  of  the 
causes  taken  separately.  The  law  of  the  complex  effect  is  explained, 
by  being  resolved  into  the  separate  laws  of  the  causes  which  contribute 
to  it.  Thus,  the  law  of  the  motion  of  a  planet  is  resolved  into  the  law 
of  the  tangential  force,  which  tends  to  produce  an  miiform  motion  in 
the  tangent,  and  the  law  of  the  centripetal  force,  which  tends  to  pro- 
duce an  accelerating  motion  towards  the  sun ;  the  real  motion  being  a 
compound  of  the  tWo. 

It  is  necessary  here  to  remark,  that  in  this  resolution  of  the  law  of  a 
complex  effect,  the  laws  of  which  it  is  compounded  are  not  the  only  ele- 
ments. It  is  resolved  into  the  laws  of  the  separate  causes,  together 
with  the  fact  of  itheir  coexistence.  The  one  is  as  essential  an  ingredi- 
ent as  the  other ;  whether  the  object  be  to  discover  the  law  of  the  effect, 
or  only  to  explain  it.  To  deduce  tKe  laws  of  the  heavenly  motions, 
we  require  not  only  to  know  the  law  of  a  rectilineal  and  that  of  a  grav- 
itative  force,  but  the  existence  of  both  these  forces  in  the  celestial 
regions,  and  even  their  relative  ajnoimt.  The  complex  laws  of  causa- 
tion are  thus  resolved  into  two  distinct  kinds  of  elements :  the  one, 
simpler  laws  of  causation,  the  other  (in  the  aptly  selected  language  of 
Dr.  Chalmers)  collocations  ;  the  collocations  consisting  in  the  existence 
of  certain  agents  or  powers,  in  certain  circumstances  of  place  and  time. 
We  shall  hereafter  have  occasion  to  return  to  this  distinction,  and  to 
dwell  upon  it  at  such  alenj^th  as  dispense^  with  the  necessity  of  further 
insisting  iipon  it  here.  The  first  mode,  then,  of  the  explanation  of 
Laws  of  Causation,  is  when  the  law  of  an  effect  is  resolved  into  the  va- 
rious tendencies  of  which  it  is  the  result,  and  into  the  laws  of  those 
tendencies. 


272  INDUCTION. 

§  3.  A  second  case  is  when,  between  what  seemed  the  cause  and 
what  was  supposied  to  be  its  effect,  further  observation  detects  an  in- 
termediate hnk ;  a  fact  caused  by  the  antecedent,  and  in  its  turn  caus- 
ing the  consequent ;  so  that  the  cause  at  first  assigned  is  but  the  remote 
cause,  operating  through  the  intermediate  phenomenon.  A  seemed 
the  cause  of  C,  but  it  subsequently  appeared  that  A  was  only  the  cause 
of  B,  and  that  it  is  B  which  was  the  cause  of  C.  For  example:  man- 
kind were  aware  that  the  act  of  touching  an  outward  object  caused  a 
sensation.  It  was,  however,  at  last  discovered,  that  after  we  have 
touched  the  object,  and  before  we  experience  the  sensation,  some 
change  takes  place  in  a  kind  of  thread  called  9.  nerve,  which  extends 
from  our  outward  organs  to  the  brain.  Touching  the  object,  therefore, 
is  only  the  remote  cause  of  our  sensation;  that  is,  not  the  cause,  prop- 
erly speaking,  but  the  cause  of  the  cause  :  the  real  cause  of  the  sensa- 
tion is  the  change  in  the  state  of  the  nerve.  Future  experience  may  not 
only  give  us  more  knowledge  than  we  now  have  of  the  particular 
nature  of  this  change,  but  may  also  interpolate  another  link :  between 
the  contact  (for  example)  of  the  object  with  our  outward  organs,  and 
the  production  of  the  change  of  state  in  the  nerve,  there  may  take 
place  some  electric  phenomenon.  Hitherto,  however,  no  such  inter- 
mediate agency  has  been  discovered ;  and  the  touch  of  the  object  must 
be  considered,  provisionally  at  least,  as  the  proximate  cause  of  the 
affection  of  the  nerve.  The  sequence,  therefore,  of  a  sensation  of 
touch  upon  contact  with  an  object,  is  ascertained  not  to  be  an  ultimate 
law ;  is  resolved,  as  the  phrase  is,  into  two  other  laws — the  law,  that 
contact  with  an  object  produces  an  affection  of  the  neiTe  ;  and  the  law, 
that  an  affection  of  the  nerve  produces  sensation. 

To  take  another  example :  the  more  powerful  acids  corrode  or  black- , 
en  organic  compounds.  This  is  a  case  of  causation,  but  of  remote  causa- 
tion ;  and  is  said  to  be  explained  when  it  is  shown  that  there  is  an  inter- 
mediate link,  namely,  the  separation  of  some  of  the  chemical  elements  of 
the  organic  structure  from  the  rest,  and  their  entering  into  combination 
with  the  acid.  The  acid  causes  this  separation  of  the  elements,  and  the 
separation  of  the  elements  causes  the  disorganization,  and  often  the 
charring  of  the  structure.  So,  again,  chlorine  extracts  coloring  mat- 
ters (whence  its  efficacy  in  bleaching),  and  purifies  the  air  from  infec- 
tion, .This  law  is  resolved  into  the  two  following  laws.  Chlorine  haa 
a  powerful  affinity  for  bases  of  all  kinds,  particularly  metallic  bases 
and  hydrogen.  Such  bases  are  essential  elements  of  coloring  matters 
and  contagious  compounds  ;  whicli  substances-,  therefore,  are  decom- 
posed and  destroyed  by  chlorine. 

§  4.  It  is  of  importance  to  remark,  that  when  a  sequence  of  phe- 
nomena is  thus  resolved  into  other  laws,  they  are  always  laws  more 
general  than  itself  The  law  that  A  is  followed  by  C,  is  less  general 
Sian  either  of  the  laws  which  connect  B  with  C  and  A  with  B.  This 
vdll  appear  from  very  simple  considerations. 

All  laws  of  causation  ai-e  liable  to  be  counteracted,  or  frustrated,  by 
the  non-fulfilment  of  some  negative  condition  :  the  tendency,  therefore, 
of  B  to  produce  C  may  be  defeated.  Now  the  law  that  A  produces 
B,  is  equally  fulfilled  whether  B  is  followed  by  C  or  not  ;  but  the  law 
that  A  produces  C  by  means  of  B,  is  of  course  only  fulfilled  Avhen  B 
is  really  followed  by  C,  and  is  therefore  less  general  than  the  law  that 


EXPLANATION   OF  LAWS.  ^73 

A  produces  B.  It  is-  also  less  general  than  the  law  that  B  produces . 
C.  For  B  may  h^vc  other  causes  besides  A ;  and  as  A  produces  C 
only  by  means  of  B,  while  B  produces  C  whether  it  has  itself  been 
prpduced  by  A  or  by  anything  else,  tlie  second  law  embraces  a  greater 
number  of -instances,  covers  as.it  were  a  greater  space  of  ground,  than 
the  first 

Thus,- in  our  former  cxami^lc,  the  ]aw  that  the  contact-  of  an  object 
causes  a  change  in  the  state  of  the  nerve,  is  more  general  than  the 
law  that  contact  with  an  object  causes  sensation,  siuce,  for  aught  we 
know^the  change  in-  the  nerve  may  equally  take  place  when,  from 
a  counteracting  cause,  as  for  instance  strong  jneutal  excitement,  the 
sensation  docs  not  follow ;  as  in  a  battle,  where  woun,ds  are  often  re- 
ceived without  any  ctmsciousness  of  receiving  them.  And  again,  the 
law  tliat  change  in  the  state  of  a  nein-e  produces  sensation,  is  more 
general  than  the  law  that  contact  with  an  object  produces  sensation  ; 
since  the  sensation  equally  follows  the  change  in  the  nerve  when  nxjt 
produced  by  contact  with  an  object,  but  by  some  othet  cause;  as  in 
the  well  kno>vTi  case,  when  a  person  who  has  lost  a  limb  feels  the  vevj 
sensation  which  he  lias  been  accustomed  to  Call  a  pain  in  the  limb.  . 

Not  only  are  the  laws  of  more  immediate  sequence  into  which  the 
law  of  a  remote  se(]uencc  is  resolved,  laws  of  greater  generality  than 
that  law  is,  but  (as  a'  consequence  of,  or  rather  a^  implied  hi,  .thei:t: 
greater  generality,)  they  are  more  to  bq  relied  ob  ;  tliere  are  fewer 
chances  of  their  being  ultimately  found  not  to  be  universally  true. 
From  the  moment  when  the  sequence  of  A  and  C  is  i^hown  not  to  be. 
immediate,  but  to  depend  upon  an  intervening  phenomenon,  then,  how- 
ever constant  and  invariable  the  sequence  of  A  and  C  has  hitherto  been 
found,  possibilities  arise  of  its  failure,  exceeding  those  which  can  affect 
either  of  the  more  immediate  sequences,  A  B  and  BC.  The  tendency 
of  A  to  produce  C  may  be  defeated  by  Avhatevcr  is  capable  of  defeat- 
iT\g  either  the  teVidency  of  A  to  produce  B,  or  the  tendency  of  B  to 
produce  C  ;  it  is  therefore  twice  as  liable  to  failure  as  either  of  those 
rnore  elementary  tendencies  ;  and  the  generalizatioji  that  A  j&  always 
followed  by  C;  is  twice  as  likely  to  be  found  erroneous.  And  so  of  the 
converse  generalization,  that  C  is  always  preceded  and  caused  by  A; 
which  will  be  erroneous  not  only  if  there  should  happen  to  be  a  second 
immediate  mode  of  production  of  C  itself,  but  moreover  if  there  be  a 
second  mode  of  production  pfB,  the^mmediate,  antocedent  of  C-  in  the- 
sequencc/  ,  ...."■ 

The  resolutipn  of  the.  one  generalization  into,  the  ■  other  two,  not 
only  shows  that  there  are  possible  limitations-  of  the  former,  from 
which  its  two  elements  are  exempt,  but  shows  also  where  these  are  to 
be  looked  for.  Assoon  as  we  know  that  B  intervenes  between  A  and 
C,  we  also  know  that  if  there  be  cases  in  which  the  sequence  of  A 
and  C  does  not  hold,  these  are  most  likely  to  be  found  by  studying  the 
effects  and  the  conditions  of  the  phenomenon  B. 

It  appears,  then,  that  in  the  second  of  the  three  modes  in  which  a 
law  may  be  resolved  into  other  laws,  the  latter  are  more;  general,  that 
is,  extend  to  more  cases,  and  are  also  less  likely  to  retpiire  limitation 
from  subsequent  experience,  than  the  law  which  they  serve  U)  explain. 
They  are  more  nearly  unconditional ;  tlu^y  are  defeated  by  fewer  con- 
tingencies ;  they  are  a  nearer  approach  to  the  universal  truth  of  nature. 
The  same  obsen-ations  are  still  more  evidently  true  with  regard  to  the 

M  M 


274  INDUCTION. 

first  of  the  three  modes  of  resolution.  When  the  law  <yf  an  effect  of 
comMned  causes  is  resolved  into  the  separate  laws  of  the-  causes,  the 
natm-e  of  the  case  implies  that  the  law  of  the  effect  is  less  general  than 
the  law  of  any  of  the  causes,  since  it  only  holds  when  they  are  com- 
bined ;  while  the  law  of  any  one  of  the  causes  holds  good  both  then, 
and  also  when  that  cause  acts  apart  from  the  rest.  It  is  also  manifest 
that  the  complex  law  is  liable  to  be  oftener  unfulfilled  than  any  one 
of  the  simpler  laws  of  which  it  is  the  result,  since  every  contingency 
which  defeats  any  of  the  laws  prevents  so  much  of  the  effect  as 
dejjends  upon  it,  and  thereby  de-feats  the  complex  law.  The  mere 
msting, "  for  examjile,  of  some  small  part  of  a  great  machine,  often 
suffices  entirely  to  prevent  the  effect  which  ought  to  result  from  the 
joint  action  of  all  the  parts.  The  law  of  the  effect  of  a  combination 
of  causes  is  always  subject  to  the  whole  of  the  negative  conditions 
which  attach  to  the  action  of  all  the  causes  severally. 
,  There  is  another  and  a  still  stronger  reason  why  the  law  of  a  complex 
effect  must  be  less  general  than  the  laws  of  the  causes  which  conspire 
to  produce  it.  The  same  causies,  acting  according  to  the  same  laws, 
and  differing  only  in-the  proportions  in  which  they  ai"e  combined,  often 
produce  effects  which  differ  not  merely  in  quantity,  but  in  kind.  The 
combination  of  a  tangential  with  a  centripetal  force,  in  the  proportions 
which  obtain  in  all  the  planets  and  satellites  of  our  solar  system,  gives 
rise. to  an  elliptical  motion;,  but  if  the  ratio  of  the  two  forces  to  each 
other  were  slightly  altered,  it  is  demonstrable  that  the  motion  produced 
would  be  in  a  circle,-  or  a, parabola,  or  an  hyperbola:  and  it  has  been 
supposed  that  in  the  case  of  some  comets  one  of  these  is  really  the 
fact.  Yet  the  law  of  the  parabolic  motion  would  be  resolvable  into 
the- very  same-  simple  laws  into  which  that  of  the  elliptical  motion  is 
resolved,  namely,  th"e  law  of  the  permanence  of  rectilineal  motion, 
and  the  law  of  an  unifomi  centripetal  force.  If,  therefbre,  in  the 
course  of  ages,  some  .cii-cumstance  were,  to  manifest  itself  which, 
without  defeating  the  law  of  eitber  of  those  forces,  should  merely 
alter  their  proportion  to  one  another,  (such  as  the  shock  of  a  comet, 
or  even  the  accumulating  effect  of  the  resistance  of  the  medium  in 
which  astronomers  have  been  led  to  surmise  that  the  motions  of  the 
heavenly  bodies  take  j^lace;)  the_ellij3tical  motion  might  be  changed 
into  a  motion  in  some  other  curve ;  and  the  complex  law  of  the  heav- 
enly motions,  as  at  present  -understood,  would  be  depri-^ed  of  its 
universality,  although  the  discovery  would  not  at  all  detract  from  the 
universality  of  the  simpler  laws  intq  which  that  complex  law  is  resolved. 
The  law,  in  short,  of  each  of  th6  concurrent  causes  remains  the  same, 
however  their  collocations  may  vary  ;  but  the  law  of  their  joint  effect 
varies  with  every  difference  in  the  coltocations.  There  needs  no  more 
to  show  how  mueh  more  general  th6  elementai-y  laws  must  be,  than 
any  of  the  cornplex  laws  which  are  derived  from  them. 

§  5.  Besides  the  two  "modes  which  have  been". treated  of,  there  is  a 
third  mode  in  which  laVvs. are  resolved  into  one  another;  and  in  this  it 
is  self-evident  that  they  are  resolved  into  laws  more  general  tlrah  them- 
selves. This  third  rriode  is  the  subsumftion  (as  it  has  been  called)  of 
one  law  under  another;  or  (what  Comes  to  the  same  tiling)  the  gatlier- 
•ing  up  of  several  laws  into  one  more  general  law  -which  includes  them 
all.     The  most  splendid  example  of  this  operation  was,- when  tejres- 


EXPLANATION    OF    LAWS.  275 

trial  gravity  and  the  central  force  of  the  solar  system  were  brought 
together  under  the  general  law  of  gravitation.  It  had  been  proved 
antecedently  that  the  earth  and  the  other  planel^  tended  to  the  sun; 
and  it  had  been  known  from  the  earliest  times  that  all  tcnestrial  bodies 
tend  towards  the  earth.  These  were  similar  phenomena;  and  to  enable 
tliem  both  to  be  subsumed  under  one  law,  it  was  only  necessary  to 
proTe  that,  as  the  effects  were-  similar  in  quality,  so  also  they,  as  to 
quantity,  conform  to  the  same  rules.  This  was  first  shown  to  be  true 
of  the  moon,  which  agreed  wth  tcnestrial  objects  not  only  in  tending 
to  a  centre,  but  in  the  fact  that  lliis  centre  \v~as  the  earth.  The  tendency 
of  the  moon  to  the  earth  was  already  known  to  vary  as  the  inverse 
square  of  the  distance;  and  it  was  deduced  from  this,  by  direct  calcu- 
lation, that  if  the  moon  were  as  near  to  the  eiuth  as  terrestrial  objects 
are,  and  the  tangential  force  were  suspended,  the  moon  would  fall 
towards  the  earth  through  exactly  as  many  feet  in  a  second  as  those 
objects  do  by  virtue  of  their  weiglit.  Hence,  the  inference  was  irre- 
sistible, that  the  moon  also  tends  to  the  earth  by  virtue  of  its  weight : 
and  that  the  two  phenomena,  the  tendency  of  the  moon  to  the  earth 
and  tk^  tendency  of  teirestnal  objects  to  the  earth,  being  not  only 
similar  in  qdality,  but,  when  under  the  same  circumstances,  identical 
in  quantity,  are  cases  of  one  and  the  same  law  of  causation.  But  the 
tendency  of  the  moon  to  the  earth  and  the  tendency  of  the  earth  and 
planets  to  the  sun,  were  already  known  to  be  cases  of  the  same  law  of 
causation :  and  thus  the  law  of  all  these  tendencies,  and  the  law  of 
terrestrial  gravity,  were  recognized  as  identicg,l,  or,  in  other  words, 
were  subsumed  under  one  general  law,  that  of  gravitation. 

In  a  similar  manner,  the  laws  of  magnetic  phenomena  have  recently 
been  subsumed  under  Ivuown ,  laws  of  ele'ctricity.  It  is  thus  that  the 
most  general  laws  of  nature  are  usually  arrived  at:  we  mount  to  them 
by  successive  steps.  For,  to  arrive  by  con-ect  induction  at  laws  which 
hold  under  such  an  immense  variety  of  circumstances,  laws  so  general 
as  to  be  independent  of  any  varieties  of  space  or  time  which  we  are 
able  to  observe,  requires  for  the  most  part  many  distinct  sots  of  experi- 
ments or  observations,  conducted  at  dittbrent  times  aiid  by  different 
people.  One  part  of  the  law  is  first  ascertained,  afterwards  another 
part:  one  set  of  observations-teaches  us  tliat  the  law  holds  good  under 
some  conditions,  another-that  it  holds  good  under  other  conditions,  by 
combining  which  observations  we  find  that  it  holds  good  under  con- 
ditions much  more  j^eneral,  or  even  universally.  The  general  law,  in 
this  case,  is  literally  the  sum  of  all  the  partial  ones  ;  it  is  the  recog- 
nition of  the  same  sequence  in  different  sets  of  instances  ;  and  rfiay,  in 
fact,  be  regarded  as-  merely  one  step  in  the  process  of  elimination. 
That  tendency  of  bodies  towards  one  another,  which  .we  now  call 
gravity,  Jiad  at  first  been  6bsexved  only  upon  the  earth's  surface,  where 
it  manifested  itself  only  *as  a  tendency  of  all  bodies  towards  the  earth, 
and  might,  therefore,  be  asctibed  to  a  peculiar  property  of  the  earth 
itself:  one  of  the  circumstances,  namely,  tlie  proximity  of  the  earth, 
had  not  been  eliminated.  To  eliminate  this  circumstance  required  a 
fresh  set  of  instances  in  other  parts  of  the  universe  :  these  we  couli 
not  ourselves  create ;  and  though  nature  had  ci'cated  them  for  us,  we 
were  placed  in  very  unfavorable  circumstances  for  obsennng  them. 
To  make  these  observations,  fell  naturally  to  the  lot  of  a  different  set  of 
persons  from  those  who  studied  terrestrial  phenomena,  and  had,  in- 


276  INDUCTION. 

deed,  been  a  matter  of  great  interest  at  a  time  w^en  the  idea  of 
explaining  celestial  facts  by  terrestrial  laws,  was  looked  upon  as  the 
confounding  of  an  iftdefeasible  distinction.  When,  however,  the  celes- 
tial motions  were  accurately  ascertained,  and  the  deductive  processes 
performed  from  which  it  appeared  that  their  laws  and  those  of  teires- 
. trial  gl•a^'ity  corresponded,  those  celestial  observations  became  a  set  of 
•instances  which  exactly  eliminated  the  circumstance  of  proximity  to 
the  earth  ;  and  proved  that  in  "the  original  case,'  that  of  teirestrial  ob- 
jects, it  was  not  the  earth,  as  such,  that  caused  the  motion  or  the  pres^ 
sure,  but  the  circumstance  common  to  that  case  with  the  celestial 
instances,  namely,  the  presence  of  some  great  body  within  certain 
limits  of  distance. 

§  6.  There  are,  then,  three  modes  of  explaining  laws  of  causation, 
or,  which  is  the  same  thing,  resolving  them  into  other  laws.  First, 
when  the  law  of  an  effect  of  combined  causes  is  resolved  into  the  sepa- 
rate laws  of  the  causes,  together  with  the  fact  of  their  combination. 
Secondly,  when  the  law  which  connects  any  two  links,  not  proximate, 
in  a  chain  of  causation,  is  resolved  into  the  laws  which  connect  each 
with  the  inteiTnediate  links.  Both  of  these  are  cases  of  resolving  one 
law  into  two  or  more ;  in  the  third,  two  or  more  are  resolved  into  one ; 
when,  after  the  law  has  been  shown  to  hold  good  in  several  different 
classes  of  cases,  we  decide  that  what  is  true  in  each  of  these  classes  of 
cases,  is  true  under  some  more  general  supposition,  consisting  of  what 
all  those  classes  of  cases  have  in  common.  We  may  here  remark  that, 
this  last  operation  involves  none  of  the  uncertainties  attendant  upon 
induction  by  the  Method  of  Agi-eement,  since  we  need  not  suppose 
the  result  to  be  extended  by  way  of  inference  to  any  new  class  of  cases, 
different  fi-om  those  by  the  comparison  of  which  it  was  engendered. 

In  all  these  three  processes,  laws  are,  as  we  hav'e'seen,  resolved  into 
laws  more  general  than  themselves,  laws  extending  to  all  the  cases 
which  the  fonner  extend  to,  and  others  besides.  In  the  first  two 
modes  they  are  also  resolved  into  laws  more  certain,  in  other  words, 
more  universally  trtie  than  themselves ;  they  are,  in  fact,  proved  not 
to  be  themselves  laws  of  nature,  the  character  of  which  is  to  be 
universally  true,  but  results  of  laws  of  nature,  Avhich  may  be  only  true 
conditionally,  and  for  the  most  part.  No  difference  of  this  sort  exists 
in  the  third  case;  since  here  the  partial  laws  are,  in  fact,  the  very 
same  law  as  the  general  one,  and  any  exception  to  them  would  be  an 
exception  to  it  too. 

By  all  the  three  processes,  the  range  of  deductive  science  is 
extended  ;  since  the  laws,  thus  resolved,  may  be  thenceforth  deduced 
demonstratively  from  the  laws  into  which  they  are  resolved.  As 
already  remarked,  the  same  deductive  process  which  proves  a  law  or 
fact  of  causation,  if  unknown,  sei'N'es  to  explain  it  when  known. 

The  word  explanation  is  here  used  in  a  somewhat  peculiar  sense. 
Wliat  is  called  explaining  one  law  of  nature  by  another,  is  but  sub- 
stituting one  mystery  for  another;  and  does  nothing  to  render  the 
general  course  of  nature  other  than  mysterious  :  we  can  no  more  assi'gn 
a  wTiy  for  the  more  extensive  laws  than  for  the  partial  ones.  The 
explanation  may  substitute  a  mysteiy  which  has  become  familiar,  and 
has  gi-own  to  seem  not  mysterious,  for  one  which  is  still  strange.  And 
this  is  th^  meaning  of  explanation,  in  common  parlance.      But  the 


EXAMPLES  OF  THE  EXPLANATION  OF  LAWS.        277 

process  with  wliicb  we  are  here  concerned  often  does  the  very  con- 
trary; it  resolves  a  phenomenon  with  which  we  ai-e  famiHar,  into  one 
of  which  we  previously- knew  little  or  nothing;  as  when  the  connnon 
fact  of  the  fall  of  ht:avy  bodies  is  resolved  into  a  tendency  of  all  par- 
ticles of  matter  towards  oiu-  another.  It  must  be  kept  constantly  in^ 
view,  therefore,  that  wIumi  j)hilosophers  speak  of  explaining  any  of 
the  phenotneua  of  nature,  they  always  mean,  pointing  out  not  some 
more  familiar  but  merely  some  more  general  phenomenon -of  which  it 
is  a  p;utial  exempliHcatiou,  or  some  laws  of  causation  which  produce 
it  by  their  joint  or  successive  action,  and  from  which,  therefore,  its 
conditions  may  be  determined  deductively.  Every  such  operation 
brings  us  a  step  nearer  towards  answering  the  question,  which  was 
stated  some  time  agO  as  comprehending  the  whole  problem  of  the 
investigation  of  nature  viz.,  What  are  the  fewest  a.ssumptions  which 
being  gianted,  the  order  of  nature  as  it  exists  would  be  the  result  1 
Wliat  are  tlxe  fewest  general  ]iropositions  from  which  all  the  uniformities 
existing  in  natui-e  could  be  deduced  I 

The  laws,  thus  explained  or  resolved,  are  sometimes  said  to  be 
accou/ited  Jor ;  but  the  expression  is  incon-ect,  if  taken  to  mean  any- 
thing more  than  what  has  been  already  stated.  In  minds  not  habituated 
to  accurate  thinking,  there  is  often' a  confused  notion  that  the  general 
laws  are  the  causas  of  the  partial  ones  ;  that  the  law  of  general  gravita- 
tion, for  example,  causes  the  jjhenomenon  of  the  fall  of  bodies  to  the 
earth.  But  to  assert  this,  would  be  a  misuse  of  the  word  cause  : 
ten'estrial  gi'avity  is  not  an  effect  of  general  gravitation,  btit  a  case  of 
it ;  tliat  is,  one  kind  of  the  particular  instances  in  which  that  general 
law  obtains.  To  account  for  a  law  of  nature  means,  and  can  mean,  no 
more  than  to  assign  other  laws  more  general,  together  with  collocations, 
which  laws  and  collocations  being  supposed,  the  partial  law  follows 
without  any  additional  supposition. 


CHAPTER  XIII. 

MISCELLANEOUS   EXAMPLES    OF  THE  EXPLANATION  OF  LAWS  OF  NATURE. 

§  1.  So  MR  of  the  most  remarkable  instances  which  have  occurred 
since  the  great  Newtonian  generahaation,  of  the  explanation  of  laws 
of  causation  subsisting  among  complex  phenomena,  by  resolving  them 
ijito  simpler  and  more  general  laws,  are  to  be  found  among  the  recent 
speculatirjns  of  Liebig  in  organic  chemistry.  These  speculationSi 
although  they  have  not  yet  been  sufficiently  loflg  before  the  world  to 
entitle  ns  positively  to  assume  that  no  well-grounded  objection  can  be 
made  to  any  part  of  them,  aflbrd,  however,  so  admirable  an  example 
of  the  spirit  of  the  Deductive  Method,  that  I  may  be  permitted  to  pre- 
sent some  Bjjccimens  of  them  here. 

It  had  been  observed  in  certain  cases,  that  chemical  action  is,  as  it 
were,  contagious ;  that  is  to  say,  a  substance  which  would  n<»t  of  itself 
yield  to  a  particular  chemical  attraction,  (tl»e  force  of  the  attraction 
not  being  sufficient  to  overcome  cohfcjHou,  or  to  destroy  some  chemical 
combination  in  which  the  substanpe  waa  aheady  held,)  will  neverthc- 


278  INDUCTION. 

less  do  so  if  placed  in  contact  with  some  other  body  which  is  in  the 
act  of  yielding  to  the  same  force.  Nitric  acid,  for  example,  does  not 
dissolve  pure  platinum,  which  may  "  be  boiled  with  this  acid  without 
being  oxidized  by  it,  even  when  in  a  state  of  such  fine  division  that  it 
no  longer  reflects  light."  But  the  same  acid  easily  dissolves  silver. 
Now  if  an  alloy  of  silver  and  platinum  be  treated  with  nitric  acid,  the 
acid  does  not,  as  might  naturally  be  expected,  separate  the  two  metals, 
dissohang  the  silver,  and  leaving  the  platinum ;  it  dissolves  both :  the 
platinum  as  well  as  the  silver  becomes  oxidized,  and  in  that  state  com- 
bines with  the  undecomposed  portion  of  the  acid.  In  like  manner, 
"copper  does  not  decompose  water,  even  when  boiled  in  dilute  sul- 
phuric acid,  but  an  alloy  of  copper,  zinc,  and  nickel,  dissolves  easily 
in  this  acid  with  evolution  of  hydrogen  gas."  These  phenomena  can- 
not be  explained  by  the  laws  of,  what  is  termed  chemical  affinity. 
They  point  to  a  peculiar  law,  by  which  the  oxidation  which  one  body 
suffers,  causes  another,  in  contact  with  it,  to  subrriit  to  the  same  change. 
And  not  only  chemical  composition,  but  chemical  decomposition,  is 
capable  of  being  similarly  propagated.  The  peroxide'of  hydrogen,  a 
compound  formed  by  hydrogen  with  a  greater  amount  of  oxygen  than 
the  quantity  necessary  to  form  water,  is  held  together  by  a  chemical 
attraction  of  so  weak  a  nature,  that  the  slightest  circumstance  is  suffi- 
cient to  decompose  it;  and  it  even,  though  very  slowly,  gives  oft'  oxygen 
and  is  reduced  to  water  spontaneously  (being,  I  presume,  decomposed 
by  the  tendency  of  its  oxygen  to  absorb  heat  and  assume  the  gaseous 
state).  Now  it  has  been  obser^•ed,  that  if  this  decomposition  of  the 
peroxide  of  hydrogen  takes  place  in  contact  with  some  metallic  oxides, 
as  those  of  silver,  and  the  peroxides  of  lead  and  manganese,  it  super- 
induces a  coiTesponding  chemical  action  upon  those  substances ;  they 
also  give  forth  the  whole  or  a  portion  of  their  oxygen,  and  are  reduced 
to  the  metal  or  to  the  protoxide ;  although  they  do  not  undergo  this 
change  spontaneously,  and  there  is  no  chemical  affinity  at  work  to 
make  them  do  so.  Other  similar  phenomena  are  mentioned  by  Dr. 
Liebig.  "Now  no  other  explanation,"  he  observes,  "of  these  phe- 
nomena can  be  given,  than  that  a  body  in  the  act  of  combination  or 
decomposition  enables  another  body,  with  which  it  is  in  contact,  to 
enter  into  the  same  state." 

Here,  therefore,  is  a  law  of  nature  of  great  simplicity,  but  which, 
owing  to  the  extremely  special  and  limited  character  of  the  phenomena 
in  which  alone  it  can  be  detected  experimentally  (because  in  them 
alone  its  results  are  not  intermixed  and  blended  with  those  of  other 
laws),  had  been  very  little  recognized  by  chemists,  and  no  one  could 
have  ventured,  on  experimental  evidence,  to  affirm  it  as  a  law  common 
to  all  chemical  action  ;  owing  to  the  impossibility  of  a  rigorous  employ- 
ment of  the  Method  of  Difference  where  the  properties  of  different  kinds 
of  substance  are  involved,  an  impossibility  which  we  noticed  and  char- 
acterized in  a  previous  chapter.*  Now  this  extremely  special  and  ap- 
parently precarious  generalization  has,  in  the  hands  of  Liebig,  been 
converted  by  a  masterly  employment  of  the  Deductive  Method,  into  a 
law  pervading  all  nature,  in  the  same  way  as  gravitation  assumed  that 
character  in  the  hands  of  Newton ;  and  has  been  found  to  explain,  in 
the  most  unexpected  manner,  numerous  detached  generalizations  of  a 

*  Supra,  p.  239, 


EXAMPLES    OF    THE    EXPLAIN ATION    OF    LAWS.  279 

more  limltod  kind,  reducing  the  jilieiiomena  concerned  in  those  gener- 
alizations into  mere  cases  pt"  itself. 

The  contagious  inHuencc  ot' clumucal  action  is  not  a  powerful  force, 
and  is  only  capable  of  overcoming  weak  affinities  :  we  may,  therefore, 
expect  to  tind  it  principally  exeuiplitied  in  the  decomposition  of  sub- 
stances which  are  held  together  by  weak  chemical  forces.  Now  the 
force  which  holds  a  compound  eubstauce  together  is  generally  weaker, 
the  more  compound  the  substance  is  ;  and  organic  products  are  the  most 
compound  substances  known,  those  which  have  the  most  complex 
atomic  constitution.  It  is,  therefore,  upon  such  substances  that  the 
self-j>ropagating  power  of  chemical  action  is  likely  to  exert  itself  ill 
the  most  markexl  manner.  Aecoi'dingly,  first,  it  explains  the  remark- 
able laws  of  fermentation,  and  some  of  those  of  putrefaction.  "A  little 
leaven,"  that  is,  dough  in  a  certain  state  of  chemical-  action,  impresses 
a  similar  chemical  actioniipon  "  the  wliole  hnnp."  The  contact  of  any' 
decaying  substance,  occasions  the  decay  of  matter  previously  sound. 
Again,  yeast  is  a  substance  actually  in  a  process  of  decomposition  from 
the  action  of  air  and  water,  evolving  carbonic  acid  gas.  SQgar  is  a 
substance  which,  from  the  complexity  of  its  composition,  ha^  no  great 
energy  of  coherence  in  its  existing  form,  and  is  capable  of  being  easily 
converted  (by  combination  with  the  elements  of  water)  into  carbonic 
acid  and  alcohol.  Now  the  mere  presence  of  yeast,  the  mere  proxim- 
ity of  a  substance  of  which  the  elements  are  separating  from  each 
other,  and  combining  with  the  elements  of  water,  causes  sugar, to  un- 
dergo the  same  change,  giving  out  carbonic  acid  gas,  arid  becoming 
alcohol.  It  is  not  the  elements  contained-in  the  yeast  which  do  this. 
"  An  acpieous  infusion  of  yeast  may  be  mixed  with  a  solution  of  sugar, 
and  preserved  in  vessels  from  which  the  air  is  excluded,  without  either 
experiencing  the  slightest  change."  Neither  does  the  insoluble  resi- 
due of  the  yeast,  after  being  treated  with  water,  possess  the  power 
of  exciting  fermentation.  It  is  not  the  yeast  itself,  therefore  ;■  it  is 
the  yeast  in  a  state  of  decomposition.  The  sugar,  which  would  noC 
decompose  and  oxidize  by  the  mere  presence  of  Oxygen  and  waterj 
is  induced  to  do  so  when  another  oxidation  is  at  work  in  the  midst 
of  it.  ' 

J3y  the  same  principle  Liebig  is  enabled  to  explain  rrialaria;  the 
pernicious  influence  of  putrid  substances  ;  a  variety  of  poisons;  conta- 
gious diseases  ;  and  other  phenomena.  Of  all  substances,  those  com- 
-posing  the  animal  body  are  the  most  complex  in  their  Composition,  and 
in  the  least  stable  condition  of  union.  The  blood,  in  particular,  is  the 
most  unstable  compound  known.  What,  therefore,  can  be  less. sur- 
prising than  that  gaseous  or  other  substances,  in  the  act  of  undergoing 
the  chemical  changes  which  constitute,  for  instance,  putrefaction, 
should,  when  brought  into  contact  with  the  tissues  by  respiraticjn  or 
otherwise,  and  still  more  when  introduced  by  inoculation  into  the  blood 
itself,  impress  upon  some  of  the  particles  a  chemical  action  similar  to 
its  own ;  which  is  propagated  in  like  manner  to  other  particles,  until 
the  whole  system  is  placed  in  a  state  of  chemical  action  more  or  less 
inconsistent  with  the  chemical  conditions  of  vitality. 

Of  the  three  modes  in  which  we  observed  in  the  last  chapter  that  the 
resolution  of  a  special  law  into  more  general  ones  may  take  place,  this 
speculation  of  Liebig  exemplifies  the  second.  The  laws  explained 
are  such  as  this,  that  yeast  puts  sugar  into  a  state  of  fennentation. 


280  INDUCTION. 

Between  the  remote  cause,  the  presence  of  yeast,  and  the  consequent 
fermentation  of  the  sugar,  there  has  been  interpolated  a  proximate 
cause,  the  chemical  action  between  the  particles  of  the  yeast  and  the 
elements  of  air  and  water.  The  special  law  is  thus  resolved  into  two 
others,  more  general  than  itself:  the  first,  that  yeast  is  decomposed  by 
the  presence  of  air  and  water;  the  second,  that  matter  undergoing 
chemical  action  has  a  tendency  to  produce  similar  chemical  action  in 
other  matter  in  contact  with  it.  But  while  the  investigation  thus  aptly 
exhibits  the  second  mode  of  the  resolution  of  a  complex  law,  it  no  less 
happily  exemplifies  the  third ;  the  subsumption  of  special  laws  under 
a  more  general  law,  by  gathering  them  up  into  ozie  more  comprehen- 
sive expression  which  includes  them  all.  For  the  curious  fact  of  the 
contagious  nature  of  chemical  action  was  only  raised  into  a  law  of  all 
chemical  action  by  these  very  investigations  ;  just  as  the  Newtohian 
attraction  was  only  recognized  as  a  law  of  all  matter  when  it  was 
found  to  explain  the  phenomena  of  teiTestrial  gravity.  Previously  to 
Liebig's  investigations,  the  property  in  question  had  only  been  observed 
in  a  few  special  cases  of  chemical  action;  but  when  his  deductive 
reasonings  had  established  that  innumerable  effects  produced  upon 
weak  compounds,  by  substances  none  of  whose  known  peculiarities 
would  account  for  their  having  such  a  power,  might  be  explained  by 
considering  the  supposed  special  property  to  exist  in  all  those  cases, 
these  numerous  generalizations  on  separate  substances  were  brought 
together  into  one  law  of  chemical  action  in  general :  the  peculiarities 
of  the  various  substances  being,  in  fact, .  elimina,ted,  just  as  the  New- 
tonian deduction  eliminated  from  the  instances  of  terrestrial  gravity 
the  circumstance  of  proximity  to  the  earth. 

§  2.  Another  of  Liebig's  speculations,  which,  if  it  should  ultimately 
be  found  to  agi'ee  with  all  the  facts  of  the  extremely  complicated 
phenomenon  to  which  it  relates,  will  constitute  one  of  the  finest, 
examples  of  the  Deductive  Method  upon  record,  is  his  theory  of  respi- 
ration. 

The  facts  of  respiration,  or  in  other  words  the  special  laws  which 
Liebig  has  attempted  to  explain  from,  and  resolve  into,  more  general 
ones,  are,  that  the  blood  in  passing  through  the  lungs  absorbs  oxygen 
and  gives  out  carbonic  acid  gas,  changing  thei'eby  its  color  from  a 
blackish  purple  to  a  brilliant  red.  The  absorption  and  exhalation  are 
evidently  chemical  phenomena ;  and  the  carbon  of  the  ca,rbonic  acid 
must  have  been  derived  fi-om  the  body,  that  is,  must  have  been  ab- 
sorbed by  the  blood  from  the  substances  with  which  it  came  into 
contact  in  its  passage  through  the  organism..  Required  to  find  the 
intermediate  links,  the  precise  nature  of  the  two  chemical  actions  which 
take  place ;  first,  the  absorption  of  the  carbon  or  of  the  carbonie  acid 
by  the  blood,  in  its  circulation  through  the  body ;  next,  the  excretion 
of  the  carbon,  or  the  exchange  of  the  carbonic  acid  for  oxygen,  in  its 
passage  through  the  lungs. 

Dr.  Liebig  believes  himself  to  have  found  the  solution  of  tliis  vexata 
qucestio  in  a  class  of  chemical  actions  in  which  scarcely  any  less  acute 
and  accurate  inquirer  would  have  thought  of  looking  for  it. 

Blood  is  composed  of  two  parts,  the  serum  and  the  globules.  The 
serum  absorbs  and  holds  in  solution  carbonic  acid  in  great  quantity, 
but  has  no  tendency  either  to  part  with  it  or  to  absorb  oxygen.     The 


EXAMPLES    OF    THE    EXPLANATION    OF    LAWS.  281 

globules,  then>f)re,  arc  concluded  to  bo  tlio  portion  of  the  blood  wliich 
is  operative  in  respiration.  These  globules  contain  a  certain  quantity 
of  iron,  which  (rom  chemical  tests  is  inferred  to  be  in  the  state  of 
oxide. 

Dr.  Liebig  recognized,  in  tlic  known  chemical  properties  of  the 
oxides  of  iix)n,  laws  which,  if  followed  out  deductively,  wtoiild  lead  to 
the  prediction  of  the  precise  series  of  phencmena  which  respiration 
exhibits. 

There  are  two  oxides  of  iron,  a  protoxide  and  a  peroxide.  In  the 
arterial  blood  the  iron  is  in  the  form  of  peroxide  :  in  the  vtmous  blood 
we  have  no  direct  evidence  which  of  riie  oxides  is  ]>resent,  but  the 
considerations  to  be  presently  stated  will  prove  that  it  is  the  prottjxide. 
As  arterial  and  venous  blood  are  in  a  perpetual  state  of  alternate  con- 
version into  one  another,  the  question  arises,  under  what  circumstances 
the  protoxide  of  iron  is  capable  of  being  converted  into  the  i)croxide, 
and  vice  versd.  Now  the  protoxide  readily  combines  with  (jxygen  iii 
the  presence  of  water,  forming  the  hydrated  peroxide  :  these  condi- 
tions it  finds  in  passing  through  the  lungs  ;  it  derives  oxygen  from  the 
air,  and  finds  water  in  the  blood  itself  This  would  already  explain 
one  portion  of  the  phenojnena  of  respiration.  But  the  arterial  blood, 
in  (juitting  the  luntrs,  is  charged  with  hydrated  peroxide  :  in  what 
manner  is  the  peroxide  brought  back  to  its  former  state  ? 

The  chemical  conditions  for  the  reduction  of  the  hydrated -peroxide 
into  the  state  of  protoxide,  are  precisely  those  which  the  blood  meets 
with  in  circulating  through  the  body ;  namely,  contact  with  organic 
compounds. 

Hydrated  peroxide  of  iron,  when  treated  with  organic  compounds 
(whei"e  no  sulphur  is  present)  gives  forth  oxygen  and  wsiter,  which 
oxyggn,  attracting  the  carbon  from  the  organic  substance,  becomes 
carbonic  acid  ;  while  the  peroxide,  being  reduced  to  the  state  of  prot- 
oxide, combines  with  the  carbonic  acid,  and  becomes  a  carbonate. 
Now  this  carbonate  needs  only  come  again  into  contact  with  oxygen 
and  water  to  be  decomposed ;  the  carbonic  add  being  given  off,  and 
the  protoxide,  by  the  absorption  of  oxygen  and  water,  becoming  again 
the  h^-drated  peroxide. 

The  mysterious  chemical  phenomena  connected  with  respiration 
can  now,  by  a  beautiful  deductive  process,  be  completely  explained. 
The  arterial  blood,  containing  iron  in  the  form  of  hydrated  peroxide, 
passes  into  the  capillaries,  where  it  meets  with  the  decaying  tissues, 
receiving  also  in  its  course  certain  non-azotized  but  highly  carbonized 
animal  products,  in  particular  the  bile.  In  these  it  finds  the  precis^ 
conditions  required  for  decomposing  the  peroxide  into  oxyge\i  and  the 
protoxide.  The  oxygen  combines  with  the  carbon  of  the  decaying 
tissues,  and  forms  carbonic  acid,  which,  although  insufficient  in  amount 
to  neutralize  the  whole  of  the  protoxide,  combines  with  a  pcntion  (<me- 
fourth)  of  it,  and  returns  in  the  form  of  a  carl)wiiat<',  along  with  the 
other  three-fourths  of  the  i)rotoxide,  through  the  venous  system  into 
the  lungs.  There  it  again  meets  with  «jxygen  and  water :  the  free 
protoxide  becomes  hydrated  peroxide;  the  carbcmate  of  protoxide 
parts  with  its  carbonic  acid,  and  by  absorbing  oxygen  and  water,  enters 
also  into  the  state  of  hydrated  peroxid*-.  The  heat  evolvvd  in  the 
transition  from  protoxide  to  p(!roxide,  as  well  as  in  the  previous  oxidq.- 
tion  of  the  carbon  contained  in  the  tissues,  is  considered  by  Liebig  as 
.      Nn  ■ 


282  INDUCTION. 

the  cause  which  sustains  the  temperature  of  the  body.     But  into  this 
portion'  of  the  speculation  we  need  not  enter.* 

This  example  displays  the  second  mode  of  resolving  complex  laws, 
by  tlie  interpolation  of  intermediate  links  in  the  chain  of  causation ; 
and  some  of  the  steps  of  the  deduction  exhibit  cases  of  the  first  mode, 
that  which  mfers  the  joint  effect  of  two  or  more  causes  from  their 
separate  effects  ;  but  to  trace  out  in  detail  these  exemplifications  may 
be  left  to  the  intelligence  of  the  reader.  The  third  mode  is  not  em- 
ployed in  this  example,  since  the  simpler  laws  into  which  those  of 
respiration  are  resolved  (the  laws  of  the  chemical  action  of  the  oxides 
of  iron)  were  already  known  laws,  and  did  not  acquire  any  additional 
generality  fi'om  their  employment  in  the  present  case. 

§  3.  The  property  which  salt  possesses  of  presei'\'ing  animal  sub* 
stances  from  putrefaction  is  resolved  by  Liebig  into  two  more  general 
laws,  the  strong  attraction  of  salt  for  water,  and  the  necessity  of  the 
presence  of  "water  as  a  condition  of  putrefaction.  The  intermediate 
phenomenon  which  is  intei-polated  between  the  remote  cause  and  the 
effect,  can  here  be  not  merely  inferred  but  seen ;  for  it  is  a  familiar 
fact,  that  flesh  upon  which  salt  has  been  thrown  is  speedily  found 
swimming  in  brine. 

The  second  of  the  two  factors  (as  they  may  be  termed)  into  which 
the  preceding  law  has  been  resolved,  the  necessity  of  water  to  putre- 
faction, itself  affords  an  additional  example  of  the  Resolution  of  Laws. 
The  law  itself  is  proved  by  the  Method  of  Difference,  since  flesh  com- 
pletely dried  and  kept  in  a  dry  atmosphere  does  not  putrefy,  as  we 
see  .  in  the  case  of  dried  pro%-isions,  and  human  bodies  in  very  dry 
climates.  A  deductive  explanation  of  this  same  law  results  fi"om 
Liebig's  speculations.  The  putrefaction  of  animal  and  other  azotiz;ed 
bodies  is  a  chemical  process,  by  which  they  are  gi'adually  dissipated  in 
a  gaseous  form,  chiefly  in  that  of  carbonic  acid  and  ammonia ;  now  to 
convert  the  carbon  of  the  animal  substance  into  carbonic  acid  requires 
oxygen,  and  to  convert  the  azote  into  ammonia  requires  hydrogen, 
which  are  the  elements  of  water.  The  extreme  rapidity  of  the  putre- 
faction of  azotized  substances,  compai'ed  with  the  gradual  decay  of 
non-azotized  bodies  (such  as  wood  and  the  like)  by  the  action  of 
oxygen  alone,  is  explained -by  Liebig  from  the  general  law  that 
•substances  are  much  more  easily  decomposed  by  the  action  of  two 
different  affinities  upon  two  of  their  elements,  than  by  the  action  of 
only  one. 

The  purgative  effect  of  salt  with  alkaline  bases,  when  administered 
in  concentrated  solutioris,  is  explained  by  Liebig  from  the  two  follow- 
ing principles  :  Animal  tissues  (such  as  the  stomach)  do  not  absorb 
concentrated  solutions  of  alkaline  salts ;  and  such  solutions  do  dissolve 
the  solids  contained  in  the  intestines.  The  simpler,  laws  into  which 
the  complex  law  is  here  resolved,  are  the  second  of  the  two  foregoing 

*  As  corroborating  the  opinion  of  Liebig  that  the  protoxide  of  iron  in  the  venous  blood 
is  only  partially  carbonated,  the  fact  has  been  suggested  that  the  system  shows,  graet  readi- 
ness to  absorb  an  extra  quantity  of  carbonic  acid,  as  furnished  in  etrervescing  drinks.  In 
snch  cases  the  acid  must  combine  with  something,  and  that  something  is  probably  the  free 
protoxide.  It  would  be  worth  asc^taining  whether  the  protoxide  itself  or  its  carbonate 
Jias  the  greater  facility  in  absorbing  oxygen  and  turning  itself  into  hydrated  peroxide  in 
the  lungs.  If  the  carbonate,  Ihen  the  beneficial  effect,  on  the  animal  economy,  of  drinks 
which  give  an  artificial  supply  of  carbonic  acid  to  the  system,  would  be,  to  that  extent 
deductively  demonstrated. 


EXAMPLES  OF  THE  EXPLANATION  OF  LAWS.        283 

principles  combined  with  a  third,  namely,  that  the  peristaltic  contrac- 
tion acts  easily  upon  substances  in  a  state  of  solution.  The  negative 
general  proposition,  that  animal  substances  do  not  absorb  these  salts, 
oonti-ibutes  to  the  explanation  by  accounting  tor  the  absence  of  a 
counteracting  cause,  namely,  absorption  by  tho  stomach,  which  in  the 
case  of  oth(?r  substances  possessed  of  the  requisite  chemical  properties, 
interferes  to  prevent  them  from  reaching  the  substances  whicli  they 
are  destined  to  dissolve. 

§  4.  From  the  foregoing  and  similar  instances,  w6  may  see-  the  im- 
portance, when  a  law  of  nature  previously  unknown  has  been  brought 
to  light,  or  when  new  light  has  been  thrown  upon  a  known  law  by 
experiment,  of  examining  all  cases  which  present  the  conditions  neces- 
sary for  bringing  that  la\V  into  action  ;  a  process  necessarily  fertile  in 
demonstrations  of  special  laws  previously  unsuspected,  and  explana- 
tions of  others  already  empirically  known. 

■  For  instance,  Faraday  discovered  by  experiment,  that  voltaic  elec- 
tricity could  be  evolved  from  a  natural  magnet,  provided  a  conducting 
body  were  set  in  motion  at  right  angles  to  the  direction  of  the  magnet; 
and  this  he  found  to  hold  not  only  of  small  magnets,  but  of  that  great 
magnet,  the  earth.  The  law  being  thus  established  experimentally,, 
that  electricity  is  evolved,  by  a  magnet,  and  a  conductor  moving  at 
right  angles  to  the  direction  of  its  poles,  we  may  now  look  out  for  fresh 
instances  in  which  -these  conditions  meet.  Wherever  a  conductor 
moves  or  revolves  at  right  angles  to  the  direction  of  the  earth's  magnetic 
poles,  there  we  may  expect  an  evolution  of  electricity.  In  the  northei'n 
regions,  where  the  polar  direction  is  nearly  perpendicular  to  the  hori- 
zon, all  horizontal  motions  of  conductors  will  produce  electricity ;  hori- 
zontal wheels,  for  example,  made  of  metal ;  likewise  all  running  streams 
will  evolve  a  current  of  electricity  which  will  circulate  round  them ; 
and  the  air  thus  charged  with  electricity  may  be  one  of  the  causes  of 
tlie  Aurora  BoroaKs.  In  the  equatorial  regions,  on  the  contrary,  upright 
wheels  placed  parallel  to  the  equator  will  originate  a  voltaic  circuit, 
and  waterfalls  will  naturally  become  electric. 

For  a  second  example ;  it  has  recently  been  found,  chiefly  by  the 
researches  of  Professor  Graham,  that  gases  have  a  strong  tendency  to 
permeate  aramal  membranes,  and  diffuse  themselves  through  tlie  spaces 
which  such  membranes  enclose,  notwithstanding  the  presence  of  other 
gases  in  those  spaces.  Proceeding  from  this  general  law,  and  review- 
ing a  variety  of  cases  in  which  gases  lie  contiguous  to  membranes,  we 
are  enabled  to  demonstrate  or  to  explain  the  following  more  special 
laws  :  1st.  The  human  or  animal  body,  when  surrounded  with  any  gas 
not  already  contained  within  the  body,  absorbs  it  rapidly ;  such,  for 
instance,  as  the  gases  of  putrefying  matters :  which  helps  to  explain 
malaria.  2d.  The  carbonic  acid  gas  of  effervescing  drinks,  evolved 
in  tlio  stomacli,  permeates  its  membranes,  and  rapidly  spreads  tlirough 
the  system,  where,  as  suggested  in  a  former  note,  it  probably  combines 
with  tlie  iron  contained  in  the  blood.  ^  3d.  Alcohol  taken  into  the 
stomach  (the  temperature  of  tho  stf)Tnach  is  above  the  boiling  point  of 
pure  alcohol,)  passes  into  vapor  and  sprfiads  through  the  system  with 
great  rapidity;  (which  combined  with  the  high  combustibility  of  alco- 
hol, or  in  other  words  its  ready  combination  with  oxygen,  may  perhaps 
help  to  explain  the  bodily  warmth  immediately  consequent  on  drinking 


284  INDUCTION. 

spirituous  liquors.)  4th.  In  any  state  of  the  body  in  which  pecuhar 
gases  are  fonneJ  within  it,  these  wll  rapidly  exhale  through  all  parts 
of  the  body;  and  hence  the  rapidity  with  which,  in  certain  states  of 
disease,  the  suiTOunding  atmosphere  becomes  tainted.  5th.  The  putre- 
faction of  the  interior  parts  of  a  carcass  will  proceed  as  rapidly  as  that  of 
the  exterior,  from  the  ready  passage  outwards  of  the  gaseous  products. 
.6th.  The  exchange  of  oxygen  and  carbonic  acid  in  the  lungs  is  not  pre- 
vented but  rather  promoted,  by  the  intei-\'ention  of  the  membrane  of 
the  lungs  and  the  coats  of  the  blood  vessels  between  the  blood  and  the 
air.  It  is  necessary,  however,  that  there  should  be  a  substance  in  the 
blood  with  which  the  oxygen  of  the  air  may  immediately  combine, 
otherwise,  instead  of  passing  into  the  blood,  it  would  permeate  the 
whole  organism ;  and  it  is  necessary  that  the  carbonic  acid,  as  it  is 
formed  in  the  capillaries,  should  also  find  a  substance  in  the  blood  with 
which  it  can  combine  ;  other^vise  it  would  leave  the  body  at  all  points, 
instead  of  being  discharged  through  the  lungs. 

§  5.  The  foUowmg  is  a  deduction  which  confirms,  by  explaining,  the 
old  but  not  undisputed  empirical  generalization  that  soda  powders 
weaken  the  hirman  system.  These  powders,  consisting  of  a  mixture 
of  tartaric  acid  with  bicarbonate  of  soda,  from  vvhich  the  carbonic  acid 
is  set  free,  must  pass  into  the  stomach  as  tartrate  of  soda.  Now, 
neuti-al  tartrates,  citi-ates,  and  acetates  of  the  alkalis  are  found,  in  their 
passage  through  the  system,  to  be  changed  into  carbonates ;  and  to 
convert  a  tartrate  into  a  carbonate  requires  an  additional  quantity  of 
oxygen,  the  abstraction  of  which  must  lessen  the  oxygen  destined  for 
assimilation  with  the  blood,  and  to  the  quantity  of  which  the  vigorous 
action  of  the  human  system  is  proportional. 

The  instances  of  new  theories  agreeing  with  and  explaining  old  em- 
piricisms, are  innumerable.  All  the  just  remarks  made  by  experienced 
persons  on  human  character  and  conduct,  are  so  many  special  laws, 
which  the  general  laws  of  the  human  mind  explain  and  resolve.  The 
empirical  generalizations  on  which  the  operations  of  the  arts  have 
usually  been  founded,  are  continually  justified  and  confiiTned  on  the 
one  hand,  or  rectified  and  improved  on  the  other;  by  the  discovery  of 
the  simpler  scientific  laws  on  which  the  efficacy  of  those  operations 
depends.  The  effects  of  the  rotation  of  crops,  of  the  various  manures, 
and  the  other  processes  of  improved  agriculture,  have  been,  for  the 
first  time,  resolved  in  our  own  day  into  known  laws  of  chemical  and 
organic  action,  by  DaN^y  and  Liebig.  The  processes  of  the  healing 
art  are  even  now  mostly  empirical ;  their  efficacy  is  concluded,  in  each 
instance,  from  a  special  and  most  precarious  experimental  generaliza- 
tion :  but  as  science  advances,  in  discovering  the  simple  laws  of  chem- 
istry and  physiology,  progress  is  made  in  ascertaining  the  intcnnediate 
links  in  the  series  of  phenomena,  and  the  more  general  laws  on  which 
they  depend  :  and  thus,  while  the  old  processes  are  either  exploded, 
or  their  efficacy,  in  so  far  as  real,  explained,  improved  processes, 
founded  on  the  knowledge  of  proximate  causes,  are  continually  sug- 
gested and  brought  into  use,*     Many  even  of  the  tiniths  of  geometry 

*  It  was  an  old  generalization  in  surgery,  that  tight  bandaging  had  a  tendency  to  prevent 
or  dissipate  local  inflammations.  This  sequence  being,  in  the  progress  of  physiological 
knowledge,  resolved  into  more  general  laws,  led  to.  the  important  surgical  invention 
recently  made  by  Dr.  Atnott,  the  treatment  of  local  inflammation  and  tumors  by  means  of 


EXAMPLES  OF  THE  EXPLANATION  OF  LAWS.       285 

were  generalizations  fi-om  experience  before  they  were  deduced  from 
first  principles.  The  (][uadratnro  of  the  cycloid  was  first  effected  by 
measurement;  or  rather  by  weighing  a  cycloidal  card,  and  comparing 
its  weight  with  that  of  a  piece  oi"  shnilar  card  of  known  dimensions. 

§  6.  To  the  foregoing  examples  from  physical  science,  let' us  add  an- 
other from  mental.  The  following  is  one  of  the  simple  laws  of  mind : 
Ideas  of  a  pleasurable  or  pahiful  character  form  associations  more  easily 
and  strongly  than  other  ideas,  that  is,  they  bi'come  associated  after  fewer 
I'epetitions,  and  the  association  is  more  durable.  This  is  an  experi- 
mental law,  grounded  upon  the  Method  of  Difference.  By  deduction 
from  this  law,  many  of  the  more  special  laws  which  experience  showa 
to  exist  among  particular  mental  phenomena  may  be  demonstrated 
and  explained  : — the  ease  and  rapidity,  for  instanccy^with  which  thoughts 
connected  with  our  passions  or  our  more  cherished  interests  are  exci- 
ted, and  the  finn  hold  which  the  facts  relating  to  them  have  on  our 
memoiy ;  the  rixid  recollection  we  retain  of  minute  circumstances 
which  accompanied  any  object  or  event  that  deeply  interested  us,  and 
of  the  times  and  places  in  which  we  have  been  very  happy  or  very 
miserable ;  the  horror  with  Avhich  we  view '  the  accidental  instru- 
ment of  any  occurrence  which  shocked  us,  or  the  locality  where  it 
took  place,  and  the  pleasure  we  derive  fi-om  any  menwrial  of  past 
enjoyment ;  all  these  effects  being  proportional  to  the  sensibility  of 
the  indi\-idual  mind,  and  to  the  consequent  intensity  of  the  pain  or 
pleasure  from  which  the  association  originated.  It  has  been  suggested 
by  the  able  %vriter  of  a  biogiaphical  sketch  of  Dr.  Priestley,  in  one  of 
our  monthly  periodicals,  that  the  same  elementary  law  of  our  mental 
constitution,  suitably  followed  out,  would  explain  a  variety  of  mental 
phenomena  hitherto  inexplicable,  and  in  particular  some  of  the  funda- 
mental diversities  of  human  character  and  genius.  Our  associations 
being  of  two  sorts,  either  between  synchronous,  or  between  successive 
impressions ;  and  the  influence  of  the  law  which,  renders  associations- 
stronger  in  proportion  to  the  pleasurable  or  painful  character  of  the 
impressions,  being  felt  with  peculiar  force  in  the  synchronous  class  of 
associations ;  it  is  remarked  by  the  writer  refeired  to,  that  in  minds  of 
strong  organic  sensibility  synchronous  associations  will  be  likely  to 
predominate,  producing  a  tendency  to  conceive  things  in  pictures  and 
m  the  concrete,  clothed  in  all  their  attributes  and  chcumstances,  a 
mental' habit  which  is  commonly  called  Imagination,  and  is  one  of  the 
peculiarities  of  the  painter  and  the  poet ;  while  persons  of  more  modern 
ate  susceptibility  to  plciisure  and  pain  will  have  a  tendency  to  asso- 
ciate facts  chiefly  in  the  order  of  tlieir  succession,  and  if  they  possess 
mental  superiority,  will  addict  themselves  to  history  or  science  rather 
than  to  creative  art.  This  interesting  speculation  the  author  (jf  the 
present  work  has  endeavored,  on  another  occasion,  to  pursue  further, 
and  to  explain,  by  means  of  it,  the  leading  peculiarities  of  the  poetical 
temperament.  It  is  at  least  an  example  which  may  sei-ve,  instead  of 
many  others,  to  show  the  extensive  scope  which  exists  for  deductive 

an  equable  pressure,  produced  by  a  bladder  partially  filled  with  air.  The  pressure,  by 
keeping  back  the  blood  from  the  part  prevents  the  inllainination,  or  the  tumor,  from  being 
nourished :  in  the  case  of  inflamiiialion,  it  removes  the  stimulus,  which  the  organ  is  unfit 
to  receive:  in  the  case  of  tumors,  by  keeping  back  the  nutritive  fluid,  it  causes  the  absorp- 
tion of  matter  to  exceed  the  supply,  and  the  diseased  misa  is  gradually  absorbed  and  dis- 
appears. '      ,    '  , 


286  INDUCTION'. 

inTOStlgation  iu  the  important  and  so  eminently  imperfect  Science  of 
Mind. 

§  7.  The  copiousness  with  which  I  have  exemphfied  the  discoveiy 
and  explanation  of  special  laws-  of  phenomena  by  deduction  from  sim- 
pler and  more  general  ones',  was  prompted  by  a  desire  to  characterize 
clearly,  and  place  in  its  due  position  of  importance,  the  Deductive 
Method ;  which,  in  the  present  state  of  knowledge,  is  destined  iiTevo- 
cably  to  predominate  in  the  course  of  scientific  investigation  from  this 
time  forward.  A  revolution  is  peaceably  and  progi'essively  effecting 
itself  in  philosophy,  the  reverse  of  that  to  which  Bacon  has  attached  his 
name.  That  great  man  changed  the  method  of  the  sciences  from 
deductive  to  experimental,  and  it  is  now  rapidly  reverting  from  experi- 
mental to  deductive.  But  the  deductions  which  Bacon  abolished  were 
from  premisses  hastily  snatched  up,  or  arbitrarily  assumed.  The  prin- 
ciples were  neither  established  by  legitimate  canons  of  experimental 
inquiry,  nor  the  results  tested  by  that  indispensable  element  of  a 
jatiohal  Deductive  Method,  verification  by  specific  experience.  Be- 
tween the  primitive  Method  of  Deduction  and  that  which  I  have 
Attempted  to  define,  there  is  all  the  difference  which  exists  between 
the  Aristotelian  physics  and  the  Newtonian  theory  of  the  heavens. 

That  the  advances  henceforth  to  be  expected  even  in  physical,  and 
still  more  in  mental  and  social  science,  will  be  chiefly  the  result  of 
deduction,  is  evident  from  the  general  considerations  already  adduced. 
Among  subjects  really  accessible  to  our  faculties,  those  which  still 
remain  in  a  state  of  dimness  and  uncertainty  (the  succession  of  their 
phenomena  not  having  yet  been  brought  under  fixed  and  recognizable 
laws)  are  mostly  those  of  a  very  complex  character,  in  Avhich  many 
agents-  are  at  work  together,  and  their  effects  in  a  constant  state  of 
blending  and  intermixture.  -  The  disentangling  of  these  crossing  threads 
is  a  task  attended  with  difficulties  which,  as  we  have  already  shown, 
are  susceptible  of  solution  by  the  instrument  of  deduction,  alone. 
!Peduction  is  the  great  scientific  work  of  the  present  and  of  future 
ages.  The  portion  henceforth  reser\-ed  for  specific  experience  in  the 
achievements  of  science,  is  mainly  that  of  suggesting  hints  to  be  fol- 
lowed up  by  the  deductive  inquijer,  and  of  cQnfirming  or  checking  his 
conclusions. 


CHAPTER  XIV. 

OF  THE  LIMITS  TO  THE  EXPLAXATIGN  OF  LAWS  OF  NATURE ;   AND  OP 
HYPOTHESES. 

§  1.  The  preceding  considerations  "have  Jed  us  to  recognize  a  dis- 
tinction between  two  kinds  of  laws,  or  observed  uniformities  in  nature : 
ultimate  laws,  and  what  may  be  termed  derivative  laws.  Derivative 
laws  are  such  as  are  deducible  from,  and  may,  in  any  of  the  modes 
which  we  have  pointed  out,  be  resolved  into,  other  and  more  general 
ones.  Ultimate  laws  are  those  which  cannot.  We  ate  not  sure  that 
any  of  the  uniformities  which  we  are  yet  acquainted  vvith  are  ultimate 
laws ;  but  we  know  that  there' must  be  ultimate  laws  ;  and  that  eYei7 


HYPOTHESES.  287 

resolution  of  a  ilerivativc  law  into  more  general  laws,  brings  us  nearer 
to  them. 

Since  we  are  continually  discovering  that  unifoi'mities,  not  previously 
known  to  he  other  than  ultimate,  are  derivative,  and  resolvable  into 
more  general  laws;  since  (in  other  words)  we  are  continually  discover- 
ing an  explanation  of  some  sequence,  which  was  previously  known  only 
as  a  fact ;  it  becomes  an  interesting  (piestion  whether  there  are  any  ne- 
cessary limits  to  this  philosophical  operation,  or  whether  it  may  proceed 
until  all  the  uniform  sequences  in  nature  are  resolved  into  some  one 
universal  law.  For  this  seems,  at  first  sight,  to  be  the  ultimatum 
towards  which  the  progress  of  induction,  by  the  Deductive  Method 
resting  on  a  basis  of  observation  and  experiment,  is  progressively 
tending.  Projects  of  this  kind  were  universal  in  the  infancy  of  j)liilo- 
sophy ;  any  speculations  which  held  out  a  less  brilliant  prospect,  being 
in  those  early-  times  deemed  not  worth  pursuing.  And  the  .idea 
receives  so  much  apparent  countenance  from  the  nature  of  the  most 
remarkable  achievements  of  modern  science,  that  speculators  are  e^ven 
now  constantly  rising  up  (more  often  on  the  continent  of  Europe  than 
in  this  island)  who  profess  either  to  have  solved  the  problem,  or  to 
suggest  modes  in  which  it  may  one  day  be  solved.  Even  where  pre- 
tensions of  this  magnitude  are  not  made,  the  character  of  the  sohrtions 
.which  are  given,  or  sought,  of  particiilar  classes  of  phenomena,  often 
involves  such  conceptions  of  what  constitutes  explanation,  as  would 
render  the  notion  of  explaining  all  phenomena  whatever  by  means  of 
some  one  cause,  or  law^  perfectly  admissible. 

§  2.  It  is,  therefore,  useful  to  remark,  that  the  ultimate  Laws  of  Na- 
ture caimot  possibly  be  less  numerous  than  the  distinguishable  sensations 
or  other  feelings  of  our  nature ; — those,  I  mean,  which  are  distinguishable 
from  one  another  in  quality,  and  not  merely  in  quantity  or  degree.  For 
example ;  since  there  is  a  phenomenon  sui  generis,  called  color,  Avhich 
our  consciousness  testifies  to  be  not  a  particular  degree  of  some  other 
phenomenon,  as  heat,  or  odor,  or  motion,  but  intrinsically  unlike  all 
others,  it  follows  that  there  are  ultimate  laws  of  color ;  that,  ajthough 
the  facts  of  color  may  admit  of  expUmation,  they  never  can  be  ex- 
plained from  laws  of  heat  or  odor  alone,  or  of  motion  alone,  but  that 
however  far  the  .explanation  may  be  can-ied,  there  will  always  remain 
in  it  a  law  of  color.  I  do  not  mean  that  it  might  not  possibly  be  shown 
that  some  other  phenomenon,  some  chemical  or  mechanical  action,  for 
example,  invariably  precedes,  and  is  the  cause  of,  every. phenomenon 
of  color.  But  although  this,  if  proved,  would  be  an  important  exten- 
sion of  our  knowledge  of  nature,  it  would  not  explain  how  or  why  a 
motion,  or  a  chemic^al  action,  should  produce  a  sensation  of  color ;  and 
however  diligent  might  bo  our  scrutiny  of  the  phenomena,  whatever 
number  of  hidden  -links  we  might  detect  in  the  chain  of  causation 
terminating  in  the  color,  the  la.st  link  would  still  be  a  law  of  color,  not 
a  law  of  motion,  nor  of  any  other  plienomenon  whatever.  Nor  does  thid 
observation  apply  only  to  color,  as  compared  with  any  other  of  the  great 
classes  of  sensations ;  it  applies  to  every  particular  color,  as  cohnpared 
with  others.  White  color  can  in  no  manner  be  explained  exclusively 
by  the  laws  of  the  production  of  red  color.  In  any  attempt  to  explain  it, 
we  cannot  but  introduce,  as  one  element  of  the  explanation,  the  prop- 
osition that  some  antecedent  or  other  produces  the  sensation  of  white. 


288  ixDUCTiOiV. 

The  ideal  limit,  therefore,  of  the  explanation  of  natural  phenomena 
(towards  Avhich  as  towards  other  ideal  limits  we  are  constantly  tendino-, 
without  the  prospect  of  ever  completely  attaining  it,)  would  be  to  show 
that  each  distinguishable  variety  of  our  sensations,  or  other  states  of 
conscioTisness,  has  only  one  sort  of  cause;  that,  for  example,  whenever 
we  perceive  a  white  color,  there  is  some  one  condition  or  set  of  con- 
ditions which  is  always  present,  and  the  presence  of  which  always 
produces  in  us  that  sensation.  As  long  as  there  are  several  kno%\Ti 
modes  of  production  of  a  phenomenon,  (several  different  substances, 
for  instance,  which  have  the  property  of  whiteness,  and  between 
which  we  cannot  trace  any  other  resemblance)  so  long  it  is  not  im- 
possible that  one  of  these  modes  of  production  may  be  resolved 
into  another,  or  that  all  of  them  may  be  resolved  into  some  more 
general  mode  of  production  not  hitherto  recognized.  But  wiien  the 
modes  of  production  are  reduced  to  one,  we  cannot,  in  point  of  sim- 
plification, go  any  further.  This  one  may  not,  after  all,  be  the  idtimate 
mode ;  there  may  be  other  links  to  be  discovered  between  the  sup- 
posed cause  and  the  effect;  but  We  can  only  fiirther  resolve  the  knoA\Ti 
law,  by  introducing  some  other  law  hitherto  unknowTi ;  which  will  not 
diminish  the  number  of  ultimate  laws. 

In  what  cases,  accordingly,  has  science  been  most  successful  in 
explaining  phenomena,  by  resolving  their  complex  laws  into  laws  of 
greater  simplicity  and  generality?  Hitherto  chiefly  in  cases  of  the 
propagation  of  various  phenomena  through  space  :  and,  first  and  prin- 
cipally, the  most  extensive  and  important  of  all  facts  of  that  description, 
the  fact  of  motion.  Now  this  is  entirely  what  might  be  expected  from 
the  principles  which  I  have  laid  doA\Ti.  Not  only  is  motion  one  of  the 
most  universal  of  all  phenomena,  it  is  also  (as  might  be  expected 
from  the  former  ciixumstance)  one  of  those  which,  apparently  at  least, 
are  produced  in  the  greatest  number  of  ways :  but  the  phenomepon 
itself  is  always,  to  our  sensations,  the  same  in  every  respect  but  degree. 
Differences  of  duration,  or  of  velocity,  are  e^ddently  differences  in 
degree  only ;  and  differences  of  direction  in  space,  which  alone  has 
any  semblance  of  being  a  distinction  in  kind,  entirely  disappear  (so  far 
as  our  sensations  are  concerned)  by  a  change  in  our  o^^'n  position ; 
indeed  the  very  same  motion  appears  to  us,  according  to  our  position, 
to  take  place  in  every  variety  of  direction,  and  njotions  in  every 
different  direction  to  take  place  in  the  same.  And,  again,  motion  in' 
a  straight  line  and  in  a  cur\-e  are  no  otherwise  distinct  than  that  the 
one  is  motion  continuing  in  the  same  direction,  the  other  is  motion 
which  at  each  instant  changes  its  direction.  Thei-e  is,  therefore, 
according  to  the  views  I  have  stated,  no  absurdity  in  supposing  that 
all  motion  may  be  produced  in  one  and  the  same  way ;  by  the  same 
kind  of  cause.  Accordingly,  the  greatest  achievements  in  physical 
science  have  consisted  in  resolving  one  observed  law  of  the  production 
of  motion  into  the  laws  of  other  known  modes  of  production,  or  the 
laws  of  several  such  modes  into  one  more  general  mode ;  as  when  the 
fall  of  bodies  to  the  earth,  and  the  motions  of  the  planets,  were  brought 
under  the  one  law  of  the  mutual  attraction  of  all  particles  of  matter ; 
when  the  motions  said  to  be  produced  by  magnetism  were  sho'ATi  to  be 
produced  by  electricity ;  when  the  motions  of  fluids  in  a  lateral  direc- 
tion, or  even  contrary  to  the  direction  of  gravity,  were  shoAvm  to  be 
produced  by  gravity ;  and  the  like.     There  is  an  abundance  of  distinct 


IIYPOTUESES.  289 

causes  of  motion  still  unresolved  into  one  another;  gravitation,  heat, 
electricity,  chemical  action,  nervous  action,  and  so  forth  ;  but  however 
improbable  it  may  be  that  these  different  modes  of  pi'oduction  of  mo- 
tion should  ever  actually  be  resolved  into  one,  the  attempt  so  to  resolve 
them  is  perfectly  legitimate.  For  though  these  various  causes  produce, 
in  other  respects,  sensations  intrinsically  different,  and  are  not,  there- 
fore, capable  of  being  resolved  into  one  another,  yet  in  so  far  as  they 
all  produce  motion,  it  is  quite  possible  that  the  immediate  antecedent 
of  the  motion  may  in  all  these  different  cases  be  the  same ;  that  the 
other  causes  may  produce  motion  through  the  intermediate  agency  of 
heat,  for  instance,  or  of  electricity,  or  of  some  common  medium  yet 
to  be  discovered. 

We  need  not  extend  our  illustration  to  other  cases,  as  for  instance 
to  the  propagation  of  light,  sound,  heat,  electricity,  &c.,  through  space, 
or  any  of  the  other  phenomena  which  have  been  found  susceptible  of 
explanation  by  the  resolution  of  their  observed  laws  into  more  general 
laws.  Enough  has  been  said  to  display  the  difference  between  the 
kind  of  explanation  and  resolution  of  laws  which  is  chimerical,  and 
that  of  which  the  accomplishment  is  the  great  aim  of  philosophy  ;  and 
to  show  into  what  sort  of  elements  the  resolution  must  be  effected, 
if  at  all. 

§  3.  As,  however,  there  is  scarcely  any  of  the  principles  of  a  true 
method  of  philosophizing  which  does  not  require  to  be  guarded  against 
errors  on  both  sides,  I  must  enter  a  caveat  against  another  misapprehen- 
sion, of  a  kind  directly  contrary  to  the  preceding,  and  against  which 
there  is  tb'^i  more  necessity  to  be  on  our  guard,  as  it  has  the  appear- 
ance of  being  countenanced  (for  I  am  persuaded  that  it  is  cmly  the 
appearance)  by  so  great  a  thinker  as  M.  Auguste  Comte.  That  phi- 
.  losopher,  among  other  occasions  on  which  he  has  condemned,  with 
some  asperity,  any  attempt  to  ex})lain  phenomena  which  are  "  evidently 
primordial"  (meaning,  ap^>arently,  no  more  than  that  every  such  phe- 
nomenon must  have  at  least  one  peculiar  and  inexplicable  law,)  has 
spoken  of  the  attempt  to  furnish  any  explanation  of  the  color  belonging 
to  each  substance,  "la  couleur  elemcntaire  propre  a  chaque  substance," 
as  essentially  illusory.  "  No  one,"  says  he,  "  in  our  time,  attempts  to 
explain  the  particular  specific  gravity  of  each  substance  or  of  each 
structure.  WTiy  should  it  be  otherwise  as  to  the  specific  color,  the 
notion  of  which  is  undoubtedly  no  less  primordial?"* 

Now  although,  as  M.  Comte  elsewhere  observes,  a  color  must  al- 
ways remain  a  different  thing  from  a  weight  or  a  sound,  it  ought  not 
to  be  forgotten,  and  notwithstanding  these  expressions,  cannot  possibly 
be  forgotten  by  M.  Comte,  that  varieties  of  color  might  nevertheless 
follow,  or  correspond  to,  givon  varieties  of  weight,  or  sound,  or  some 
other  phenomenon  as  different  as  these  are  from  color  .itself  It  is  one 
qu(!stion  what  a  thing  is,  and  another  what  it  depends  upcm  ;  and 
although  to  ascertain  the  ccmditions  of  an  elementary  phenomenon  is 
not  to  obtain  any  new  insight  into  the  nature  of  the  phenomenon  itself, 
that  is  no  reason  against  attempting  to  discover  the  conditions.  M. 
Corat(!'s  interdict  against  endeavoring  to  reduce  distinctions  of  color  to 
any  common  pnnciple,  would  have  held  equally  good  against  a  like 

»  Cours  de  Philosophic  Positive,  ii.  656. 

Oo 


290  INDUCTION. 

attempt  on  the  subject  of  distinctions  of  sound  ;  which  nevertheless 
have  been  found  to  be  immediately  preceded  and  caused  by  distin- 
guishable varieties  in  the  vibrations  of  elastic  bodies  :  although  a  sound, 
no  doubt,  is  quite  as  different  as  a  color  is  from  any  motion  of  particles, 
vibratory  or  otherwise.  We  might  add,  that,  in  the  case  of  colors, 
there  are  strong  positive  indications  that  they  are  not  ultimate  proper- 
ties of  the  different  kinds  of  substances,  but  depend  upon  conditions 
capable  of  being  superinduced  upon  all  substances ;  since  there  is  no 
'  substance  which  cannot,  according  to  the  kind  of  light  throvra  upon  it, 
be  made  to  assume  any  color  we  think  fit ;  and  since  almost  every 
change  in  the  mode  of  aggregation  of  the  particles  of  the  same  sub- 
stgince,  is  attended  with  alterations  in  its  color,  and  in  its  optical  prop- 
erties generally. 

The  real  defect  in  the  attempts  which  have  been  made  to  account 
for  colors  by  the  vibrations  of  a  fluid,  is  not  that  the  attempt  itself  is 
unphilosophical,  but  that  the  existence  of  the  fluid,  and  the  fact  of  its  • 
vibratory  motion,  are  not  proved  ;  but  are  assumed,  on  no  other  ground 
than  the  facihty  they  are  supposed  to  aflbrd  of  explaining  the  pheiiom-- 
,ena.  And  these  considerations  lead  us  to  the  important  question  of 
the  proper  use  of  scientific  hypotheses ;  a  subject  the  connexion  of 
which  with  that  of  the  explanation  of  the  phenomena  of  nature,  and  of 
the  necessary  limits  to  that  explanation,  needs  not  be  pointed  out. 

§  4.  An  hypothesis  is  any  supposition  which  we  make  (either  with- 
out actual  evidence,  or  upon  evidence  avowedly  insuflScient),  in  order 
to  endeavor  to  deduce  from  it  conclusions  in  accordance  with  facts 
which  are  known  to  .be  real;  under  the  idea  that  if  the  conclusions 
to  which  the  hypothesis  leads  are  known  truths,  the  hypothesis  itself 
either  must  be,  or  at  least  is  likely  to  be,  true.  If  the  hypothesis  relates 
to  the  cause,  or  mode  of  production  of -a  phenomenon,  it  will  serve,  if 
adrtiitted,.  to  explain  such  facts  as  are  found  cf^able  of  being  deduced  ' 
from  it;  And  this  explanation  is  the  purpose  of  many,  if  not  most 
hypotheses.  Since  explaining  in  the  scientific  sense  means  resolving 
an  uniformity  which  is  not- a  law  of  cavisation,  into  the  laws  of  causa- 
tion from  which  it  results,  or  a  complex  law  of  causation  into  simpl'er 
and  more  general  ones  from  which  it  is  capable  of  being  deductively 
inferred  ;  if  there  do  not  exist  any  known  laws  which  fulfill  this  re(]uire- 
ment,  we  may  feign  or  imagine  some  which  would  fulfill  it ;  and  this  is 
making  an  hypothesis.  i 

An  hypothesis  being  a  mere  supposition,  there  are  no  other  limits 
to  hypotheses  than  those  of- the  human  imagination;  we  may,  if  we 
please,  imagine,  by  way  of  accounting  for  an  effect,  some  cause  of  a 
kind  utterly  unknown,  and  acting  according  ta  a  law  altogether  fic- 
titious. But  as  hypotheses  of  this  sort  would  not ,  have  any  of  the 
plausibility  belonging  to  those  which  ally  themselves  by  analogy  with 
known  laws  of  nature,  and  besides  would  not  supply  the  want  which 
arbitrary  hypotheses  are  generally  invented  to  satisfy,  by  enabling  the 
•  imagination  to  represent  to  itself  an  obscure  phenomenon  in  a  familiar 
light ;  there  is  probably  no  hypothesis  in  the  history  of  science  in  which 
both  the  agent  itself  and  the  law  of  its  operation  were  fictitious.  Either 
the  phenomenon  assigned  as  the  cause  is  real,  but  the  law  accol-ding  to 
which  it  acts  merely  supposed  ;  or  the  cause  is 'fictitious,  but  is  sup- 
posed to  produce  its  effects  according  to  laws  similar  to  those  of  some 


HYPOTHESES.  201 

known  class  of  plicnomena.  An  instance  of  the  first  kind  is  afforded 
by  the  dift'ercnt  suppositions  respecting  the  law  of  the  planetary  cen- 
tral force,  anterior  to  the  discovery  of  the  true  law,  that  the  force  vaines 
as  the  inverse  square  of  the  distance  ;  which  was  itself  suggested  by 
Newton,  nn  the  first  instance,  as  an  hypothesis,  and  was  verified  by 
proving  that  it  led  deductively  to  Kepler's  laws.  Hypotheses  of  the 
second  kind  are  such  as  the  vortices  of  Descartes,  which  were  fictitious, 
but  were  supposed  to  obey  the  known  laws  of  rotatory  motion  ;  or  the 
two  rival  hypotheses  respecting  the  nature  of  light,  the  one  ascribing 
the  phenomena  to  a  fluid  emitted  fiom  all  luminous  bodies,  the  other 
(now  more  generally  received)  attributing  them  to  vibratory  motions 
among  the  particles  of  an  ether  peiTading  all  space.  Of  the  existence 
of  either  fluid  there  is  no  evidence,  save  the  explanation  they  are  cal- 
culated to  afford  of  some  of  the  phenomena;  but  they  are  supposed  to 
produce  their  effects  according  to  known  laws  ;  the  ordinary  laws  of 
continued  locomotion  in  the  one  case,  and  in  the  other,  those  of  the 
propagation  of  undulatory  movements  among  the  particles  of  an  elastic 
fluid. 

According  to  the  foregoing  remarks,  hypotheses  are  invented  to  en- 
able the  Deductive  Method  to  be  earlier  applied  to  phenomena.  But* 
in  order  to  discover  the  cause  of  any  phenomena  by  the  Deductive 
Method,  the  process  mTist  consist  of  three  parts ;  induction,  ratiocin- 
ation, and  verification.  Induction,  (the  place  of  which,  however,  may 
be  supplied  by  a  prior  deduction,)  to  ascertain  the  laws  of  the  causes ; 
ratiocination,  to  compute  from  those  laws,  how  the  causes  will  oper- 
ate in  the  particular  combination  known  to  exist  in  the  case  in  hand  ;• 
verification,  by  comparing  this  calculated  effect  with  the  actual  phe- 
nomenon. No  one  of  these  three  parts  of  the  process  can  be  dis- 
pensed with.  In  the  great  deduction  which  proves  the  identity  of 
gravity  and  the  central  force  of  the  solar  system,  all  the.  three  are 
found.  First,  it  is  proved  from  the  moon's  motions,  that  the  earth 
a;ttracts  her  with  a  force  varying  as  the  inverse  square  of  the  distance. 
This  (though  partly  dependent  on  prior  deductions)  con-esponds  to 
'  the  first,  or  purely  inductive  step,  the  ascertainment  of  the  law  of  the 
cause.  Secondly,  fi-om  this  law,  and  from  the  knowledge  previously 
obtained  of  the  moon's  mean  distance  from  the  earth,  and  of  the  actual 
amount  of  her  deflexion  fi'om  the  tangent,  it  is  ascertained  with  what 
rapidity  the  earth's  attraction  would  cause  her  to  fall,  if  she  were  no 
further  off*,  and  no  more  acted  upon  by  extraneous  forces,  than  teiTes- 
ti'ial  bodies  are:  this  is  the  second  step,- the  ratiocination.  Fing,lly, 
this  calculated  velocity  being  compared  with  the  observed  velocity 
with  whicli  all  heavy  bodies  fall,  by  mere  gi-aVity,  towards  the  surface 
of  the  earth,  (namely  sixteen  feet  in  the  first  second,  forty-eight  in  the 
second,  and  so  forth,  in  thq^ratio  of  the  odd  numbers,  1,  3,  5,  &c.,)  the 
two  quantities  were  found  to  agree.  The  order  in  which  I  liaye  here 
presented  the  three  steps  was  not  the  exact  -order  of  their  discovery  ; 
but  it  is  their  correct  logical .  order,  as  portions  of  the  proof  that  the 
same  attraction  of  the  earth  wliich  causes  the  nioon's  motion,  causes 
also  the  fall  of  heavy  bodies  to  the  earth :  a,  proof  which  is  thus  com- 
plete In  all  its  parts.  '  ' 

Now,  the  Hypothetical  Method  suppresses  the  first  of  the  three  steps, 

»  Vide  supra,  p.  264. 


292  INDUCTION. 

the  induction  to  ascertain  the  law ;  and  contents  itself  with  the  other 
two  operations,  ratiocination  and  verification ;  the  law,  which  is  rea- 
soned from,  being  assumed,  instead  of  proved. 

This  process  may  evidently  be  legitimate  upon  one  supposition, 
namely,  if  the  nature  of  the  case  be  such  that  the  final  step,  the  verifi- 
cation, shall  amount  to,  and  fulfill  the  conditions  of,  a  complete  induc- 
tion. We  want  to  be  assured  that  the  law  we  have  hypothetically 
assumed  is  atrue  one  ;  and  its  leading  deductively  to  true  results  will 
afford  this  assurance,  provided  the  case  he  such  that  a  false  law  can- 
not lead  to  a  true  result ;  provided  no  law,  except  the  very  one  which 
we  have  assumed,  can  lead  deductively  to  the  same  conclusions  which 
that  leads  to.  And  this  proviso  is  very  often  realized.  For  example, 
in  that  perfect  specimen  of  deduction  which  we  just  cited,  the  original 
mgj or  premiss  of  the  ratiocination,  the  law  of  the  atti'active  force,  was 
ascertained  in  this  very  mode  ;  by  this  legitimate  employment  of  the 
Hypothetical  Method.  Newton  began  by  an  assumption,  that  the 
force  which  at  each  instant  deflects  a  planet  from  its  rectilineal  course, 
and  makes  it  describe  a  curve  round  the  sun,  is  a  force  tending  directly 
towards  the  sun;  He  then  proved  that  if  this  be  so,  the  planet  will  de- 
scribe, as  we  know  by  Kepler's  first  law  that  it  does  describe,  equal 
areas  in  equal  times  ;  and,  lastly,  he  proved  that  if  the  force  acted  in 
any  other  direction  whatever,  the  planet  would  not  describe  equal 
areas  in  equal  times.  It  being  thus  shown  that  no  other  hypothesis 
could  accord  with  the  facts,  the  assumption  was  proved;  the  hypothe- 
sis became  a  law,  established  by  the  Method  of  Difference.  Not  only 
did  Newton  ascertain,  by  this  hypothetical  process,  the  direction  of  the 
deflecting  force  ;  he  proceeded  in  exactly  the  same  manner  to  ascer- 
tain the  law  of  variation  of  the  quantity  of  that  force.  He  assumed 
that  the  force  varied  inversely  as  the  square  of  the  distance  ;  showed 
that  from  this  assumption  the  remaining  two  of  Kepler's  laws  might  be 
deduced';  and,  finally,  that  any  other  law  of  variation  would  give  re- 
sults inconsistent  with  those  laws,  and  inconsistent,  therefore,  with  the 
real  motions  of  the  planets,  of  wliich  Kepler's  laws  were  k■now^l  to  be 
a  correct  expression. 

It  is  thus  perfectly  possible,  and  indeed  is  a  very  common  occur- 
rence, that  what  is  an  hypothesis  at  the  beginning  of  the  inquiry 
becomes  a  proved  law  of  nature  before  its  close.  But  this  can  only 
happen  when  the  inquiry  has  for  its  object,  not  to  detect  an  unknown 
cause,  but  to  detennine  the  precise  law  of  a  cause  already  ascertained. 
If  it  had  not  been  already  known  that  the  planets  were  hindered  from 
mo\ang  in  straight  lines  by  some  force  tending  towards  the  interior  of 
their  orbit,  though  the  exact  du-ection  was  doubtful ;  or  if  it  had  not 
been  known  tliat  the  force  inci'eased  in  some  proportion  or  other  as  the 
distance  diminished,  and  diminished  as  it-irncreased  ;  Newton's  argu- 
ment would  not  have  proved  his  conclusion.  These  facts,  however, 
being  already  certain,  the  range  of  admissible  suppositions  was  limited 
to  the  various  possible  directions  of  a  line,  and  the  various  possible 
numerical  relations  between  the  variations  of  the  distance  and  the 
variations  of  the  attractive  force :  now  among  these  it  was  easily 
shown  that  different  suppositions  could  not  lead  to  identical  conse- 
quences. 

Accordingly,  Newton  could  not  have  performed  his  second  great 
philosophical  operation,  that  of  identifying  teiTestrial  giavity  with  the 

E  E 


HYPOTHESES.  293 

Central  force  of  the  solar  system,  by  the  same  hypothetical  method. 
When  the  law  of  tlie  moon's  attraction  had  been  proved  from  the  data 
of  the  moon  itself,  then  on  finding  the  same  law  to  accord  with  the  phe- 
nomena of  teiTOstrial  gravity,  he  was  wan-anted  in  adopting  it  as  the 
law  of  those  phenomena  likewise  :  but  it  would  not  have  bcim  allow- 
ai)le  for  him,  without  any  lunar  data,  to  assume  that  the  moon  was 
attracted  towards -the  earth  with  a  force  as  the  inverse  square  of  the 
distance,  merely  because  that  ratio  would  enable  him  to  account  for 
gravity  by  a  similar  attraction :  for  it  would  have  been  impossible  for 
him  to  prove  that  the  observed  law  of  the  fall  of  heavy  bodies  to  the 
earth  could  not  result  from  any  force,  save  one  extending  to  the  moon, 
and  proportional  to  the  inverse  square. 

It  appears,  then,  to  be  a  condition  of  a  genuinely  scientific  hy- 
pothesis, that  it  be  not  destined  always  to  remain  an  hypothesis, 
but  be  certain  to  be  either  proved  or  disproved  by  that  comparison 
with  observed  tacts  which  is  tenned  Verification.  In  hypotheses  of 
this  character,  if  they  relate  to  causation  at  all,  the  effect  must  be  al- 
ready known  to  depend  upon  the  very  cause  supposed,  and  the  hypo- 
thesis must  relate  only  to  the  precise  mode  of  dependence ;  the  law  of 
the  variation  of  the  effect  according  to  the  variations  in  the  quantity  or 
in  the  relations  of  the  cause.  With  these  may  be  classed  the  hypo- 
theses which  do  not  make  any  supposition  with  regard  to  causation, 
but  only  with  regard  to  the  law  of  coiTespondence  between  facts  which 
accompany  each  other  in  their  variations,  though  there  may  be  no  rela- 
tion of  cause  and  effect  between  them.  Such  are  the  different  false 
hypotheses  which  Kepler  made  respecting  the  law  of  the  refraction  of 
light.  It  was  known  that  the  direction  of  the  line  of  refi-action  varied 
with  every  variation  in  the  direction  of  the  line  of  incidence,  but  it  was 
not  known  hoAV ;  that  is,  what  changes  of  the  one  corresponded  to  the 
different  changes  of  the  other.  In  this  case  any  law,  different  from  the 
true  one,  must  have  led  to  false  results.  And,  lastly,  we  must  add  to 
these,  all  hypothetical  modes  of  merely  descrihhig  phenomena;  such  as 
the  hypothesis  of  the  ancient' astronomers  that  the  heavenly  bodies 
moved  in  circles ;  the  various  hypotheses  of  eccentrics,  deferents,  and 
epicycles,  which  were  added  to  that  original  hypothesis  ;  the  nineteen 
false  hypotheses  which  Kepler  made  and  abandoned  respecting  the 
form  of  the  planetary  orbits ;  and  even  the  true  doctrine  in  which  he 
finally  rested,  that  those  orbits  are  ellipses,  which  was  but  an  hypo- 
thesis like  the  rest  until  verified  by  facts. 

In  all  these  cases,  verification  is  proof;  if  the  supposition  accords 
with  the  phenomena  there  needs  no  other  evidence  of  it.  But  in 
order  that  tWs  may  be  the  case,  it  is  (as  we  have  seen)  necessary, 
when  the  hypothesis  relates  to  causation,  that  the  sup])osed  cause 
should  not  only  be  a  real  phenomenon,  something  actually  existing  in 
nature,  but  should  be  already  known  to  have  some  influence  upon  the 
supposed  effect ;  the  precise  degree  and  manner  of  the  influence  being 
the  only  point  undetermined.  In  any  other  case,  it  is  no  evidence  of 
the  truth  of  the  hypothesis  that  we  are  able  to  deduce  the  real  phe- 
nomena from  it.  -  f 

Is  it,  then,  never  allowable,  in  a  scientific  hypothesis,  to  assume  a 
cause ;  but  only  to  ascribe  an  assumed  law  to  a  known  cause  ?  I  do 
not  assert  this.  I  only  say,  that  in  the  latter  case  alone  can  the  hypo- 
thesis be  received  as  true  merely  because  it  explains  the  phenomena : 


294  ixVDUCTiox. 

in  the  former  case  it  is  only  useful  by  suggesting  a  line  of  investigation 
which  may  possibly  terminate  in  obtaining  real  proof  For  this  pixr- 
pose,  as  is  justly  remarked  by  M.  Comte  (who  of  all  philosophers 
seems  to  me  to  have-  approached  the  nearest  to  a  sound  view  of  this 
important  subject),  it  is  indispensable  that  the  cause  suggested  by  the 
hypothesis  should  be  in  its  o\%ti  nature  susceptible  of  being  proved  by 
other  evidence.  This  seems  to  be  the  philosophical  import  of  Newton's 
maxim  (so  often  cited  with  approbation  by  subsequent  A\Triters),  that 
the  cause  assigned  for  any  phenomenon  must  not  only  be  such  as  if 
admitted  would  explain  the  phenomenon,  but  must  also  be  a  vera  causa. 
What  he  meant  by  a  vera  causa  Newton  did  not  indeed  very  explicitly 
define  ;  and  I\Ir.  AVhewell,  who  dissents  from  the  propriety  of  any  such 
restriction  upon  the  latitude  of  framing  hypotheses,  has  had  little  diffi- 
culty in  showing*  that  his  conception  of  it  was  neither  precise  nor  con- 
sistent with  itself:  accordingly  his  optical  theory  was  a  signal  instance 
of  the  violation  of  his  owm  rule.  And  Mr.  AVhewell  is  clearly  right  in 
denying  it  to  be  necessary  that  the  cause  assigned  should  be  a  cause 
already  known ;  else  how  could  we  ever  become  acquainted  with  any 
new  cause?  But  what  is  true  in  the  maxim  is,  that  the  cause,  although 
not  kno-vvn  previously,  should  be  capable  of  being  kno\vn  thereafter ; 
that  its  existence  should  be  capable  of  being  detected,  and  its  con- 
nexion with  the  effect  ascribed  to  it,  susceptible  of  being  proved,  by 
independent  e\-idence.  The  hypothesis,  by  suggesting  obsei"\-ations 
and  experiments,  puts  us  upon  the  road  to  that  independent  evidence 
if  it  be  really  attainable ;  and  till  it  be  attained,  the  hypothesis  ought 
not  to  count  for  more  than  a  suspicion. 

§  5.  This  function,  however,  of  hypotheses,  is  one  which  must  be 
reckoned  absolutely  indispensable  in  science.  A\'Tien  Newton  said, 
"  Hypotheses  non  fingo,"  he  did  not  mean  that  he  deprived  himself  of 
the  facilities  of  investigation  afforded  by  assuming  in  the  first  instance 
what  he  hoped  ultimately  to  be  able  to  prove.  Without  such  assump- 
tions, science  could  never  have  attained  its  present  state :  they  are 
necessary  steps  in  the  progress  to  something  more  certain  ;  ajid  nearly 
everything  which  is  now  theory  was  once  hypothesis.  Even  in  purely 
experimental  science,  some  inducement  is  necessary  for  tiying  one 
•experiment  rather  than  another ;  and  although  it  is  abstractedly  possi- 
ble that  all  the  experiments  which  have  been  tried,  might  have  been 
produced  by  the  mere  desire  to  ascertain  what  would  happen  in  certain 
■cii'cumstances,  without  any  previous  conjecture  as  to  the  result ;  yet 
in  point  of  fact  those  unobvious,  delicate,  and  often  cumbrous  and 
tedious  processes  of  experiment,  which  have  thrown  most  light  upon 
the  general  constitution  of  nature,  would  hardly  ever  have  been  under- 
taken by  the  persons  or  at  the  time  they  were,  unless  it  had  seemed 
to  depend  upon  them  whether  some  general  doctrine  or  theory  which 
had  been  suggested,  but  not  yet  proved,  should  be  admitted  or  not. 
If  this  be  true  even  of  merely  experimental  inquiry,  the  conversion  of 
experimental  into  deductive  truths  could  still  less  have  been  effected 
without  large  temporary  assistance  from  hypotheses.  The  process  of 
tracing  regularity  in  any  complicated  and  at  first  sight  confused  set  of 
appearances,  is  necessarily  tentative  :  we  begin  by  making  any  suppo 

*  Philosophy  of  the  Inductive  Sciences,  vol,  ii.,  pp.  441-6. 


HYrOTHESES.  205 

sition,  even  a  false  one,  to  see  what  consequences  will  follow  from  it  ; 
and  by  observing  how  these  differ  from  the  real  phenomena,  we  learn 
what  corrections  to  make  in  our  assumption.  The  simplest  supposition 
which  accords  with  any  of  the  most  obvious  facts,  is  the  best  to  begin 
•with ;  because  its  conseciuences  are  the  most  easily  traced.  This  rude 
hypothesis  is  then  rudely  corrected,  and  the  operation  repeated ;  and 
the  comparison  of  the  consequences  deducible  from  the  corrected  hypo- 
thesis, with  the  observed  facts,  sugge^sts  still  further  correction,  until 
the  deductive  results,  are  at  last  made  to  tally  with  the  phenomena. 
"Some  fact,"  says  M.  Comte,*  "is  as  yet  little  understood,  or  some 
law  is  unknown :  we  frame  on  the  subject  an  hypothesis  as  accordant 
a.s  possible  with  the  whole  of  the  data  already  possessed;  and  the 
science,  being  thus  enabled  to  move  forward  freely,  always  ends  by 
leading  to  new  comsequences  capable  of  observation,  which  either- con^ 
firm  or  reflite,  unequivocally,  the  first  supposition."  Neither  indiiction 
nor  deduction,  he  justly  remarks,  would  enable  us  to  understand  even 
the  simplest  phenomena,  "if  we  did  not  often  conimcnce  by  a.nticipa-^ 
ting  on  the  results  ;  by  making  a  provisional  supposition,  at  first  essen- 
tially conjectural,  as  to  some  of  the  very  notions  which  constitute  the 
final  object  of  the  inquiry. "t  Let  any  one  watch  the  manner  in  which 
he  himself  unravels  any  complicated  mass  of  evidence  ;  let  him  observe 
how,  for  instance,  he  elicits  the  true  history  of  any  occurrence  from 
the  involved  statements  of  one  or  of  many  witnesses :  he  will  find  that 
he  does  not  take  all  the  items  of  evidence  into  his  mind  at  once,  and 
attempt  to  weave  them  together :  the  human  faculties  are  not  equal  to 
such  an  undertaking :  he  extemporizes,  from  a  few  of  the  particulars, 
a  first  rude  theory  of  the  rhode  in  which  the  facts  took  place,  and  then 
looks  at  the  other  statements  one  by  one,  to  try  whether  they  can  be 
reconciled  ^vith  that  provisional  theory,  or  what  corrections  or  additions 
it  requires  to  make  it  square  with  tliem.  In  this  Avay,  which,  as  M. 
Comte  remarks,  has  some  resemblance  to  the  Methods  of  Approxima- 
tion of  mathematicians,  we  arrive,  by  means  of  hypotheses  at  cojiclu- 
sions  not  hypothetical.!     • 

Cours  de  Philosophic  Positive,  ii.,  p.  437  t  Ibid,  p.  434. 

X  As  an  example  of  a  legititnate  hypotnesis  according  to  ihe.  test  here  laid  down,  M. 
Comte  cites  that  of  Broussais,  who,  proceeding  on  tht^  very  rational  principle  that  every 
disease  must  originate  in  some  definite  part  or  other  of  the  organism,  boldly  assumed  that 
certain  fevers,  which  not  being  known  to  bo  local  were  called  constitutional,  had  their 
origin  in  the.  mucous  membrane  of  the  alimentary  canal.  The  supposition  was  indeed,  as 
there  is  strong  ground  to  believe,  erroneous  ;  but  he  was  justified  jn  making  it,  since  by 
deducing  the  consequences  of  the  supposition;  and  comparing  them  with  the  facts  of  those 
maladies,  he  might  be  certain  of  disproving  his  hypothesis  in  case.itwas  ill  founded,  and 
might  expect  that  the  comparison  would  materially  aid  him  in  framing  another  more  con- 
formable to  the  phenomena. 

The  doctrine,  now  ontversally  received,  that  the  earth  is  a.  great  natural  magnet  with 
two  poles,  was  originally  an  hypothesis  of  the  celebrated  Gilbert. 

Another  hypothesis,  to  the  legitimacy  of  which  no  objection  can  lie,  and  one  which  is 
well  calculated  to  light  the  path  of  scientific  inquiry,  is  that  spggested  both  by  Dr.  Arnott 
and  Sir  John  Herschel,  that  the  brain  is  a  voltaic  pile,  and  that  each  of  its  pulsations  is  a 
discharge  of  electricity  through  the  system.  It  has  been  remarked  that  the  scnsatinn  felt 
by  the  hand  from  the  beating  of  a  brain,  or  even  of  the  great  arteries,  bears  a  strong  resem- 
blance to  a.  voltaic  shock.  And  the.  hypothesis,  if  followed  to  its  consequen<ies,. might 
afford  a  plausible  explanation  of  many  physiological  facts,  while  there  is  nothing  to  dis- 
courage the  hope  that  we  may  in  time  sufficiently  understand  the  conditions  of  voltaic 
phenomena  to  render  the  truth  of  the  hypothesis  amenable  to  observation  and  experiment. 

The  attempt  to  localize,  iri  different  regions  of  the  brain,  the  physical  organs  of  our  dif- 
ferent mental  faculties  and  propensities,  was,  on  the  part  of  its  original  author,  a  strictly 
legitimate  example  of  a  scientific  hypothesis ;  arid  we  ought  not,  therefore,  to  blame  him 
for  the  extremely  slight  grounds  on  which  he  often  proceeded,  in  an  operation  which 


296  INDUCTION. 

§  6.  It  is  perfectly  consistent  witli  the  spirit  of  the  method,  to  assume 
in  this  provisional  manner  not  only  an  hypothesis  respecting- the  law  of 
what  we  alreatly  know  to  be  the  cause,  but  an  hypoihesis  respecting 
the  cause  itself.  It  is  allowable,  useful,  and  often  even  necessary,  to 
begin  by  asking  ourselves  what  cause  7nay  have  produced  the  effect, 
in  order  that  we  may  know  in  what  direction  to  look  out  for  evidence 
to  determine  whether  it  actually  did.  The  vortices  of  Descartes  would 
have  been  a  perfectly  legitimate  hypothesis,  if  it  had  been  possible,  by 
any  mode  of  exploration  which  we  could  entertain  the  hope  of  ever 
possessing,  to  bring  the  question,  whether  such  vortices  exist  or  not, 
within  the  reach  of  our  observing  faculties.  The  hypothesis  was  vicious,- 
simply  because  it  could  not  lead  to  any  course  of  investigation  capable 
of  converting  it  from  an  hypothesis  into  a  proved  fact.  The  prevailing 
hypothesis  of  a  luminiferous  ether  I  cannot  but  consider,  with  M.  Comte, 
to  be  tainted  with  the  same  vice.  It  can  never  be  brought  to  the  test 
of  observation,  because  the  ether  is  supposed  wanting  in  all  the  proper- 
ties by  means  of  which  our  senses  take  cognizance  of  external  phe- 
nomena. It  can  neither  be  seen,  heard,  smelt,  tasted,  nor  touched. 
The  possibility  of  deducing  from  its  supposed  laws  a  considerable 
number  of  the  phenomena  of  light,  is  the  sole  evidence  of  its  existence 
that  we  have  ever  to  hope  for;  and  this  evidence  cannot  be  of  the 
smallest  value,  because  we  cannot  have,  in  the  case  of  such  an  hypoth- 
esis, the  assurance  that  if  the  hypothesis  be  false  it  must  lead  to  results 
at  variance  with  the  true  facts. 

Accordingly,  most  thinkers  of  any  degree  of  sobriety  allow,  that  an 
hypothesis  of  this  kind  is  not  to  be  received  as  probably  true  because 
it  accounts  for  all  the  known  phenomena;  since  this  is  a  condition 
often  fulfilled  equally  well  by  two  conflicting  hypotheses ;  and  if  we 
give  ourselves  the  license  of  inventing  the  causes  themselves  as  well  as 
their  laws,  a  person  of  fertile  imagination  might  devise  a  hundred 
modes  of  accounting  for  any  given  fact,  while  there  are  probably  a 
thousand  more  which  are  equally  possible,  but  which,  for  want  of 
anything  analogous  in  our  experience,  our  minds  are  unfitted  to  con- 
ceive. But  it  seems  to  be  thought  that  an  hypothesis  of  the  sort  in 
question  is  entitled  to  a  more  favorable  reception,  if  besides  account- 
ing for  all  the  facts  previously  known,  it  has  led  to  the  anticipation  and 
prediction  of  others  which  experience  afterwards  verified;  as  the  un- 
dulatory  theory  of  light  led  to  the  prediction,  subsequently  realized  by- 
experiment,  that  two  luminous  rays  might  meet  each  other  in  such  a 
manner  as  to  produce  darkness.  Such  predictions  and  their  Hilfilment 
are,  indeed,  well  calculated  to  strike  the  ignorant  vulgar,  whose  faith 
in. science  rests  solely  upon  similar  coincidences  between  its  prophe- 
cies and-  what  comes  to  pass.  But  it  is  strange,  that  any  considerable 
stress  should  be  laid  upon  such  a  coincidence  by  scientific  thinkers.  If 
the  laws  of  \k\e  propagation  of  light  accord  with  those  of  the  vibra- 

could  only  be  tentative,  though  we  may  regret  that  materials  barely  sufficient  for  a  first 
rude  hypothesis  should  have  been  hastily  worked  up  by  his  successors  into  the  vain  sem- 
blance of  a  science.  Whatever  'there  may  be  .of  reality  in  the  connexipn  between  the 
scale  of  mental  endowments  and  the  various  degrees  of  complication  in  the  ceiehral  system 
(and  that  there  is. some  such  connexion  comparative  anatomy  seems  strongly  to  indicate), 
it  was  in  no  other  way  so  likely  to  be  brought  to  light  as  by  framing,  in  the  first  instance, 
an  hypothesis  similar  to  that  of  Gall.  But  the  verification  of  any  such  hypothesis  is  at- 
tended, from  the  peculiar  nature  of  the  phenomena,  with  difficulties  whi<;h  phrenologists 
have  not  hitherto  shown  themselves  §ven  competent  to  appreciate,  much  less  to  over- 
come. .  " 


HYPOTHESES.  297 

tions  of  an  clastic  fluicl  in  as  many  respects  as  is  necessary  to  make  the 
hypothesis  a  plausible  explanation  of  all  or  most  of  the  phenomena 
known  at  the  time,  it  is  nothing  strange  that  they  should  accord  with 
each  other  in  one  respect  more.  Though  twenty  such  coincidences 
should  occur,  tliey  would  not  prove  the  reality  of  the  undulatory  ether ; 
it  would  not  follow  that  the  phenomena  of  light  were  results  of  the  laws 
of  elastic  fluids,  but  at  most  that  they  are  governed  by  laws  in  some 
measure  analogous  to  these ;  which,  we  may  observe,  is  already  cer- 
tain, from  the  fact  that  the  hypothesis  in  question  could  be  for  a  mo- 
ment tenable.  There  are  many  such  harmonics  ninning  through  the 
laws  of  phenomena  in  other  respects  radically  distinct.  The  remark- 
able resemblance  between  the  laws  of  light  and  many  of  the  laws  of 
heat  (while  others  are  as  remarkably  diflbrent),  is  a  case  in  point. 
There  is  an  extraordinary  similarity  running  through  the  properties, 
considered  generally,  of  certain  substances,  as  chlorine,  iodine,  and 
brome,  or  sulphur  and  phosphorus ;  so  much  so  that  when  chemists 
discover  any  new  property  of  the  one,  they  not  only  are  not  surprised, 
but  expect,  to  find  that  the  other  or  others  have  a'property  analogous 
to  it.  But  the  hypothesis  that  chlorine,  iodine,  and  brome,  or  that 
sulphur  and  phosphorus,  are  the  same  substances,  would,  no  doubt, 
be  quite  inadmissible. 

I  do  not,  like  M.  Comte,  altogether  condemn  those  who  employ  them- 
selves in  working  out  into  detail  this  sort  of  hypotheses ;  it  is  useful  to 
-ascertain  what  are  the  known  phenomena  to  the  laws  of  which  those 
of  the  subject  of  inquiry  bear  the  greatest,  or  even  a  great  analogy, 
since  this  may  suggest  (as  in  the  case  of  the  luminiferous  ether  it  ac~ 
tually  did)  experiments  to  determine  whether  the  analogy  which  goes 
so  far  does  not  extend  still  further.  But  that  in  doing  this,  men  should 
imagine  themselves  to  be  seriously  inquiring  whether  the  hypothesis  of 
an  ether,  an  electric  fluid,  or  the  like,  is  true ;  that  they  should  fancy 
it  possible  to  obtain  the  assurance  that  the  phenomena  are  produced 
in  that  way  and  no  other ;  seems  to  me,  I  confess,  as  unworthy  of  the 
present  improved  conceptions  of  the  methods  of  physical  science,  as  it 
does  to  M.  Comte.  And  at  the  risk  of  being  charged  with  want  of 
modesty,  I  cannot  help  expressing  astonishment  that  a  philosopher  of 
the  extraordinary  attainments  of  INIr.  Whewell,  should  have  written  an 
elaborate  treatise  on  the  philosophy  of  induction,  in  which  he  recog- 
nizes absolutely  no  mode  of  induction  except  that  of  trying  hypothesis 
after  hypothesis  until  one  is  found  which  fits  the  phenomena ;  which 
one,  when  found,  is  to  be  assumed  as  true,  with  np  other  reservation 
than  that  if  on  reexamination  it  should  appear  to  assume  more  than  is 
needfid  for  explaining  the  phenomena,  the  superfluous  part  of  the,  as- 
sumption sliould  be  cut  off".  It  is  no  exaggeration  to  say  that  the  pro- 
cess which  we  have  described  in  these  few  words,  is  the  beginning, 
middle,  and  end  of  the  phitosojdiy  of  induction  as  Mr.  Whewell  con- 
ceives it.  And  this  without  the  slightest  distinction  between  the  cases 
in  which  it  may  be  known  beforehand  that  two  different  hypotheses 
cannot  lead  to  the  same  result,  and  those  in  which,  for  aught  we  can- 
ever  know,  the  range  of  suppositions,  all  equally  consistent  with  the 
phenomena,  may  be  infinite. 

§  7.  It  is  necessary,   before  quitting  the  subject  of  hypotheses,  to 
guard  against  the  appearance  of  reflecting  upon  the  philosophical  eer- 
P  p 


298  INDUCTION. 

tainty  of  several  branches  of  physical  inquiry,  which,  although  only  in 
their  infancy,  I  hold  to  be  strictly  inductive.  There  is  a  gi'eat  differ- 
ence between  inventing  laws  of  nature  to  account  for  classes  of  phe- 
njomena,  and  merely  endeavoring,  in  conformity  with  known  laws,  to 
conjecture  what  collocations,  now  gone  by,  may  have  given  birth  to 
individual  .facts  still  in  existence.  The  latter  is  the  strictly  legitimate 
operation  of  inferring  from  an  observed  effect,  the  existence,  in  time 
past,  of  a  cause  similar  to  that  by  which  we  know  it  to  be  produced  in 
all  cases  in  whiqh  we  have  actual  experience  of  its  origin.  This,  for 
example,  is  the  scope  of  the  inquiries  of  geology ;  and  they  ai'e  no 
more,  illogical  or  visionary  than  judicial  inquiries,  which  also  aim  at 
discovering  a  past  event  by  inference  from  those  of  its  effects  which 
still  subsist.  As  we  can  ascertain  whether  a  man  was  murdered  or 
died  a  natural  death,  from  the  indications  exhibited  by  the  corpse, 
the  presence  or  absence  of  signs  of  struggling  on  the  ground  or  on  the 
adjacent  objects,  the  marks  of  blood,  the  footsteps  of  the  supposed 
murderers,  and  so  on,  proceeding  throughout  upon  uniformities  ascer- 
tained-by  a  perfect  induction  without  any  mixture  of  hypothesis ;  so  if 
we  find,  on  and  beneath  the  surface  of  our  planet,  masses  exactly 
similar  to  deposits  from  water,  or  to  results  of  the  cooling  of  matter 
melted  by  fire^  we  may  justly  conclude  that  such  has  been  their  origin ; 
and  if  the  effects,  though  similar  in  kind,  are  on  a  far  larger  scale  than 
any  which  are  produced  now,  we  may  rationally,  and  without  hypoth- 
esis, conclude  that;  the  causes  existed  formerly  with  greater  intensity. 
Further  than  this  no  geologist  of  authority  has,  since  the  rise  of  the 
present  enlightened  school  of  geological  speculation,  attempted  to  go. 
In  many  geological  inquiries  it  doubtless  happens,  that  although  the 
laws  to  which  the  phenomena  are  ascribed  are  known  laws,  and  the 
agents  known  agents,  those  agents-  are  not  known  to  have  been  pres- 
ient  in  the  particular  case,.  Thus  in  the  speculation  respecting  the 
igneous  origin,  of  trap  or  granite,  the  fact  does  not  admit  of  direct 
proof,  that  those  substances  have  been  actually  subjected  to  intense 
heat.  But  the  same  thing  might  be  said  of  all  judicial  inquiries  -which 
proceed  upon  circumstantial  evidence.  We  can  conclude  that  a  man 
was  murdered,  although  it  is  not  proved  by  the  testimony  of  eye-wit- 
nesses  that  a  man  who  had  the  intention  of  murdering  him  was  present 
on  the  spot.  It  is  enough  if  no  other  known  cause  could  have  gener- 
ated the  effects  shown  to  have  been  produced.  And  so,  in  geology, 
it  is  enough  that  no  other  known  agent  than  heat  could,  according  to 
any  known  law,  have  produced  the  unstratified  rocks,  while  there  is 
the  strongest  reason  to  believe  that  any  terrestrial  agent  capable  of 
operating  on  so  large  a  scale  would  not  have  remained  unknown. 

The  celebrated  speculation  of  La.place,  now  very  generally  received 
as  probable  by  astronomers,  concerning  the  origin  of  the  earth  and 
planets,  participates  essentially  in  the  strictly  inductive  character  of 
modern  geological  theory.  The  speculation  is,  that  the  atmosphere  of 
the  sun  originally' extended  to  the  present  limits  of  the  solar  system; 
irom  which,  by  the  process  of  cooling,  it  has  contracted  to  its  present 
dimensions ;  and  since,  by  the  general  principles  of  mechanics,  the 
rotation  of  the  sun  and  of  its  accompanying  atmosphere  must  increase 
in  rapidity  as  its  volume  diminishes,  the  increased  centrifugal  force 
generated  by  the  more  rapid  rotation,  overbalancing  the  action  of  grav- 
itation^ would  cause  the  eun  to  abandon  successive  rings  of  vaporous 


HYPOTHESES.  299 

matter,  which  are  supposed  to  have  condensed  by  cooling,  and  to  have 
hecome  our  planets.  There  is  in  this  theory  no  unknown  substance 
introduced  ujuin  supposition,  nor  any  unknown  property  or  law  ascribed 
to  a  known  substance.  Tlic  known  laws  of  matter  authorize  us  to 
suppose  that  a  body  which  is  constantly  giving  out  so  large,  an  amount 
of  heat  as  the  sun  is,  must  be  jjrogressively  cooling,  and  that  by  the 
process  of  Qooling  it  must  contract ;  if,  therefore,  we  etideavor,  from 
the  present  state  of  that  luminary,  to  infer  its  state  in  a  time  long  past, 
we  must  necessarily  suppose  that  its  atmosphere  extended  much  fur- 
ther than  at  present,  and  we  are  entitled  to  suppose  that  it  extended  as 
far  as  we  can  trace  those  effects  which  it  would  naturally  leave  behind 
it  on  retiring ;  and  such  the  planets  are.  These  suppositions  being 
made,  it  follows  from  known  laws  that  successive  zones  of  the  solar 
atmosphere  would  be  abandoned  ;  that  these  would  continue  to  revolve. 
round  the  sun  with  the  same  velocity  as  when  they  formed  part  of  his 
substance ;  and  that  they  would  cool  down,  long  before  the  sun  him- 
self, to  any  given  temperature,  and  consequently  to  that  at  which  the 
greater  part  of  the  vaporous  rnatter  of  which  they  consisted  would 
become  liquid  or  solid.  The  known  law  of  gravitation  would  then 
cause  them  to  agglomerate  in  masses,  which  would  assume  the  shape 
our  planets  actually  exhibit;  would  acquire,  each  round  its  own  axis, 
a  rotaXory  movement  ;  and  would  in  that  state  revolve,  as  the  planets 
actually  do,  about  the  sun,  in  the  same  direction  with  the  sun's  rota- 
tion, but  with  less  velocity,  and  each  of  them  in  the  same  periodic  time 
which  the  sun's  rotation  occupied  when  his  atmosphere  extended  to 
that  point;  and  this  also  M.  Comte  has,  by  the  necessary  calculations, 
ascertained  to  be  true  within  certain  small  limits  of  error.*  There  is,  thus, 
in  Laplace's  theory,  nothing  hypothetical :  it  is  an  example  of  legitimate 
reasoning  from  a  present  effect  to  its  past  cause,  according  to  the  known 
laws  of  that  cause  ;  it  assumes  nothing  more  than  that  objects  which 
really  exist,  obey  the  laws  which  arc  known  to  be  obeyed  by  all  ter- 
restrial objects  resembling  them.  The  theory  therefore  is,  as  I  have 
said,  of  a  similar  character  to  the  theories  of  geologists ;  inferior  to 
them  in  certainty,  in  about  the  same  ratio  as  those  are  inferior  to  facts 
conclusively  established  by  a  judicial  inquiry.  For,  the  uncertainty 
whether  the  laws,  of  nature  which  prevail  on  our  earth  prevail  in  the 
whole  solar  system,  is  about  equal  to  the  uncertainty  whether  the  laws 
which  prevail  in  our  earth  to-day  prevailed  there  a  thousand  ages  ago. 
Laplace's  theory  requires  both  these  assumptions,  geology  the  latter 
only,  and  judicial  inquiries  require  neither.! 

♦  Cours  de  Pkilosophie  Positive,  ii.,  pp.  378-383. 

t  See,  for  an  interesting  exi)dsition  of  this  theory  of  Laplace,  the  Architecture  of  tht 
Heavens,  by  Professor  Nichol,  of  Glasgow ;  a  book  professedly  popular  rather  than  scien- 
tilic,  but  the  production  of  a  thinker  who,  both  in  this  and  in  other  departments,  is  capable 
of  much  more  than  merely  expounding  the  speculations  of  his  predecessors. 


300  iNDUCTiorJ. 

CHAPTER  XV. 

OF  PKOGRESSIVE  EFFECTS;  AND  OF  THE  CONTtNUEU  ACTION  OF  CAUSES. 

§  1.  In  the  la^t  four  chapters,  we  have  traced  the  general  outhnes 
-of  the  theory  of  the  generation  of  derivative  laws  fi-om  ultimate 
ones.  In  the  present  chapter  our  attention  will  be  directed  to  a 
particular  case  of  the  derivation  of  laws  from  other  laws,  but  a  case 
so  general,  and  so  important,  as  not  only  to  repay  but  to  require  a 
separate  examination.  This  is,  the  case  of  a  complex  phenomenon 
resulting  from  one  simple  law,  by  the  continual  addition  of  an  effect  to 
itself. 

There  are  some  phenomena,  some  bodily  sensations  for  example, 
which  are  essentially  instantaneous,  and  whose .  existence  can  only  be 
prolonged  by  the  prolongation  of  the  existence  of  the  cause  by  which 
they  are  produced.  But  most  phenomena  are  in  their  own  nature 
permanent ;  having  begun  to  exist,  they  would  exist  for  ever  unless 
some  cause  intervened  having  a  tendency  to  alter  or  destroy  them. 
Such,  for  example,  are  all  the  facts  or  phenomena  which  we  call  bodies. 
Water  once  produced,  will  not  of  itself  relapse  into  the  state  of  hydro- 
gen and  oxygen ;  such  a  change  requires  some  agent  ha\'ing  the  power 
of  d-ecomposing  the  compound.  Such,  again,  are  the  positions  in 
space,  and  the  movements,  of  bodies.  No  object  at  rest  alters  its 
position  without  the  intei'vention  of  some  conditions  extraneous  to 
itself;  and  when  once  in  motion,  no  object  returns  to  a  state  of  rest, 
or  alters  either  its  direction  or  its  velocity,  unless  some  new  external 
conditions  are  superinduced.  It,  therefore,  perpetually  happens  that 
a  temporary  cause  gives  rise  to  a  permanent  effect.  The  contact  of 
iron  with  moist  air  for  a  few  hours,  produces  a  rust  which  may  endure 
for  centuries ;  or  a  projectile  force  which  launches  a  cannon  ball  into 
space,  produces  a  motion  which  would  continue  for  ever  unless  some 
other  force  counteracted  it. 

Between  the  two  examples  which  we  have  here  given,  there  is  a 
difference  worth  pointing  out.  In  the  former,  (in  which  the  phenom- 
enon produced  is  a  substance,  and  not  a  motion  of  a  substance,) 
since  the  rust  remains  for  ever  and  unaltered  unless  some  new  cause 
sujjervenes,  we  may  speak  of  the  contact  of  air  a  hundred  years  ago 
as  even  the  proximate  cause  of  the  rust  which  has  existed  from  that 
time  until  now.  But  when  the  effect  is  motion,  which  is  itself  a  change, 
we  must  use  a  different  language.  The  permanency  of  the  effect  is 
,now  only  the  permanency  of  a  series  of  changes.  The  second  foot, 
or  inch,  or  mile  of  motion,  is  not  the  mere,  prolonged  duration  of 
the  first  foot,  or- inch,  or  mile,  but  another  fact  which  succeeds,  and 
which  may  in  some  respects  be  very  unlike  the  former,  since  it 
carries  the  body  through  a  different  region  of  space.  Now,  the 
original  projectile  force  which  set  the  body  moving  is  the  remote 
cause  of  all  its  motion,  however  long  continued,  but  the  proximate 
cause  of  no  motion  except  that  which  took  place  at  the  first  instant. 
The  motion  at  any  subsequent  instant  is  proximately  caused  by  the 
motion  which  took  place  at  the  instant  preceding.  It  is  on  that, 
and  not  on  the  original  moving  cause,  that  the  motion  at  any  given 


PROGRESSIVE    EFFECTS.  301 

moment  depcn<ls.  For,  suppose  that  the  body  passes  through  some 
resisting  medium,  which  partially  counteracts  the  effect  of  the  original 
impuLso,  and  by  so  doing  retards  the  motion:  thia  counteraction  (it 
needs  scarcely  here  be  repeated)  is  as  strict  an  example  of  obedience 
to  the  law  of  the  impulsi-,  as  if  the  body  had  gone  on  moving  with  its 
original  velocity  ;  but  the  motion  which  results  is  different,  being  now 
a  compound  of  the  effects  of  two  causes  acting  in  contrary  dij.'iections, 
instead  of  the  one  effect  of  one  cause.  Now,  what  cause  does  the 
body  obey  in  its  subsequent  motion  ?  The  original  cause  of  motion, 
or  tiie  actual  motion  at  the  preceding. instant"?  The  latter:  for  when 
the  object  issues  from  the  resisting  medium,  it  continues  moving  not 
with  its  original,  but  with  its  retarded,  velocity.  The  motion  having 
once  been  diminished,  all  that  which  follows  is  diminished.  The 
effect  changes,  because  the  cause  which  it  really  obeys,  the  proximate 
cause,  the  real  cause  in  fact,  has  changed.  This  principle  is  recognized 
by  mathematicians  when  they  enumerate  among  the  causes  by  which 
the  motion  of  a  body  is  at  any  instant  determined,  the  force  generated 
by  the  previous  motion;  an  expression  which  would  be  absurd  if 
taken  to  imply  that  this  "force"  was  an  intermediate  link  between  the 
cause  and  the  effect,  but  which  really  means  only  the  previous  motion 
itself,  considered  as  a  cause  of  further  motion.  We  must,  therefore, 
if  we  would  speak  with  perfect  precision,  consider  each  .link  in  the 
succession  of  motions  as  the  effect  of  the  link  preceding  it.  But  if, 
for  the  convenience  of  discourse,  we  speak  of  tlie  whole  series  as  one 
effect,  it  must  be  as  an  effect  produced  by  the  original  impelling  force; 
a  permanent  effect  produced  by  an  instantaneous  cause,  and  possessing 
the  property  of  self-perpetuation. 

Let  us  now  suppose  that  the  original  agent  or  cause,  instead  Off 
being  instantaneous,  is  permanent.  Wliatever  effect  has  been  pro- 
duced up  to  a  given  time,  would  (unless  prevented  by  the  inter^'entiotl 
of  some  new  cause)  subsist  permanently,  even  if  the  cause  were  to 
perish.  Since,  however,  the  cause  does  not  perish,  but  continues  to 
exist  and  to  operate,  it  must  go  on  producing  more  and  more  of  the 
effect;  and  instead  of  an  uniform  effect,  we  have  a  progressive  series 
of  effects,  arising  from  the  accumulated  influence  of  a  permanent  cause. 
Thus,  the  contact  of  iron  with  the  atmosphere  causes  a  portion  of  it  to 
rust ;  and  if  the  cause  ceased,  the  effect  already  produced  would  be 
permanent,  but  no  further  effect  would  be  added.  If,  however,  the 
cause,  namely,  exposure  to  moist  air,  continues,  more  and  more  of  the 
iron  becomes  rusted,  until  it  is  all  converted  into  a  red  powder,  when 
one  of  the  conditions  of  the  production  of  rust,  namely,  the  presence 
of  unoxidized  iron,  has  ceased,  and  the  effect  cannot  any  longer  be 
produced.  Again,  the  earth  causes  bodies  to  fall  towards  it,  that  is',- 
the  existence  of  the  earth  at  a  given  instant,  causes  an  unsupported 
body  to  move  towards  it  at  the  succeeding  instant :  and  if  the  earth 
were  instantly  annihilated,  as  much  of  the  effect  as  is  already  produced 
would  continue  ;  the  object  would  go  on  moving  in  the  same  direction, 
with  its  acquired  velocity,  until  intercf^pted  by  some  body  or  deflected 
by  some  other  force.  The  earth,  however,  not  being  annihilated,  goes 
on  producing  in  the  second  instant  an  effect  similar  and  of  equal 
amount  to  the  first,  which  two  effects  being  added  together,  there 
results  an  accelerated  velocity ;  and  this  operation  being  repeated  at 
each  successive  instant,  the  mere  permanence  of  the  cause,  although 


302  INDUCTION.     , 

without  increase,  gives  rise  to  a  constant  progressive  increase  of  the 
effect,  so  long  as  all  the  conditions,  negative  and  positive,  of  the  pro- 
duction of  that  effect  continue  to  be  realized. 

'  It  must  be  obvious  that  this  state  of  things  is  merely  a  case  of  the 
Composition  of  Causes.  A  cause  which  continues  in  action,  must  on 
a  strict  analysis  be  considered  as  a  number  of  causes  exactly  similar, 
successively  introduced,  and  producing^  by  their  combination  the  sum 
of  the  effects  which  they  would  severally  produce  if  they  acted  singly. 
The  progi-essive  rusting  of  the  iron  is  in  strictness  the  sum  of  the 
effects  of  many  particles  of  air  acting  in  succession  upon  coiTespond- 
ing  particles  of  iron.  The  continued  action  of  the  earth  upon  a  falling 
body  is  equivalent  to  a  series  of  forces,  applied  in  successive  instants, 
each  tending  to  produce  a  certain  constant  quantity  of  motion:  and 
the  motion  at  each  instant  is  the  sum  of  the  effects  of  the  new  force 
applied  at  the  preceding  instant,  and  of  the  motion  already  acquired. 
In  each  instant,  a  fVesh  effect  of  which  gravity  is  the  proximate  cause, 
is  added  to  the  effect  of  which  it  was  the  remote  cause :  or  (to-  express 
the  same  thing  in  a^iother  manner)  the  effect  produced  .by  the  earth's 
influence  at  the  instant  last  elapsed,  is  added  to  the  sum  of  the  effects 
of 'which  the  remote  causes  were  the  influ^ncee  exerted  by  the  earth 
at  a^l  the  previous  instants  since  the  rhotion  began.  The  case,  there- 
fore, comes  under  the  principle  of  a  concun^ence  of  causes  producing 
,ail  effect  equal  to  the  suin  of  their  separate  effects.  But  as  the  causes 
come  into  play  not  all  at  once,  but  successively,  and  as  the  effect  at 
each  instant  is  the  suto  of  the  effects  of  those  causes  only  which  have 
come  into  action  up  to  that  instant,  the  result  assumes  the  form  of  an 
ascending  series;  a  succession  of  sums,  each  greater  than  that  which 
preceded  it ;  and  we  have  thus  a  progressiva  effect,  ^om  the  continued 
action  of  -a.  cause. "  , "  . ,  ' 

■Since  the  continuance  of  the  cause  influences  the  effect  only  by 
adding  to  its  quantity,  and  since  the  addition  takes  plaCe  according  to 
a  fixed  law  (equal  quantities  in  equal  times),  the  result  is  capable  of 
being  coTuputed  on  mathematical  princijjles..  In  fact,  this  case,  being 
that  of  infinitesimal  increments,  is  precisely  the  case  which  the  differ- 
ential calculus  was  invented  to  meet.  The  questions,  what  effect  will 
result  from  the  continual  addition  of  a  given  cause  to  itself?  and,  what 
amount  of  the  cause,  being  continually  added  to  itself,  will  produce  a 
■given  amount  of  the  effect/?  are  evidently  mathematical  questions,  and 
to  be  treated,  therefore,  deductively.  If,  as  we  have  seen,  cases  of  the 
Composition  of  Causes  are  seldom  adapted  for  any  other  than  deduc- 
tive investigation,  this  is  especially  true  in  the  case  now  examined,  the 
continual  composition  of  a  cause  with  its  own  previous  effects ;  since 
such  a  ease  is  peculiarly  amenable  to  the  deductive  method,  while  the 
undistinguishahle  manner  in  which  the  effects  are  blended  with  one 
another  and  vdth  the  causes,  must  make  the  treatment  of  such  an 
instance  experimentally,  still  more  chimerical  than  in  any  other  case. 

§  2.  We  shall  next  advert  to  a  rather  more  intricate  operation  of  the 
same  principle,  namely,  when  the  cause  docs  not  merely  continue  in 
action,  but  undergoes,  during  the  same  time,  a  progi-essive  change  in 
those  of  its  circumstances  which  contribute  to  determine  the  effect.  In 
this  case,  as  in  the  former,. the  total  effect  goes  on  accumulating,  by 
the  continual  addition  of  a  fresh  effect  to  that  already  produced,  but 


PROGRESSIVE    EFFECTS.  303 

it  is  no  longer  by  the  addition  of  equal  quantities  in  equal  times  ;  the 
quantities  added  are  unequal,  and  eventhe  quality  nyiy  now  be  differ- 
ent. If  the  change  in  the  state  of  the  pennanent  cause  be  progressive, 
the  effect  will  go  through  a  double  series  of  changes,  arising  partly 
from  the  accumulated  action  of  the  cause,  and  partly  trom  the  changes 
in  its  action.  The  effect  is  still  a  progressive  effect,  produced,  how- 
ever, not  by  the  mere  continuance  of  a  cause,  but  by  its  continuance 
and  its  progressiveness  combined. 

A  familiar  example  is  afforded  by  the  increase  of  the  temperature 
as  summer  advances,  that  is,  as  the  sun  draws  nearer  to  a  vertical 
posititju,  and  remains  a  greater  number  of  hours  above  the  horizon. 
This  instance  exemplifies  in  a  very  interesting  manner  the  twofold 
operation  on  the  ettect,  arising  from  the  continuance  of  the  cause  and 
from  its  progi'essive  change.  When  once  the  sun  .  has  come  near 
enough  to  the  zenith,  and  remains  above  the  horizon  long  enough,  to 
give  more  warmth  during  one  dim'nal  rotation  than  the  counteracting 
cause,  the  earth's  radiation,  can  caiTy  off,  the  mere  continuance  of]  the 
cause  would  progressively  inci'ease  the  effect,  even  if  the  sun  came  no 
nearer  and  the  days  gi'evv  no  longer ;  but  in  addition  to  tliis,  a  change 
takes  place  in  the  accidents  of  the  cause  (its-series  of  diurnal  posi- 
tions), tending  to  increase  the  quantity  of  the  effect.  When  the  suni- 
mer  solstice  has  passed,  the  progressive  change  in  the  cause  begins  to 
take  place  the  reverse  way ;  but,  for  some  time,  the  accumulating 
effect  of  the  mere  continuance  of  the  cause  exceeds  the  effect,  of  the 
changes  in  it,  and  the  tempei-ature  continues  to  increase.  ■ 

Again,  tlife  motions  of  a  planet  are  a  progressive  effect,  produced 
by  causes  at  once  permanent  and  progressive.  The  orbit  of  a  planet 
is  determined  (omitting  perturbations)  by  two  causes:  first,  the  action 
of  the  central  body,  a- permanent  cause,  wliich  alternately  increases 
and  diminishes  as  the  planet  draws  nearer  to  or  goes  further  from  its 
perihelion,  and  wliich  acts  moreover  at  every  point  in  a-  difllerent  direc- 
tion; and,  secondly,  the  tendency  of  the  planet  to  continue  moving  in 
the  direction  and  with  the  velocity  which  it  has  already  acquired. 
This  force  also  grows  greater  as  the  planet  draws  nearer  to  its  perihe- 
lion, because  as  it  does  so  its  velocity  increases;  and  less,  as  it  recedes 
from  its  jierihelion  :  and  this  force  as  well  as  the  other  acts  at  each  point 
in  a  different  directioi^,  because  at  every  point  the  action  of  the  central 
force,  by  deflecting  the  platiet  from  its  previous  direction,  alters  the 
line  in  which  it  tends  to  continue  moving.  The  motion  at 'each  instant 
is  determined  by  the  amount  and  dirc.-ction  of  the  motion  and  the 
amount  arid  direction  of  the  sun's  action  at. the  previous  instant:  arid 
if  we- speak  of  the  entire  revolution  of.  tho  planet  as  one  pheilomenon 
(which,, as  it  is  periodicidand  similar  to  itself,  we  often  find  it  conve- 
nient to  do),  that  ptienomenon  is  the  pi-ogre^sive  effect  of  two  perma- 
nent and  progressive  causes,  the  central  force  andi  the  acquired  motion. 
Those  causes  happening  to  be  progressive  in  tlie  particular  way  which 
is  called  periodical,  the  effect  necessarily  is  so  too ;  because,  the  quan- 
tities to  be  added  together  returning  in  a  regular  order,  the  same  sums 
inust  also  regularly  return. 

This  example  is,  well  worthy  of  consideration  also  in  another  respect. 
Although  the  causes  themselves  are  permanent,  and  hiflepcndcnt  of  all 
conditions  known  to  us,  the  changes' which  take  place  in  the  quantities 
and  relations  of  the 'causes  are  actually  caused  by  tKe  periodical  changes 


304  INDUCTION. 

in  the  effects.  The  causes,  as  they  exist  at  any  moment,  having  pro- 
duced a  certain  motion,  that  motion,  becoming  itself  a  cause,  reacts  on 
the  causes,  and  produces  a  change  in  them.  By  altering  the  distance 
and  direction  of  the  central  body  relatively  to  the  planet,  and  the  direc- 
tion and  quantity  of  the  tangential  force,  it  alters  the  elements  which 
determine  the  motion  at  the  next  succeeding  instant.  This  change 
renders  the  next  motion  sojnewhat  different ;  and  this  difference,  by  a 
fresh  reaction  upon  the  causes,  renders  the  next  motion  still  more  dif- 
ferent, and  so  on.  The  original  state  of  the  causes  might  have  been 
such,  that  this  series  of  actions  modified  by  reactions  woukLnot  have 
been  periodical.  The  sun's  action,  and  the  original  impelling  force, 
might  have  been  in  such  a  ratio  to  one  another,  that  the  reaction  of  the 
effect  would  have  been .  such  as  to  alter  the  causes  more  and  more, 
without  ever  bringing  them  back  to  what  they  were  at  any  former 
time.  The  planet  would  then  have  moved  in  a  parabola,  or  an  hyper- 
bola,' cui-ves  not  returning  into  themselves.  The  quantities  of  the  two 
forces  were,  however,  originally  such,  that  the  successive  reactions  of 
the  effect  bring  back  the  causes,  after  a  certain  time,  to  what  they  were 
before  ;  and  from  that  time  all  the  variations  continue  to  recur  again 
and  again  in  the  same  periodical  order,  and  miist  so  continue  while  the 
causes  subsist  and  ^are  not  counteracted. 

§  3^.  In  all  cases  of  progi-essive  effects,  whether  aiising  from  the  ac- 
cumulation of  an  unchanging  or  of  changing  elements,  there  is  an  uni- 
formity of  succession  not  merely  between  the  cause  and  the  eftect,  but 
between  the  first  stages  of  the  effect  and  its  subsequent  stages.  That 
a  body  in  vactio  falls  sixteen  feet  in  the  first  second,  forty-eight  in  the 
second,  and  so  on  in  the  ratio  of  the  odd  numbers,  one,  three,  five,  &c., 
is  as  much  an  uniform  sequence  as  that  when  the  supports  are  removed 
the  body  falls.  The  sequence  of  sjjring  and  summer  is  as  regular  and' 
invariable  as  that  of  the  approach  of  the  sun  and  spring  :  but  we  do 
not  consider  sju'ing  to  be  the  cause  of  summer,  it  is  evident  that  they 
are  both  effects  of  the  increased  heat  received  from  the  sun,  and  if  that 
cause  did  not  exist,  spring 'might  continue  for  ever,  without  having 
the  slightest  tendency  to  produce  stimmer.  As  we  have  so  often  re- 
marked, not  the  conditional,  but  the  unconditional  invariable  antece- 
dent, is  termed  the  cause.  That  which  would  not  be  followed  by  the 
effect  unless  something  else  had  preceded,  is  not  the  cause,  however 
invariable  the  sequence  may  in  fact  be. 

.  ■  It  is  in  this  way  that  most  of  these  uniformities  of  succession  are 
generated',  which  are  not  cases  of  causation.  When  a  phenomenon 
goes  on  increasing,  or  periodically  increases  and  diminishes,  or  goes 
through  any  continued  and  unceasing  process  of  variation  reducible  to 
an  uniform  nile  or  law  of  succession,  we  do  not  on  this  account  presume 
that  any  two  successive  tei-ms  of  the  series  are  cause  and  effect.  We 
presume  the  conti-ary ;  we  expect  to  find  that  the  whole  series  originates 
either  from  the  continued  action  of  fixed  causes  or  from  causes  which  go 
through  a  con-esponding  process  of  continuous  change.  A  tree  grows 
from  half  an  inch  high  to  mi  hundred  feet ;  -and  some  trees  will  gener- 
ally grow  to  that  height  unless  prevented  by  some  counteracting  cause. 
But  we  do  not  call  the  .seedling  the  cause  of  the  full  grown  tree  ;  the 
invariable  antecedent  it  certainly  is,  and  we  know  very  imperfectly 
upon  what  other  antecedents  the  sequence  is  contingent,  but  we  are 


EMPIRICAL    LAWS.  305 

convinced  that  it  is  contingent  upon  something ;  because  the  homoge- 
neousness  of  tlie  antecedent  with  the  consequent,  the  close  resemblance 
of  the  seedling  to  the  tree  in  all  respects  except  magnitude,  and  the 
graduality  of  the  growth,  so  exactly  resembling  the  progi'essiv^ly  accu- 
mulating effect  produced  by  the  long  action  of  some  one  cause,  leave 
scarcely  a  possibility  of  doubting  that  the  seedling  and  the  tree  are 
really  two  terms  in  a  series  of  that  description,  the  first  tenn  of  which 
is  yet  to  seek.  The  conclusion  is  further  confirmed  by  this,  that  we 
are  able  to  prove  by  strict  induction  the  dependence  of  the  gi'owth  of 
tlie  tree,  and  even  of  the  continuance  of  its  existence,  upon  the  con- 
tinued repetition  of  certain  pi-ocesses  of  nutrition,  the  rise  of  the  sap, 
the  absorptions  and  exhalations  by  the  leaves,  &:c.,  and  the  same  ex- 
periments would  probably  prove  to  us  that  the  growth  of  the  tree  is 
the  accumulated  sum  of  the  effects  of  these  continued  processes,  were 
we  not,  for  want  of  sufficiently  microscopic  eyes,  unable  to  obseiTe 
correctly  and  in  detail  what  those  effects  are. 


CHAPTER  XVI.  ^ 

OF  EMPIRICAL  LAWS. 

§  1.  Experimental  philosophers  usually  give  the  name  of  Empirical 
Laws  to  those  uniformities  which  observation  or  experiment  has  shown 
to  exist,  but  upon  which  they  hesitate  to  rely  in  cases  varying  much 
from  those  which  have  been  actually  observed,  for  want  of  seeing  any 
reason  why  such  a  law  should  exist.  It  is  implied,  therefore,  in  the 
notion  of  an  empirical  law,  that  it  is  not  an  ultimate  law ;  that  if  true 
at  all,  its  truth  is  capable  of  being,  and  requires  to  be,  accounted  for. 
It  is  a  derivative  law,  the  derivation  of  which  is  not  yet  known.  To 
state  the  explanation,  the  why  of  the  empuical  law,  would  be  to  state 
the  laws  from  which  it  is  derived;  the  ultimate  causes  upon  which 
it  is  contingent.  And  if  we  knew  these,  wc  should  also  know  what 
are  its  limits ;  under  what  conditions  it  .would  cease  to  be  fulfilled. 

The  periodical  return  of  eclipses,  as  originally  ascertained  by  the 
persevering  obsei-vation  of  the  early  eastern  astronomers,  was  an  em- 
pirical law,  until  the  general  laws  of  the  celestial  motions  had 
accounted  for  it.  The  following  are  empirical  laws  still  waiting  to  be 
resolved  into  the  simpler  laws  from  which  they  are  derived.  The  local 
laws  of  the  flux  and  reflux  of  the  tides  in  different  places  :  the  succes- 
sion of  certain  kinds  of  weather  to  certain  appearances  of  sky :  the  ap- 
parent exceptions  to  the  almost  universal  tmth  that  bodies  expand  by 
increase  of  temperaturej:  the  law  that  breeds,  both  animal  and  vegeta- 
ble, are  improved  by  crossing:  that  gases  have  a  strong  tendency  to 
permeate  animal  membranes  :  that  opium  and  alcohol  intoxicate:  that 
sub:>tanccs  containing  a  veiy  high  proportion  of  nitrogen  (such  as  hy- 
drocyanic acid  and  morphia)  are  powcrfid  poisons:  that  when  different 
metals  are  fused  together  the  alloy  is  harder  than  the  various  elements: 
that  the  number  of  atoms  of  acid  required  to  neutralize  one  atom  of 
any  base,  is  equal  to  the  number  of  atoms  of  oxygen  in  the  base :  that 


306  INDUCTION. 

the  solubility  of  substances  in  one  another,  depends*  (at  least  in  some 
degree)  on  the  similarity  of  their  elements. 

An  empirical  law,  then,  is  an  observed  unifonnity,  presumed  to  be 
resolvable  into  simpler  laws,  but  not  yet  resolved  into  them.  The  as- 
certainment of  the  empirical  laws  of  phenomena,  often  precedes  by  a 
long  interval  the  explanation  of  those  laws  by  the  Deductive  Method : 
and  the  verification  of  a  deduction  usually  consists  in  the  comparison 
of  its  results  with  empirical  laws  previously  ascertained. 

§  2.  From  a  limited  number  of  ultimate  laws  of  causation,  there  are 
necessarily  generated  a  vast  number  of  derivative  unifonnities,  both 
of  succession  and  of  coexistence.  Some  are  laws  of  succession  or  of 
coexistence  between  different  effects  of  the  same  cause :  of  these  we 
had  abundant  examples  in  the  last  chapter.  Some  are  laws  of  suc- 
cession between  effects  and  their  remote  causes ;  resolvable  into  the 
laws  which  connect  each  with  the  intermediate  link.  Thirdly,  when 
causes  act  together  and  compound  their  effects,  the  laws  of  those 
causes  generate  the  fundamental  law  of  the  eftect,  namely,  that  it  de- 
pends upon  the  coexistence  of  those  causes.  And,  finally,  the  ordei 
of  succession  or  of  coexistence  which  obtains  among  effects,  necessa- 
rily depends  upon  their  causes.  If  they  are  effects  of  the  same  cause, 
it  depends  upon  the  laws  of  that  cause ;  if  of  different  causes,  it  de- 
pends upon  the  laws  of  those  causes  severally,  and  upon  the  circum- 
stances which  determine  their  coexistence.  If  we  inquire  further  when 
and  how  the  causes  will  coexist,  that,  again,  depends  upon  their  causes : 
and  we  may  thus  trace  back  the  phenomena  highei*  and  higher,  until 
the  different  series  of  effects  meet  in  a  point,  and  the  whole  is  shown 
to  have  depended  ultimately  upon  some  common  cause ;  or  until,  in- 
stead of  converging  to  one  point,  they  terminate  in  different  points, 
and  the  order  of  the  effects  is  proved  to  have  arisen  fr-om  the  original 
collocation  of  some  of  the  primeval  causes,  or  natural  agents.  For 
example,  the  order  of  succession  and  of  coexistence  among  the 
heavenly  motions,  which  is  expressed  by  Kepler's  laws,  is  derived 
from  the  coex'istence  of  two  primeval  causes,  the  sun,  and  the  original 
impulse  or  projectile  force  impressed  upon  each  planet.t  Kepler's 
laws  are  resolved  into  the  laws  of  these  causes  and  the  fact  of  their 
coexistence. 

Derivative  laws,  therefore,  do  not  depend  solely  upon  the  ultimate 
laws  into  which  they  are  resolvable  :  they  mostly  depend  upon  those 
ultimate  laws  and  an  ultimate  fact ;  namely,  the  mode  of  coexistence 
of  some  of  the  original  elements  of  the  universe.  The  ultimate  laws 
of  causation  might  be  the  same  as  at  present,  and  yet  the  derivative 
laws  completely  different,  if  the  causes  coexisted  in  different  propor- 
tions, or  with  any  difference  in  those  of  their  relations  by  which  the 
effects  are  influenced.     If,  for  example,  the  sun's  attraction,  and  the 

*  Thus,  water,  of  which  eight-ninths  in  weight  are  oxygen,  dissolves  most  bodies  which 
contain  a  high  proportion  of  oxygen,  such  as  all  the  nitrates,  (which  have  more  oxygen 
than  any  others  of  the  common  salts,)  most  of  the  sulphates,  many  of  the  carbonates.  &c. 
Again,  bodies  largely  composed  of  combustible  elements,  like  hydrogen  and  carbon,  are 
soluble  in  bodies  of  similar  composition  ;  rosin,  for  instance,  will  dissolve  in  alcohol,  tar  in 
oil  of  turpentine.  This  empirical  generalization  is  far  from  being  universally  true ;  no 
doubt  because  it  is  a  remote,  and  therefore  easily  defeated,  result  of  general  laws  too  deep 
for  us  at  present  to  penetrate :  but  it  will  probably  in  time  suggest  processes  of  inquiry, 
leading  to  the  discovery  of  these  laws. 

+  Or  (according  to  Laplace's  theory)  the  sun,  and  the  sun's  rotation. 


EMPIRICAL    LAWS.  307 

original  projectile  force,  had  existed  in  some  other  ratio  to  one  another 
than  thoy  did  (and  we  know  of  no  reason  why  this  shoidd  not  have 
been  the  case),  the  derivative  laws  of  the  heavenly  motions  might 
have  been  quite  dift'erent  from  what  they  are.  The  proportions  which 
exist  happen  to  be  such  as  to  produce  regular  elliptical  motions ;  any 
other  pi-oportions  would  have  produced  diflerent  ellipses,  or  circular, 
or  parabohc,  or  hyperbolic  motions,  but  still  regular  ones  ;  because  the 
effects  of  each  of  the  agents  accumulate  according  to  an  uniform  law; 
and  two  I'egular  series  of  quantities,  when  their  corresponding  terms 
are  added,  must  produce  a  regular  scries  of  some  sort,  whatever  the 
quantities  themselves  are. 

§  3.  Now  this  last  mentioned  element  in  the  resolution  of  a  deriva- 
tive law,  the  element  which  is  not  a  law  of  causation  but  a  collocation 
of  causes,  cannot  itself  be  reduced  to  any  law.  There  is  (as  formerly 
remarked*)  no  uniformity,  no  norma,  principle,  or  rule,  perceivable  in 
the  distribution  of  the  primeval  natural  agents  through  the  universe. 
The  different  substances  composing  the  earth,  the  powers  that  pervade 
the  universe,  stand  in  no  constant  relation  to  one  another.  One  sub- 
stance is  more  abundant  than  others,  one  power  acts  through  a  larger 
extent  of  space  than  others,  without  any  pervading  analogy  that  we 
can  discover.  We  not  only  do  not  know  of  any  reason  why  the 
sun's  attraction  and  the  tangential  force  coexist  in  the  exact  propor- 
tion they  do,  but  we  can  trace  no  coincidence  between  it  and  the 
proportions  in  which  any  other  elementary  powers  in  the  universe  are 
intermingled.  The  utmost  disorder  is  apparent  in  the  combination  of 
the  causes  ;  which  is  consistent  with  the  most  perfect  order  in  their 
effects ;  for  when  each  agent  carries  on  its  own  operations  according  to 
an  uniform  law,  even  the  most  capricious  combination  of  agencies  will 
generate  a  regularity  of  some  sort,  as  we  see  in  the  kaleidoscope, 
where  any  casual  arrangement  of  colored  bits  of  glass  produces  by 
the  laws  of  reflection  a  beautiful  regularity  in  the  effect. 

§  4.  In  the  above  considerations  lies  the  justification  of  the  limited 
degi-ee  of  reliance  which  philosophers  are  accustomed  to  place  in  em- 
pirical laws. 

A  derivative  law  which  results  wholly  from  the  operation  of  some 
one  cause,  will  be  as  universally  true  as  the  laws  of  the  cause  itself; 
that  is,  it  will  always  be  true  except  where  some  one  of  those  effects 
of  the  cause,  on  which  the  derivative  law\  depends,  is  defeated  by  a 
coimteracting  cause.  But  when  the  denvative  law  results  not  from 
different  effects  of  one  cause,  but  from  effects  of  several  causes,  we 
cannot  be  certain  that  it  will  be  tnic  under  any  variation  in  the  mode 
of  coexistence  of  those  catises,  or  of  the  primitive  natural  agents  on 
which  the  causes  ultimately  depend.  The  proposition  that  coal  beds 
rest  upon  certain  descriptions  of  strata  exclusively,  though  true  on 
the  earth  so  far  as  our  observation  has  reached,  cannot  be  extended  to 
the  moon  or  the  other  planets,  supposing  coal  to  exist  there  ;  because 
we  cannot  be  assured  that  the  original  constitution  of  any  other  planet 
was  such  as  to  produce  the  different  dejjositions  in  the  same  order  as 
in  our  globe.     The  derivative  law  in  this  case  depends  not  solely 

*  Supra,  p.  206. 


308  INDUCTION. 

upon  laws  but  upon  a  collocation ;   and  collocations  cannot  be  reduced 
to  any  law. 

Now  it  is  the  very  nature  of  a  derivative  law  which  has  not  yet  been 
resolved  into  its  elements,  in  other  words,  an  empirical  law,  that  we 
do  not  know  whether  it  results  from  the  different  effects  of  one  cause 
or  fi-om  effects  of  different  causes.  We  cannot  tell  whether  it  depends 
wholly  upon  laws,  or  partly  upon  laws  and  partly  upon  a  collocation. 
If  it  depends  upon  a  collocation,  it  will  be  true  in  all  the  cases  in  which 
that  particular  collocation  exists.  But  since  we  are  entirely  ignorant,  in 
case  of  its  depending  upon  a  collocation,  what  the  collocation  is,  we  are 
not  safe  in  extending  the  law  beyond  the  limits  of  time  and  place  in 
which  we  have  actual  experience  of  its  truth.  Since  within  those  limits 
the  law  has  always  been  found  true,  we  have  evidence  that  the  colloca- 
tions, whatever  they  are,  upon  which  it  depends,  do  really  exist  within 
those  limits.  But  knowing  of  no  rule  or  principle  to  which  the  collo- 
cations themselves  conform,  we  cannot  conclude  that  because  a  collo- 
cation is  proved  to  exist  within  certain  limits  of  place  or  time,  it  will 
exist  beyond  those  limits.  Empirical  laws,  therefore,  can  only  be  held 
true  within  the  limits  of  time  and  place  in  which  they  have  been  found 
true  by  observation:  and  not  merely  the  limits  of  time  and  place,  but 
of  time,  place,  and  circumstance  :  for  since  it  is  the  very  meaning  of  an 
empirical  law  that  we  do  not  know  the  ultimate  laws  of  causation  upon 
which  it  is  dependent,  we  cannot  foresee,  without  actual  trial,  in  what 
manner  or  to  what  extent  the  introduction  of  any  new  circumstance 
may  effect  it. 

§  5.  But  how  are  we  to  know  that  an  uniformity,  ascertained  by 
experience,  is  only  an  empirical  law  1  Since,  by  the  supposition,  we 
have  not  been  able  to  resolve  it  into  higher  laws,  how  do  we  know 
that  it  is  not  an  ultimate  law  of  causation  ] 

I  answer,  that  no  generalization  amounts  to  more  than  an  empirical 
law  when  the  only  proof  upon  which  it  rests  is  that  of  the  Method  of 
Agreement.  •  For  it  has  been  seen  that  by  that  method  alone  we  never 
can  arrive  at  causes.  All  that  the  Method  of  Agreement  can  do  is,  to 
ascertain  the  whole  of  the  circumstances  common  to  all  cases  in  which 
a  phenomenon  is  produced  :  and  this  of  course  includes  not  only  the 
cause  of  the  phenomenon,  but  all  phenomena  with  which  it  is  con- 
nected by  any  derivative  uniformity,  whether  as  being  collateral 
effects  of  the  same  cause,  or  effects  of  any  other  cause  which,  in  all  the 
instances  we  have  been  able  to  obsei^e,  coexisted  with  it.  The  method 
affords  no  means  of  determining  which  of  these  unifoiTtiities  are  laws  of 
causation,  and  which  are  merely  derivative  laws  resulting  fi'om  those 
laws  of  causation  and  fi-om  the  collocation  of  the  causes.  None  of 
them,  therefore,  can  be  received  in  any  other  character  than  that  of 
derivative  laws,  the  derivation  of  which  has  not  been  traced ;  in  other 
words,  empirical  laws :  in  which  light,  all  results  obtained  by  the 
Method  of  Agreement  (and  therefore  almost  all  the  truths  obtained  by 
simple  observation  without  experiment)  must  be  considered,  until 
either  confirmed  by  the  Method  of  Difference,  or  explained  deduc- 
tively, in  other  words,  accounted  for  a  priori. 

These  empirical  laws  may  be  of  greater  or  of  less  authority,  accord- 
ing as  there  is  reason  to  presume  that  they  are  resolvable  into  laws 
only,  or  into  laws  and  collocations  together.     The  sequences  which  we 


EMPIRICAL  LAWS.  309 

observe  in  the  production  and  subsequent  life  of  an  animal  or  a  vop^e- 
table,  resting  upon  the  Method  of  Agreement  only,  are  mere  empirical 
laws  ;  but  though  the  antecedents  in  those  sequences  may  not  be  the 
causes  of  the  consequents,  both  the  one  and  the  other  are  probably,  in 
the  main,  successive  stages  of  a  progressive  effect  originating  iu  a 
common  cause,  and  therefore  independent  of  collocations.  The  unifor- 
mities, on  the  otlier  hand,  in  the  order  of  superposition  of  strata  on  the 
earth,  are  empirical  laws  of  a  much  weaker  kind,  since  they  are  not 
only  not  laws  of  causation,  but  there  is  no  reason  to  believe  that  they 
depend  upon  any  common  cause  :  all  appearances  are  in  favor  of 
their  depending  upon  the  particular  collocation  of  natural  agents  which 
primitively  existed  on  our  globe,  and  from  which  no  inference  can  be 
dra\vn  as  to  the  collocation  which  exists  or  has  existed  iu  any  other 
portion  of  the  universe. 

6.  Our  definition  of  an  empirical  law  including  not  only  those 
uniformities  which  are  not  known  to  be  laws  of  causation,  but  also 
those  which  are,  provided  there  be  reason  to  presume  that  they  are 
not  ultimate  laws ;  this  is  the  proper  place  to  consider  by  what  signs 
we  may  judge  that  even  if  an  observed  uniformity  be  a  law  of  causa- 
tion, it  is  not  an  ultimate  but  a  derivative  law. 

The  first  sign  is,  if  between  the  antecedent  a  and  the  consequent  b 
there  be  evidence  of  some  intermediate  link ;  some  phenomenon  of 
which  we  can  collect  the  existence,  although  from  the  imperfection  of 
our  senses  or  of  our  instruments  we  are  unable  to  ascertain  its  precise 
nature  and  laws.  If  there  be  such  a  phenomenon  (which  may  be 
denoted  by  the  letter  x),  it  follows  that  even  if  a  be  the  cause  of  h,  it 
is  but  the  remote  cause,  and  that  the  law,  a  causes  b,  is  resolvable  into 
at  least  two  laws,  a  causes  x,  and  x  causes  b.  This  is  a  very  frequent 
case,  since  the  operations  of  nature  mostly  take  place  on  so  minute  a 
scale,  that  many  of  the  successive  steps  are  either  imperceptible,  or 
very  indistinctly  perceived. 

Take,  for  example,  the  laws  of  the  chemical  composition  of  substan- 
ces ;  as  that,  hydrogen  and  oxygen  being  combined  water  is  produced. 
All  we  see  of  the  process  is,  that  the  two  gases  being  mixed  in  certain 
proportions,  and  heat  or  electricity  being  applied,  an  explosion  takes 
place,  the  gases  disappear,  and  water  remains.  There  is  no  doubt 
about  the  law,  or  about  its  being  a  law  of  causation.  But  between  the 
antecedent  (the  gases  in  a  state  of  mechanical  mixture,  heated  or  elec- 
trified), and  the  consequent  (the  production  of  water),  there  must  be 
an  inteiTnediate  process  which  we  do  not  see.  For  if  we  take  any 
portion  whatever  of  the  water,  and  subject  it  to  analysis,  we  find  that 
it  always  contains  some  hydrogen  and  some  oxygen  :  nay,  the  very 
same  proportions  of  them,  namely,  two-thirds,  in  volume,  of  hydrogen, 
and  one-third  oxygen.  This  is  true  of  a  single  drop  ;  it  is  true  of  the 
minutest  portion  which  our  instruments  are  capable  of  appreciating. 
Since,  then,  the  smallest  perceptible  portion  of  the  water  contains  both 
those  substances,  portions  of  hydrogen  and  oxygen  smaller  than  the 
smallest  perceptible  must  have  come  together  in  every  such  minute 
portion  of  space  ;  must  have  come  closer  together  than  when  the  gases 
were  in  a  state  of  mechanical  mixture,  since  (to  mention  no  other 
reasons)  the  water  occupies  far  less  space  than  the  gases.  Now  as  we 
cannot  see  this  contact  or  close  approach  of  the  minute  particles,  we 


310  INDUCTION. 

cannot  observe  with  what  circumstances  it  is  attended,  or  according  to 
what  laws  it  produces  its  effects.  The  production  of  water,  that  is,  of 
the  sensible  phenomena  which  characterize  the  compound,  may  be  a 
very  remote  effect  of  those  laws.  There  may  be  innumerable  inter- 
vening links;  and  we  are  sure  that  there  must  be  some.  Having  full 
proof  that  corpuscular  action  of  some  kind  takes  place  previous  to  any 
of  the  great  transformations  in  the  sensible  properties  of  substances, 
we  can  bave  no  doubt  that  the  laws  of  chemical  action,  as  at  present 
knowTi,  are  not  ultimate  but  derivative  laws;  however  ignorant  we 
may  be,  and  even  though  we  should  for  ever  remain  ignorant,  of  the 
nature  of  the  laws  of  corpuscular  action  from  which  they  are  derived. 

In  like  manner  all  the  processes  of  vegetative  life,  whether  in  the 
vegetable  properly  so  called  or  in  the  animal  body,  are  corpuscular 
processes.  Nutrition  is  the  addition  of  particles  to  one  another,  in 
part  replacing  other  particles  separated  and  excreted,  in  part  occasion- 
ing an  increase  of  bulk  or  weight,  so  gradual,  that  only  after  a  long 
continuance  does  it  become  perceptible.  Various  organs,  by  means 
of  peculiar  vessels,  secrete  from  the  blood,  fluids,  the  component  par- 
ticles of  which  must  have  been  in  the  blood,  but  which  differ  from  it 
most  widely  both  in  mechanical  properties  and  in  chemical  composition. 
Here,  then,  are  abundance  of  unknown  links  to  be.  filled  up ;  and  there 
can  be  no  doubt  that  the  laws  of  the  phenomena  of  vegetative  or  organic 
life  are  derivative  laws,  dependent  upon  properties  of  the  corpuscles, 
and  of  those  elementary  tissues  which  are  comparatively  simple  com- 
binations of  corpuscles. 

The  first  sign,  then,  from  which  a  law  of  causation,  though  hitherto 
unresolved,  may  be  infeiTed  to  be  a  derivative  law,  is  any  indication 
of  the  existence  of  an  intermediate  link  or  links  between  the  antece- 
dent and  the  consequent.  The  second  is,  when  the  antecedent  is  an 
extremely  complex  phenomenon,  and  its  effects,  therefore,  probably,  in 
part  at  least,  compounded  of  the  effects  of  its  different  elements  ;  since 
we  know  that  the  case  in  which  the  effect  of  the  whole  is  not  made  up 
of  the  effects  of  its  parts,  is  exceptional,  the  Composition  of  Causes 
being  by  far  the  more  ordinary  case. 

We  will  illustrate  this  by  two  examples,  in  one  of  which  the  ante- 
cedent is  the  sum  of  many  homogeneous,  in  the  other  of  heterogeneous, 
parts.  The  weight  of  a  body  is  made  up  of  the  weights  of  its  minute 
particles  ;  a  truth  which  astronomers  express  in  its  most  general  terms, 
when  they  say  that  bodies,  at  equal  distances,  gravitate  to  one  another 
in  proportion  to  their  quantity  of  matter.  All  true  propositions,  there- 
fore, which  can  be  made  concerning  gravity,  are  derivative  laws ;  the 
ultimate  law  into  which  they  are  all  resolvable  being  that  every  par- 
ticle of  matter  atti'acts  every  other.  As  our  second  example,  we  may 
take  any  of  the  sequences  observed  in  meteorology  :  for  instance,  that 
a  diminution  of  the  pressure  of  the  atmosphere  (indicated  by  a  fall  of 
the  barometer)  is  followed  by  rain.  The  antecedent  is  here  a  com- 
plex phenomenon,  made  up  of  heterogeneous  elements;  the  columu 
of  the  atmosphere  over  any  particular  place  consisting  of  two  parts,  a 
column  of  air,  and  a  column  of  aqueous  vapor  mixed  with  it ;  and  the 
change  in  the  two  together,  manifested  by  a  fall  of  the  barometer,  and 
followed  by  rain,  must  be  either  a  change  in  one  of  these,  or  in  the 
other,  or  in  both.  We  might,  then,  even  in  the  absence  of  any  other 
evidence,  form  a  reasonable  presumption,  fi'om  the  invariable  presence 


EMPIRICAL    LAWS.  311 

of  both  those  elements  in  the  antecedent,  that  the  sequence  is  j)voba- 
bly  not  an  ultimate  law,  but  a  result  of  the  laws  of  the  two  ditVcrent 
agents  :  a  presumption  only  to  be  destroyed  when  we  had  made 
ourselves  so  well  acquainted  with  the  laws  of  both,  as  to  be  able  to 
affirm  that  those  laws  could  not  by  themselves  produce  the  observed 
result. 

§  7.  There  are  but  few  known  cases  of  succession  from  very  complex 
antecedents,  which  have  not  cither  been  actually  accounted  for  from 
simpler  laws,  or  inferred  with  great  probability  (from  the  ascertained 
existence  of  intermediate  links  of  causation  not  yet  understood)  to  be 
capable  of  being  so  accounted  for.  It  is,  therefore,  highly  j)robable 
that  all  sequences  from  complex  antecedents  are  thus  resolvable,  and. 
that  ultimate  laws  are  in  all  cases  comparatively  simple.  If  tliere 
were  not  the  other  reasons  already  mentioned  for  believing  that  the 
laws  of  organized  nature  are  resolvable  into  simpler  laws,  it  would  be 
almost  a  sufficient  reason  that  the  antecedents  in  most  of  the  sequences 
ai'e  so  very  complex. 

There  are  appearances  strongly  favoring  the  suspicion,  that  these 
phenomena  are  really  resolvable  into  much  simpler  laws  than  might  at 
first  be  expected.  The  growth  of  an  animal  from  infancy  to  maturity, 
of  a  plant  from  infancy  till  death,  and  even  that  process  of  decay 
which  is  but  a  slow  death,  bear  a  most  striking  resemblance  to  the 
progressive  effect  of  the  continued  action  of  some  cause,  proceeding 
until  it  meets  agencies  which  overpower  it,  or  until  its  accumulated 
effects  give  rise  to  conditions  inconsistent  with  its  own  existence. 
This  supposition  by  no  means  requires  that  the  effect  should  not, 
during  its  progress,  undergo  many  modifications  besides  those  of 
quantity,  or  that  it  should  not  sometimes  appear  to  undergo  a  very 
marked  change  of  character.  This  may  be,  either  because  the  unknown 
cause  consists  of  several  component  elements  or  agents,  whose  effects, 
accumulating  according  to  different  laws,  are  compounded  in  different 
proportions  at  different  periods  in  the  existence  of  the  organized 
being ;  or  because,  at  certain  points  in  its  progress,  fresh  causes  or 
agencies  come  in,  or  are  evolved,  which  intermix  their  laws  with 
those  of  the  prime  agent. 

This  great  problem,  the  most  difficult  in  all  physics,  the  ascertain- 
ment of  the  ultimate  laws  of  organized  nature,  is  one  which  natural 
science  in  its  progress  seems  now  at  least  to  have  fairly  come  up  to ; 
and  a  beginning  has  been  made  at  the  point  where  the  phenomena 
appear  most  accessible  to  experiment,  namely,  in  separating  the  effects 
of  partial  from  those  of  general  causes.  The  result,  as  far  as  it  goes, 
fully  accords  with  the  above  surmise.  I  allude  to  the  new  and  infant 
science  of  morphology,  created  with  respect  to  animals  by  the  genius 
of  Cuvier  and  St.  Hilaire,  and  with  respect  to  vegetables  by  that  of 
the  illustrious  Goethe,  to  whom  the  world  owes  so  much  in  cjuite  a 
different  field  of  intellect,  and  whose  researches  on  the  "  Metamor- 
phoses of  Plants"  have  met  with  a  more  favorable  reception  from  the 
scientific  world  than  his  speculaticms  on  colors.  It  seems  to  be  now 
considered  by  natural  philosophers  as  sufficiently  established,  that 
plants  and  animals,  in  the  process  of  growing  up  from  their  genns, 
have  a  tendency  to  develop  themselves  in  a  much  more  uniform  man- 
ner than  they  in  fact  do ;  that  the  differences,  for  example    of  leaf. 


312  INDUCTION. 

flower,  and  fruit,  are  mere  modifications  of  one  general  phenomenon ; 
or  (which  is  only  another  expression  for  the  same  idea)  joint  results  of 
one  common  tendency  and  of  several  partial  causes  combining  with  it. 

§  8.  In  the  preceding  discussion  we  haye  recognized  two  kinds  of 
empirical  laws  :  those  known  to  be  laws  of  causation,  but  presumed 
to  be  resolvable  into  simpler  laws ;  and  those  not  known  to  be  laws  of 
causation  at  all.  Both  these  kinds  of  laws  agree  in  the  demand  which 
they  make  for  being  explained  by  deduction,  and  agi-ee  in  being  the 
appropriate  means  of  verifying  such  deduction,  since  they  represent 
the  experience  with  which  the  result  of  the  deduction  must  be  com- 
pared. They  agree,  further,  in  this,  that  until  explained,  and  con- 
nected with  the  ultimate  laws  from  which  they  result,  they  have  not 
attained  the  highest  degi-ee  of  certainty  of  which  laws  are  susceptible. 
It  has  been  shown  on  a  fonner  occasion  that  laws  of  causation  which 
are  derivative,  and  compounded  of  simpler  laws,  are  not  only,  as  the 
nature  of  the  case  implies,  less  general,  but  even  less  certain,  than  the 
simpler  laws  from  which  they  result ;  not  so  positively  to  be  relied  upon 
as  universally  true.  The  inferiority  of  evidence,  however,  which 
attaches  to  this  class  of  laws,  is  trifling  compared  with  that  which  is 
inherent  in  unifonnities  not  kno^vn  to  be  laws  of  causation  at  all.  So 
long  as  these  are  unresolved,  we  cannot  tell  upon  how  many  colloca- 
tions, as  well  as  laws,  their  truth  may  be  dependent ;  and  can  never, 
therefore,  extend  them  with  perfect  confidence  to  cases  in  which  we 
have  not  assured  ourselves,  by  trial,  that  the  necessary  collocation  of 
causes,  whatever  it  may  be,  exists.  It  is  to  this  class  of  laws  alone 
that  the  property,  which  philosophers  usually  consider  as  characteristic 
of  empirical  laws,  belongs  in  all  its  strictness ;  the  property  of  being 
unfit  to  be  relied  on  beyond  the  limits  of  time,  place,  and  circumstance, 
in  which  the  observations  have  been  made.  These  are  empirical  laws 
in  a  more  emphatic  senses  and  when  I  employ  that  term  (except 
where  the  context  manifestly  indicates  the  reverse)  I  shall  generally 
mean  to  designate  those  uniformities  only,  whether  of  succession  or 
of  coexistence,  which  are  not  knovm  to  be  laws  of  causation. 


CHAPTER  XVII. 

OF  CHANCE,  AND   ITS   ELIMINATION. 


§  1.  Considering,  then,  as  empirical  laws  only  those  observed  uni- 
formities respecting  which  the  question  whether  they  are  laws  of  causa- 
tion must  remain  undecided  until  they  can  be  explained  deductively, 
or  until  some  means  are  found  of  applying  the  Method  of  Difference  to 
the  case ;  it  has  been  shown  in  the  preceding  chapter,  that  until  an 
uniformity  can,  in  one  or  the  other  of  these  modes,  be  taken  out  of  the 
class  of  empirical  laws,  and  brought  either  into  that  of  laws  of  causa- 
tion or  of  the  demonstrated  results  of  laws  of  causation,  it  cannot  with 
any  assurance  be  pronounced  true  beyond  the  local  and  other  limits 
within  which  it  has  been  found  so  by  actual  observation.  It  remains  to 
consider  how  we  are  to  assure  ourselves  of  its  truth  even  within  those 


CHANCE,   AND  ITS  ELIMINATION.  313 

limits  ;  after  wliat  quantity  of  experience  a  generalization  which  rests 
solely  upon  the  Method  of  Agreement,  can  be  considered  sufficiently 
established,  even  as  an  empirical  law.  In  a  former  chapter,  when 
treating  of  the  Methods  of  Direct  Induction,  we  expressly  reserved  this 
question,*  and  the  time  is  now  come  for  endeavoring  to  solve  it. 

We  found  that  the  Method  of  Agreement  has  the  defect  of  not 
proving  causation,  and  can  therefore  only  be  employed  for  the  ascer- 
tainment of  empirical  laws.  But  we  found,  moreover,  that  besides  this 
deficiency,  it  labors  under  a  characteristic  imperfection,  tending  to 
render  uncertain  even  such  conclusions  as  it  is  in  itself  adapted  to 
prove.  This  imperfection  arises  from  Plurality  of  Causes.  Although 
two  or  more  cases  in  which  the  phenomenon  a  has  been  met  with,  may 
have  no  common  antecedent  except  A,  this  does  not  prove  that  there 
is  any  connexion  between  a  and  A,  since  a  may  have  many  causes,  and 
may  have  been  produced,  in  these  different  instances,  not  by  anything 
which  the  instances  had  in  common,  but  by  some  of  those  elements  in 
them  which  were  different.  We,  nevertheless,  observed,  that  in  propor- 
tion to  the  multiplication  of  instances  pointing  to  A  as  the  antecedent, 
the  characteristic  uncertainty  of  the  method  diminishes,  and  the  exist- 
ence of  a  law  of  connexion  between  A  and  a  more  nearly  approaches 
to  certainty.  It  is  now  to  be  determined,  after  what  amount  of  expe- 
rience this  certainty  may  be  deemed  to  be  practically  attained,  and  the 
connexion  between  A  and  a  may  be  received  as  an  empirical  law. 

This  question  may  be  otherwise  stated  in  more  familiar  terms : — 
After  how  many  and  what  sort  of  instances  may  it  be  concluded,  that 
an  observed  coincidence  between  two  phenomena  is  not  the  effect  of 
chance  ? 

It  is  of  the  utmost  importance  for  understanding  the  logic  of  induc- 
tion, that  we  should  form  a  distinct  conception  of  what  is  meant  by 
chance,  and  how  the  phenomena  which  common  language  asciibes  tx> 
that  abstraction  are  really  produced. 

§  2.  Chance  is  usually  spoken  of  in  direct  antithesis  to  law ;  what- 
ever (it  is  supposed)  cannot  be  ascribed  to  any  law,  is  attributed  to 
chance.  It  is,  however,  certain,  that  whatever  happens  is  the  result 
of  some  law  ;  is  an  effect  of  causes,  and  could  have  been  predicted 
from  a  knowledge  of  the  existence  of  those  causes,  and  from  their  laws. 
If  I  turn  up  a  particular  card,  that  is  a  consequence  of  its  place  in  the 
pack.  Its  place  in  the  pack  was  a  consequence  of  the  manner  in 
which  the  cards  were  shuffled,  or  of  the  order  in  which  they  were 
played  in  the  last  game  ;  which,  again,  were  the  effects  of  prior  causes. 
At  every  stage,  if  we  had  possessed  an  accurate  knowledge  of  tlie 
causes  in  existence,  it  would  have  been  abstractedly  possible  to  foretell 
the  effect. 

An  event  occurring  by  chance,  may  be  described  as  a  coincidence 
from  which  we  have  no  ground  to  infer  an  uniformity  :  the  occurrence 
of  a  phenomenon  in  certain  circumstances,  without  our  having  reason 
on  that  account  to  infer  that  it  will  happen  again  in  those  circum- 
stances. This,  however,  when  looked  closely  into,  implies  that  the 
enumeration  of  the  circumstances  is  not  complete.  Whatever  the  fact 
be,  since  it  has  occurred  once,  we  may  be  sure  that  if  all  the  same  cir- 

*  Supra,  p.  252. 


314  INDUCTION. 

cumstances  were  repeated,  it  would  occur  again  ;  and  not  only  if  all, 
but  there  is  some  particular  portion  of  those  circumstances  upon  which 
the  phenomenon  is  invariably  consequent.  With  most  of  them,  how- 
ever, it  is  not  connected  in  any  peiTnanent  manner  :  its  conjmiction 
with  those  is  said  to  be  the  effect  of  chance,  to  be  merely  casual. 
Facts  casually  conjoined  are  separately  the  effects  of  causes,  and 
therefore  of  laws;  but  of  different  causes,  and  causes  not  connected 
by  any  law. 

It  is  incorrect,  then,  to  say  that  any  phenomenon  is  produced  by 
chance  ;  but  we  may  say  that  two  or  more  phenomena  are  conjoined 
by  chance,  that  they  coexist  or  succeed  one  anotlier  only  by  chance  j 
meaning  that  they  are  in  no  way  related  through  causation  ;  that  they  ai'e 
neither  cause  and  effect,  nor  effects  of  the  same  cause,  nor  effects  of 
causes  between  which  there  subsists  any  law  of  coexistence,  nor  even 
effects  of  the  same  original  collocation  of  piimeval  causes. 

If  the  same  casual  coincidence  never  occurred  a  second  time,  we 
should  have  an  easy  test  for  distinguishing  such  from  the  coincidences 
which  are  results  of  a  law.  As  long  as  the  phenomena  had  been  found 
together  only  once,  so  long,  unless  we  knew  some  more  general  laws 
from  which  the  coincidence  might  have  resulted,  we  could  not  distin- 
guish it  from  a  casual  one ;  but  if  it  occurred  twice,  we  should  know 
that  the  phenomena  so  conjoined  must  be  in  some  way  connected 
through  their  causes. 

There  is,  however,  no  such  test.  A  coincidence  may  occur  again 
and  again,  and  yet  be  only  casual.  Nay,  it  would  be  inconsistent  with 
what  we  know  of  the  order  of  nature,  to  doubt  that  every  casual  coin- 
cidence will  sooner  or  later  be  repeated,  as  long  as  the  phenomena 
between  which  it  occurred  do  not  cease  to  exist,  or  to  be  produced. 
The  recurrence,  therefore,  of  the  same  coincidence  more  than  once, 
or  even  its  fi-equent  recurrence,  does  not  prove  that  it  is  an  instance  of 
any  law ;  does  not  prove  that  it  is  not  casual,  or,  in  common  language, 
the  effect  of  chance. 

And  yet,  when  a  coincidence  cannot  be  deduced  fi'om  knowni  laws, 
nor  proved  by  experiment  to  be  itself  a  case  of  causation,  the  fi-equency 
of  its  occurrence  is  the  only  evidence  fi'om  which  we  can  infer  that.it 
is  the  result  of  a  law.  Not,  however,  its  absolute  fi-equency.  The 
question  is  not  whether  the  coincidence  occurs  often  or  seldom,  in  the 
ordinary  sense  'of  those  terms  ;  but  whether  it  occurs  7fiore  often  than 
chance  will  account  for;  more  often  than  might  rationally  be  expected 
if  the  coincidence  were  casual.  We  have  to  decide,  therefore,  what 
degi'ee  of  frequency  in  a  coincidence  chance  will  account  for.  And  to 
this  there  can  be  no  general  answer.  We  can  only  state  the  piinciple 
by  which  the  answer  must  be  deteiiained :  the  answer  itself  will  be 
different  in  every  different  case. 

^  Suppose  that  one  of  the  phenomena,  A,  exists  always,  and  the  other 
phenomenon,  B,  only  occasionally  :  it  follows  that  every  instance  of  B 
will  be  an  instance  of  its  coincidence  with  A,  and  yet  the  coincidence 
will  be  merely  casual,  not  the  result  of  any  connexion  between  them. 
The  fixed  stars  have  been  constantly  in  existence  since  the  beginning 
of  human  experience,  and  all  phenomena  that  have  come  under  human 
observation  have,  in  every  single  instance,  coexisted  with  them ;  yet 
this  coincidence,  although  equally,  invariable  with  that  which  exists 
between  any  of  those  phenomena  and  its  ovni  cause,  does  not  prove 


CHANCE,    AND    ITS    ELIMINATION.  315 

that  the  stars  are  its  cause,  nor  that  they  arp  in  anywise  connected 
with  it.  As  strong  a  case  of  coincidence,  therefore,  as  can  possibly 
exist,  and  a  much  stronger  one  in  point  of  mere  frequency  than  most 
of  those  which  prove  laws,  does  not  here  prove  a  law:  whyl  because, 
since  the  stars  exist  always,  they  must  coexist  with  every  other  phe- 
nomenon, whether  connected  with  them  by  causation  or  not.  The 
uniformity,  gieat  though  it  be,  is  no  greater  than  would  occur  on  the 
supposition  that  no  such  connexion  exists. 

On  the  other  hand,  suppose  that  we  were  inquiring  whether  there 
be  any  connexion  between  raiu  and  any  particular  wind.  Rain,  we 
know,  occasionally  occurs  with  every  wind ;  therefore  the  connexion, 
if  it  exists,  cannot  be  an  actual  law ;  but  still,  rain  may  be  connected 
wth  some  particular  wind  through  causation ;  that  is,  although  they 
cannot  be  always  effects  of  the  same  cause  (for  if  &o  they  would  always 
coexist),  there  may  be  so77ie  causes  common  to  the  two,  so  that  in  so 
far  as  either  is  produced  by  those  common  causes,  they  \vill,  from  the 
laws  of  the  causes,  be  found  to  coexist.  How,  then,  shall  we  ascertain 
this  ]  The  obx'ious  answer  is,  by  obsci"ving  whether  rain  occurs  with 
one  wind  more  frequently  than  with  any  other.  That,  however,  is  not 
enough ;  for  perhaps  that  one  wind  blows  more  fi-equently  than  any 
other ;  so  that  its  blowing  more  fiequently  in  rainy  weather  is  no  more 
than  would  happen,  although  it  had  no  connexion  wth  the  causes  of 
rain,  provided  it  were  not  connected  with  causes  adverse  to  rain.  In 
England,  westerly  winds  blow  during  about  twice  as  great  a  portion 
of  the  year  as  easterly.  If,  therefore,  it  rains  only  twice  as  often  with 
a  westerly,  as  with  an  easterly  wind,  we  have  no  reason  to  infer  that 
any  law  of  nature  is  concerned  in  the  coincidence.  If  it  rains  more 
than  twice  as  often,  we  may  be  sure  that  some  law  is  concenied  ; 
either  there  is  some  cause  in  nature  tending  to  produce  both  rain  and 
a  westerly  wind,  or  a  westerly  wind  has  itself  some  tendency  to  pro- 
duce rain.  But  if  it  rains  less  than  twice  as  often,  we  may  draw  a 
directly  opposite  inference ;  the  one,  instead  of  being  a  cause,  or  con- 
nected with  causes  of  the  other,  must  be  connected  with  causes  ad- 
verse to  it,  or  with  the  absence  of  some  cause  which  produces  it ;  and 
although  it  may  still  rain  much  oftener  with  a  westerly  wind  than  with 
an  easterly,  so  far  would  this  be  from  proving  any  connexion  between 
the  phenomena,  that  the  connexion  proved  would  be  between  rain  and 
an  easterly  wind,  the  wind  to  which,  in  mere  frequency  of  coincidence, 
it  is  least  allied. 

Here,  then,  are  two  examples :  in  one,  the  greatest  possible  fre- 
quency of  coincidence,  with  no  instance  whatever  to  the  contrary,  does 
not  prove  that  there  is  any  law ;  in  the  other,  a  much  less  frequency 
of  coincidence,  even  when  non-coincidence  is  still  more  frequent,  does 
prove  that  there  is  a  law.  In  both  cases  the  principle  is  the  same.  In 
bfith  we  consider  the  positive  frequency  of  the  phenomena  themselves, 
and  how  groat  frequency  of  coincidence  that  must  of  itself  bring  about, 
without  supposing  any  connexion  between  them,  provided  there  be  no 
repugnance  ;  provided  neither  bo  connected  with  any  cause  tending 
to  frustrate  the  other.  If  we  find  a  greater  frequency  of  coincidence 
than  this,  we  conclude  that  there  is  some  connexion  ;  if  a  less  fre- 
quency, that  there  is  some  repugnance.  In  the  former  case,  we  con- 
clude that  one  of  the  phenomena  can  under  some  circumstances  cause 
the  other,  "or  that  there  exists  something  capableof  causing  them  both; 


316  INDUCTION. 

in  the  latter,  that  one  of  them,  or  some  cause  which  produces  one  o 
them,  is  capable  of  counteracting  the  production  of  the  other.  We 
have  thus  to  deduct  from  the  observed  frequency  of  coincidence,  as 
much  as  may  be  the  effect  of  chance,  that  is,  of  the  mere  frequency  of 
the  phenomena  themselves  ;  and  if  anything  remains,  what  does  re- 
main is  the  residual  fact  which  proves  the  existence  of  a  law. 

The  frequency  of  the  phenomena  can  only  be  ascertained  within 
definite  limits  of  space  and  time  ;  depending  as  it  does  on  the  quantity 
and  distribution  of  the  primeval  natural  agents,  of  which  we  can  know 
nothing  beyond  the  boundaries  of  human  observation,  since  no  law,  no 
regularity,  can  be  traced  in  it,  enabling  us  to  infer  the  unknown  from 
the  known.  But  for  the  present  purpose  this  is  no  disadvantage,  the 
question  being  confined  within  the  same  limits  as  the  data.  The  coin- 
cidences occurred  in  certain  places  and  times,  and  within  those  we  can 
estimate  the  frequency  with  which  such  coincidences  would  be  pro- 
duced by  chance.  If,  then,  we  find  from  observation  that  A  exists  in 
one  case  out  of  every  two,  and  B  in  one  case  out  of  every  three  ;  then 
if  there  be  neither  connexion  nor  repugnance  between  them,  or  be- 
tween any  of  their  causes,  the  instances  in  which  A  and  B  will  both 
exist,  that  is  to  say  will  coexist,  will  be  one  case  in  every  six.  For  A 
exists  in  three  cases  out  of  six  ;  and  B,  existing  in  one  case  out  of 
every  three  without  regard  to  the  presence  or  absence  of  A,  will  exist 
in  one  case  out  of  those  three.  There  will  therefore  be,  of  the  whole 
number  of  cases,  two  in  which  A  exists  without  B  ;  one  case  of  B 
without  A ;  two  in  which  neither  B  nor  A  exists,  and  one  case  out  of 
six  in  which  they  both  exist.  If  then,  in  point  of  fact,  they  are  found 
to  coexist  oftener  than  in  one  case  out  of  six  ;  and,  consequently  A 
does  not  exist  without  B  so  often  as  twice  in  three  times,  nox  B  with- 
out A  so  often  as  once  in  every  twice ;  there  is  some  cause  in  exist- 
ence, which  tends  to  produce  a  conjunction  between  A  and  B. 

Generalizing  the  result,  we  may  say,  that  if  A  occurs  in  a  larger 
proportion  of  the  cases  where  B  is,  than  of  the  cases  where  B  is  not ; 
then  will  B  also  occur  in  a  larger  proportion  of  the  cases  where  A  is, 
than  of  the  cases  where  A  is  not ;  and  there  is  some  connexion,  through 
causation,  between  A  and  B.  If  we  could  ascend  to  the  causes  of  the 
two  phenomena,  we  should  find,  at  some  stage,  either  proximate  or 
remote,  some  cause  or  causes  common  to  both;  and  if  we  could  ascer- 
tain what  these  are,  we  could  frame  a  generalization  which  would  be 
time  without  restriction  of  place  or  time  :  but  until  we  can  do  so,  the 
fact  of  a  connexion  between  the  two  phenomena  remains  an  em- 
pirical law. 

§  3.  Having  considered  in  what  manner  it  may  be  deteimined 
whether  any  given  conjunction  of  phenomena  is  casual  or  the  result  of 
some  law;  to  complete  the  theory  of  chance,  it  is  necessary  that  we 
should  now  consider  those  effects  which  are  partly  the  result  of  chance 
and  partly  of  law :  or  in  other  words,  in  which  the  effects  of  casual 
conjunctions  of  causes  are  habitually  blended  in  one  result  with  the 
effects  of  a  constant  cause. 

This  is  a  case  of  Composition  of  Causes;  and  the  peculiarity  of  it 
is,  that  instead  of  two  or  more  causes  intermixing  their  effects  in  a 
regular  manner  with  those  of  one  another,  we  have  now  one  constant 
cause,  producing  an  effect  which  is  successively  modified  by  a  series 


CHANCE,    AND    ITS    ELIMINATION,  317 

of  variable  causes.  Thus,  as  summer  advances,  the  approach  of  the 
sun  to  a  vertical  position  tends  to  produce  a  constant  increase  of  tem- 
perature ;  but  with  this  efl'ect  of  a  constant  cause,  there  are  blended 
the  effects  of  many  variable  causes,  winds,  clouds,  evaporation,  elec- 
tric agencies,  and  the  like,  so  that  the  temperature  on  any  given  day 
depends  in  part  upon  these  fleeting  causes,  and  only  in  part  upon  the 
constant  cause.  If  the  effect  of  die  constant  cause  is  always  accom- 
panied and  disguised  by  effects  of  variable  causes,  it  is  impossible  to 
ascertain  the  law  of  the  constant  cause  in  the  ordinary  manner,  by 
separating  it  from  all  other  causes  and  observing  it  apart.  Hence 
ai-ises  the  necessity  of  an  additional  rule  of  experimental  inquiry. 

When  the  action  of  a  cause  A  is  liable  to  be  interfered  with,  not 
steadily  by  the  same  cause  or  causes,  but  by  different  causes  at  differ- 
ent times,  and  when  these  are  so  frequent,  or  so  indeterminate,  that 
we  camiot  possibly  exclude  all  of  them  from  any  experiment,  although 
we  may  vary  them  ;  our  resource  is,  to  endeavor  to  ascertain  what  is 
the  effect  of  all  the  variable  causes  taken  together.  In  order  to  do 
this,  we  make  as  many  trials  as  possible,  preserving  A  invariable.  The 
results  of  these  diffi>rent  trials  will  naturally  be  different,  since  the 
indeterminate  modifying  causes  are  different  in  each :  if,  then,  we  do 
not  flud  these  results  to  be  progressive,  but  on  the  contrary  to  oscillate 
about  a  certain  point,  one  experiment  giving  a  result  a  little  greater, 
another  a  little  less,  one  a  result  tending  a  little  more  in  one  direction, 
another  a  little  more  in  the  contrary  direction ;  while  the  average,  or 
middle  point,  does  not  vary,  but  different  sets  of  experiments  (taken 
under  as  great  a  variety  of  circumstances  as  possible)  yield  the  same 
mean,  provided  only  they  be  sufficiently  numerous ;  then  that  mean, 
or  average  result,  is  the  part,  in  each  experiment,  which  is  due  to  the 
cause  A,  and  is  the  effect  which  would  have  been  obtained  if  A  could 
have  acted  alone :  the  variable  remainder  is  the  effect  of  chance,  that 
is,  of  causes  the  coexistence  of  which  with  the  cause  A  was  merely 
casual.  The  test  of  the  sufficiency  of  the  induction  in  this  case  is, 
when  any  increase  of  the  number  of  trials  from  which  the  average  is 
struck,  does  not  materially  alter  the  average. 

This  kind  of  elimination,  in  which  we  do  not  eliminate  any  one 
assignable  cause,  but  the  multitude  of  floating  unassignable  ones,  may 
be  termed  the  Elimination  of  Chance.  We  afford  an  example  of  it 
when  we  repeat  an  experiment,  in  order,  by  taking  the  mean  of  differ- 
ent results,  to  get  rid  of  the  effects  of  the  unavoidable  eri'ors  of  each 
individual  experiment.  Wlien  tliere  is  no  permanent  cause  such  as 
would  produce  a  tendency  to  error  peculiarly  in  one  direction,  we  are 
wananted  by  experience  in  assuming  that  the  errors  on  one  side  will, 
in  a  ceitain  number  of  experiments,  about  balance  the  errors  on  the 
contrary  side.  We  have,  therefore,  to  repeat  the  experiment,  until 
any  change  which  is  produced  in  the  avetage  of  the  wliole  by  further 
repetition,  f;iJls  within  limits  of  eiTor  consistent  with  the  degree  of 
accuracy  required  by  the  purpose  we  have  in  view. 

§  4.  In  the  supposition  hitherto  made,  the  effect  of  the  constant  cause 
A  has  been  assumed  to  form  so  great  and  conspicuous  a  part  of  the 
general  result,  that  its  existence  never  could  be  a  matter  of  uncer- 
tainty, and  the  object  of  the  eliminating  process  was  only  to  ascertain 
how  much  is  attributable  to  that  cause ;  what  is  its  exact  law.     Cases, 


318  INDUCTION. 

however,  occur  in  which  the  effect  of  a  constant  cause  is  so  small, 
compared  with  that  of  some  of  the  changeable  causes  with  which  it  is 
liable  to  be  casually  conjoined,  that  of  itself  it  escapes  notice,  and  the 
very  existence  of  any  effect  arising  from  a  constant  cause  is  first  learnt, 
by  the  process  which  in  general  serves  only  for  ascertaining  the  quantity 
of  that  effect.  This  case  of  induction  may  be  characterized  as  follows. 
A  given  effect  is  known  to  be  chiefly,  and  not  known  not  to  be  wholly, 
determined  by  changeable  causes.  If  it  be  wholly  so  produced,  then 
if  the  aggregate  be  taken  of  a  sufiicient  number  of  instances,  the 
effects  of  these  different  causes  will  cancel  one  another.  If,  therefore, 
we  do  not  find  this  to  be  the  case,  but,  on  the  contrary,  after  such  a 
number  of  trials  has  been  made  that  no  further  increase  alters  the 
average  result,  we  find  that  average  to  be,  not  zero,  but  some  other 
quantity,  around  which,  though  small  in  comparison  with  the  total 
effect,  the  effect  nevertheless  oscillates,  and  which  is  the  middle  point 
in  its  oscillation ;  we  may  conclude  this  to  be  the  effect  of  some  con- 
stant cause ;  which  cause,  by  some  of  the  methods  already  treated  of, 
we  may  hope  to  detect.  This  may  be  called  the  discovery  of  a  residual 
plienomenon  by  elmiinating  the  effect  of  chance. 

It  is  in  this  manner,  for  example,  that  loaded  dice  may  be  discovered. 
Of  course  no  dice  are  so  climisily  loaded  that  they  must  always  throw 
certain  numbers ;  otherwise  the  fraud  would  be  instantly  detected. 
The  loading,  a  constant  cause,  mingles  with  the  changeable  causes 
which  determine  what  cast  will  be  thrown  in  each  individual  instance. 
If  the  dice  were  not  loaded,  and  the  throw  were  left  to  depend  entirely 
upon  the  changeable  causes,  these  in  a  sufiicient  number  of  instances 
would  balance  one  another,  and  there  would  be  no  preponderant 
number  of  throws  of  any  one  kind.  If,  therefore,  after  such  a  number 
of  trials  that  no  further  increase  of  their  number  has  any  material 
effect  upon  the  average,  we  find  a  preponderance  in  favor  of  a  partic- 
ular throw;  we  may  conclude  with  assurance  that  there  is  some  constant 
cause  acting  in  favor  of  that  throw,  or  in  other  words,  that  the  dice 
are  not  fair  ;  and  moreover  the  exact  amount  of  the  unfairness.  In  a 
similar  manner,  what  is  called  the  diurnal  variation  of  the  barometer, 
which  is  very  small  compared  with  the  variations  arising  from  the 
irregular  changes  in  the  state  of  the '  atmosphere,  was  discovered  by 
comparing  the  average  height  of  the  barometer  at  different  hours  of 
the  day.  When  this  comparison  was  made,  it  was  found  that  there 
was  a  small  difference,  which  on  the  average  was  constant,  however 
the  absolute  quantities  might  vary,  and  which  difference,  therefore, 
must  be  the  effect  of  a  constant  cause.  This  cause  was  afterwards 
asceitained,  deductively,  to  be  the  rarefaction  of  the  air,  occasioned 
by  the  increase  of  temperature  as  the  day  advances. 

§  5.  After  these  general  remarks  on  the  nature  of  chance,  we  are 
prepared  to  consider  in  what  manner  assurance  may  be  obtained  that 
a  conjunction  between  two  phenomena,  which  has  been  obseiTed  a 
certain  number  of  times,  is  not  casual,  but  a  result  of  causation,  and 
to  be  received  therefore  as  one  of  the  uniformities  in  nature,  although 
(until  accounted  for  a  priori)  only  as  an  empirical  law. 

We  will  suppose  the  strongest  case,  namely,  that  the  phenomenon  B 
has  never  been  observed  except  in  conjunction  with  A.  Even  then, 
the  probability  that  they  are  connected  is  not  measured  by  the  total 


CALCULATION    OP    CHANCES.  319 

numl>er  of  instances  in  which  they  have  been  found  together,  but  by 
the  excess  of  that  number  above  the  number  due  to  the  absolute  fre- 
quency of  A.  If,  for  example,  A  exists  always,  and  therefore  coexists 
with  everything,  no  number  of  instances  of  its  coexistence  with  B 
would  prove  a  connexion  ;  as  in  our  example  of  the  fixed  stars.  If  A 
be  a  fact  of  such  common  occurrence  that  it  may  be  presumed  to  be 
present  in  half  of  all  the  cases  that  occur,  and  therefore  in  half  the 
cases  in  which  B  occurs,  it  is  only  the  proportional  excess  above  half, 
that  are  to  be  reckoned  as  evidence  towards  proving  a  connexion 
between  A  and  B. 

In  addition  to  the  question,  What  is  the  number  of  coincidences 
which,  on  an  average  of  a  great  multitude  of  trials,  may  bo  i^xpected 
to  arise  from  chance  alone  ?. there  is  also  another  question,  namely,  Of 
what  extent  of  deviation  from  that  average  is  the  occuiTence  credible, 
fi-om  chance  alone,  in  some  number  of  instances  smaller  than  that 
which  constitutes  a  fair  average  ?  It  is  not  only  to  be  considered  what 
is  the  general  result  of  the  chances  in  the  long  run,  but  also  what  are 
the  exti-eme  limits  of  variation  from  that  general  result,  which  may 
occasionally  be  expected  as  the  result  of  some  smaller  number  of 
instances. 

The  consideration  of  the  latter  question,  and  any  consideration  of 
the  former  beyond  that  already  given  to  it,  belong  to  what  mathema- 
ticians term  the  doctrine  of  chances,  or,  in  a  phrase  of  greater  preten- 
sion, tlie  Theory  of  Probabilities.  An  attempt  at  a  philosophical  ajxpre- 
ciation  of  that  doctrine  is,  therefore,  a  necessary  portion  of  our  task. 


CHAPTER  XVIII. 

OF  THE  CALCULATION  OF  CHANCES. 

§  1.  "  Probability,"  says  Laplace,*  "  has  reference  partly  to  our 
ignorance,  partly  to  our  knowledge.  We  know  that  among  three  or 
more  events,  one,  and  only  one,  must  happen ;  but  there  is  nothing 
leading  us  to  believe  that  any  one  of  them  will  happen  rather  than  the 
others.  In  this  state  of  indecision,  it  is  impossible  for  us  to  pronounce 
with  certainty  on  their  occurrence.  It  is,  however,  probable  that  any 
one  of  these  events,  selected  at  pleasure,  will  not  take  jjlace ;  because 
we  perceive  several  cases,  all  equally  possible,  which  exclude  its  oc- 
cuiTcnce,  and  only  one  which  favors  it." 

Such  is  this  great  mathematician's  statement  of  the  logical  founda- 
tion upon  which  rests,  according  to  him,  the  theory  of  chances  :  and  if 
his  um-ivaled  command  over  the  means  which  mathematics  supply  for 
calculating  the  results  of  given  data,  necessarily  implied  an  equally 
surt;  judgment  of  what  the  data  ought  to  be,  I  should  luu"dly  dare  give 
utterance  to  my  conviction,  that  in  this  opinion  he  is  entirely  wrong ; 
that  his  foundation  is  altogether  insuflRcient  for  the  superstnu^ture 
erected  upon  it ;  and  that  there  is  implied,  in  all  rational  calculation 
of  the  probabilities  of  events,  an  essential  condition,  which  is  cither 

*  Essai  Philosophique  sur  les  Probabililis,  fifth  Palis  edition,  p.  7. 


320  INDUCTION. 

overlooked  in  Laplace's  statement,  or  so  vaguely  indicated  as  neither 
to  be  suggested  to  the  reader,  nor  kept  in  view  by  the  WTiter  himself. 
To  a  calculation  of  chances,  according  to  Laplace,  two  things  are 
necessary:  we  must  know  that  of  several  events  some  one  will  cer- 
tainly happen,  and  no  more  than  one ;  and  we  must  not  know,  nor 
have  any  reason  to  expect,  that  it  will  be  one  of  these  events 
rather  than  another.  I  contend  that  these  are  not  the  only  requis- 
ites, and  that  anotber  supposition  is  necessary.  This  supposition  it 
might  be  imagined  that  Laplace  intended  to  indicate,  by  saying 
that  all  the  events  must  be  equally  possible  {egalement  possibles). 
But  his  next  sentence  shows  that,  by  this  expression,  he  did  not 
mean  to  add  anything  to  the  two  conditions  which  he  had  already 
suggested.  "  The  theory  of  chances  consists  in  reducing  all  eventa 
of  the  same  kind  to  a  certain  number  of  cases  equally  possible, 
that  is,  such  that  we  ax'e  equally  undecided  as  to  their  existence ;  and 
to  determine  the  number  of  these  cases  which  are  favorable  to  the 
event  of  which  the  probability  is  sought."  By  "  events  equally  possi- 
ble," then,  he  only  means  events  "  such  that  we  are  equally  undecided 
as  to  their  existence ;"  that  we  have  no  reason  to  expect  one  rather 
than  another ;  which  is  not  a  third  condition,  but  the  second  of  the 
two  previously  specified.  I,  therefore,  feel  warranted  in  affirming 
that  Laplace  has  overlooked,  in  this  general  theoretical  statement, 
a  necessary  part  of  the  foundation  of  the  doctrine  of  chances. 

§  2.  To  be  able  to  pronounce  two  events  equally  probable,  it  is  not 
enough  that  we  should  know  that  one  or  the  other  must  happen,  and 
should  have  no  ground  for  conjecturing  which.  Experience  must 
have  shown  that  the  two  events  are  of  equally  frequent  occurrence. 
Why,  in  tossing  up  a  halfpenny,  do  we  reckon  it  equally  probable 
that  we  shall  throw  cross  or  pile  ]  Because  experience  has  shown 
that  in  any  gi'eat  number  of  throws,  cross  and  pile  are  throwTi  about 
equally  often ;  and  that  the  more  throws  we  make,  tlie  more  nearly 
the  equality  is  perfect.  We  call  the  chances  even,  because  if  we 
stake  equal  sums,  and  play  a  certain  large  number  of  times,  experi- 
ence proves  that  our  gains  and  losses  will  about  balance  one  another ; 
and  will  continue  to  do  so,  however  long  afterwards  we  continue  play- 
ing :  while  on  the  contrary,  if  we  give  the  slightest  odds,  and  play  a 
great  number  of  times,  we  are  sure  to  lose ;  and  the  longer  we  con- 
tinue playing,  the  greater  losers  we  shall  be.  If  experience  did  not 
prove  this,  we  should  proceed  as  much  at  haphazard  in  staliing  equal 
sums  as  in  laying  odds  ;  we  should  have  no  more  reason  for  expecting 
not  to  be  losers  by  the  one  wager  than  by  the  other. 

It  would  indeed  require  strong  evidence  to  persuade  any  rational 
person  that  by  a  system  of  operations  upon  numbers,  our  ignorance 
can  be  coined  into  science ;  and  it  is  doubtless  this  strange  pretension 
which  has  driven  a  profound  thinker,  M.  Comte,  into  the  contrary 
extreme  of  rejecting  altogether  a  doctrine  which,  however  imperfectly 
its  principles  may  sometimes  have  been  conceived,  receives  daily  veri- 
fi.cation  from  the  practice  of  insurance,  and  from  a  great  mass  of  other 
positive  experience.  The  doctrine  itself  is,  I  conceive,  soimd,  but  the 
manner  in  which  its  foundations  have  been  laid  by  its  gi-eat  teachers  is 
most  seriously  objectionable.  Conclusions  respecting  the  probability 
of  a  fact  rest  not  upon  a  diflerent,  but  upon  the  very  same  ba^is,  as 


CALCULATION  OF  CHANCES.  321 

conclusions  respecting  its  certainty  ;  namely,  not  our  ignorance,  but 
our  knowledge  :  knowledge -obtained  by  experience,  of  the  proportion 
between  the  cases  in  which  the  tact  occurs,  and  those  in  whi(;h  it  does 
not  occur.  Every  calculation  of  chances  is  grounded  on  an  induction  : 
and  to  render  the  calculation  legitimate,  the  induction  must  be  a  valid 
one.  It  is  not  less  an  induction,  though  it  does  not  prove  that  the 
event  occurs  in  all  cases  of  a  given  description,  but  only  that  out  of  a 
given  number  of  such  cajios,  it  occurs  in  about  so  many.  The  fraction 
\vhich  mathematicians  use  to  designate  tlie  probability  of  an  event, 
is  the  ratio  of  these  two  immbers  ;  the  ascertained  proportion  between 
the  number  of  case^  in  which  the  event  occurs,  and  the  sum  of  all  the 
cases,  those  in  which  it  occurs  and  in  which  it  does  not  occur  taken 
together  In  playing  at  cross  and  pile,  the  description  of  cases  con- 
cerned are  tlirows,  and  the  probability  of  cross  is  one  half,  because  it 
is  found  that  if  we  throw  often  enough,  cross  is  thrown  about  once  in 
every  two  throws  ;  and  because  this  induction  is  made  under  circum- 
stances justifying  the  belief  that  the  propt)rtion  will  be  the  same  in 
other  cases  as  in  the  cases  examined.  In  the  cast  of  a  die,  the  proba- 
bility of  ace  is  one-sixth ;  not,  as  Laplace  would  say,  because  there 
are  six  possible  throws,  of  vphich  aqe  is  one,  and  because  we  do  not 
know  any  reason  why  one  should  turn  up  rather  than  another ;  but 
because  wo  do  know  that  in  a  hundred,  or  a  million  of  throws,  ace  will' 
be  throAvn  about  one-sixth  of  that  number,  or  once  in  six  times. 

Not  only  is  this  third  condition  indispensable,  but  if  we  have  that, 
we  do  not  want  Laplace's  two.  It  is  not  necessary  that  we  should 
knoAV  how  many  possibilities  there  are,  or  that  we  should  have  no 
more  reason  for  expecting  one  of  them  than  another.  If  a  north  wind 
blows  one  day  in  every  ten,  the  ptobability  of  a  north  wind  on  any 
given  day  will  be  one-tenth,  even  though  of.  the  remaining  possibilities 
a  west  wind  should  be  greatly  the  most  probable.  ,  If  we  know  that 
half  the  trees  in  a  particular  forest  are  oaks,  though  we  may  be.  quite 
igirorant  how  many  other  kinds  of  trees  it  contains,  the  chance  that  a 
tree  indiscximinately  selected  will  bo  an  oak  is  an  even  chance,  or,  in 
mathematical  language,  one-half.  So  that  the  condition  which  Laplace 
omittqd  is  not  merely  one  of  the  requisites  for  the  possibility  of  a  cal- 
culation of  chances  ;  it  is  the  only  requisite.     .  , 

In  saying  that  he  has  omitted  this  condition,  I  am  far  firom  meaning 
to  assert,  that  he  does  not  frequently  take  it  into  consideration  in  par- 
ticular instances:  nor  indeed  could  he  fail  to  do  so,  since  whenever 
any  experience  bearing  upon  the  case  really  exists,  he  would  naturally 
consult  that  experience  to  assure  himself  of  the  fulfilment  of  his  second 
condition,  that  there  be  no  reason  for  expecting  one  event  rather  tjian 
another.  When  experience  is  to  be  had,  he  takes  that  experience  as 
the  measure  of  the  probabiUty :  his  error  is  only  in  imagining  that 
there  can  be  a  measurement  of  probability  where  there  is  no  expe- 
rience. The  consequence  of  this  en-or  has  been  his  adoption  of  con- ' 
elusions  n(»t  indeed  contrary  to,  but  unsupported  by,  experience.  He 
has  been  led  to  push  the  theoiy  and  its  applications  beyond  the  bounds 
which  confine  all  legitimate  inferences  of  the  human  mind  ;  by  extend- 
ing them  to  subjects  on  which  the  absence  of  any  giound  fur  deter- 
mining between  two  suppositions,  does  not  arise  from  our  having  equal 
grounds  for  presuming  both,  but  from  our  haring  an  equal  absence  of 
gi-ounds  for  piesuming  either. 
Ss 


3.22  INDUCTION. 

According  to  his  views,  indeed,  the  calculation  of  chances  should  be 
much  more  universally  applicable  to  things  of  vv'hich  we  are  com- 
pletely ignorant,  than  to  things  of  which  we  have  partial  knowledge. 
Where  we  have  some  experience  of  the  occurrence  of  each  of  the  con- 
flicting possibilities,  it  may  often  be  difficult,  according  to  the  prescrip- 
tions of  the  theory,  to  reduce  those  possibilities  to  a  definite  number  of 
cases,  all  equally  probable  ;  but  when  the  case  is  out  of  the  reach  of 
all  experience,  so  that  we  have  no  difficulty  in  being  "  equally  unde- 
cided" respecting  the  possibilities,  there  is  nothing  to  make  us  halt  or 
waver  in  applying  the  theory.  If  the  question  be  whether  the  inhabit- 
ants of  Saturn  have  red  hair,  we  need  only  know  the  number  of  the 
prismatic  colors,  and  of  th-eir  more  marked  compounds,  and  we  can  at 
once  assign  the  fraction  corresponding  to  the  probability !  It  is  evi- 
dent that  probability,  in  any  sense  in  which  it  can  operate  upon  our 
belief  or  conduct,  has  nothing  to  do  with  such  chimerical  evaluations, 
and  that  entire  suspension  of  judgment,  where  we  have  no  evidence,  is 
the  only  course  befitting  a  rational  being.  To  entitle  us  to  affirm  any-  . 
thing  positive  abovit  uncertain  facts,  whether  it  be  that  one  supposition 
is  more  probable  than  another,  or  only  that  it  is  equally  probable,  we 
must  have  the  testimony  of  experience,  that,  taking  the  whole  of  some 
class  of  cases,  the  one  guess  will  be  oftener  right,  or  as  often  right  as 
the  other.  The  estimation,  in  short,  of  chances,  like  that  of  certain- 
ties, is  only  rational  when  grounded  upon  a  complete  induction  by 
observation  or  experiment.* 

§  3.  From  these  principles  it  is  easy  to  deduce  the  demonstration  of 
that  theorem  of  the  doctrine  of  probabilities,  which  is  the  foundation 
of  its  principal  application  to  judicial  or  other  inquiries  for  ascertain- 
ing the  occurrence  of  a  given  event,  or  the  reality  of  an  individual 
fact.     The  signs  or  evidences  by  which  a  fact  is  usually  proved,  are 

*  Confusion  is  sometimes  introduced  into  this  subject  by  not  adverting  to  the  distinction 
between  the  chances  that  a  given  event  will  happen,  and  the  chances  that  a  guess,  not  yet 
made,  respecting  its  occurrence,  will  be  right.  Supposing  that  I  have  rio  more  reason  to. 
expect  one  event  than  another,  it  is  (frotn  experience  of  human  actions)  an  equal  chance 
whether  I  guess  A  or  B  ;  but  it  is  not,  therefore,  an  equal  chance  whether  A  or  B  takes 
place. 

The  fallacy  has  been  stated  thus.  Suppose  tliat  either  A  or  B  must  happen:  and  let 
the  chance  that  A  will  happen  be  x:  as  certainty  is  represented  by  1,  the  chance  that  B 
will  happen  is  1  —x.  Now,  the  chance  that  the  event  I  guess  will  come  to  pass,  is  made 
up  of  two  chances:  the  chance  that  I  shall  guess  A  and  that  A  will  happen,  plus  the 
chance  that  I  shall  guess  B  and  that  B  wil)  happen.  The  chance  that  1  shall  guess  A 
being  \  ;  the  chance  that  1  shall  guess  A  and  that  A  will  happen,  is  compounded  of  \  and  x : 
it  is  therefore  1^.  The  chance  that  I  shall  guess  B  being  also  .1,  the  chance  that  I  shall 
guess  B  and  that  B  will  happen,  is-^  (1  —  ^)-  But  the  sum  of  ihcse  two  is  \  :  therefore  th^ 
chance  that  the  event  I  guess  will  come  to  pass,  is  always  an  even  chance.  But  since  it 
is  an  even  chance  that  my  guess  will  be  right,  it  is  an  even  chance  which  of  the  two  e.vents 
will  occur,  whatever  may  be  their  comparative  frequency  in  nature. 

The  whole  of  this  reasoning  is  sound  up  to  the  last  step,  but  that  step  is  a  non  se.qvUxa, 
Before  I  have  guessed,  or  until  I  have  made  my  guess  known,  it  is  an  even  chance  that  I 
guess  right ;  but  when  1  have  guessed,  and  guessed  A,  it  is  no  longer  an  even  chance  that 
I  have  guessed  right :  otherwise  there  would  be  an  even  chance  in  favor  of  the  most  im- 
probable event.  Let  the  question  be.  Is  Queen  Victoria  at  this  moment  alive  :■  and  let  me 
be  required  to  guess  aye  or  no,  without  knowing  about  what,  in  order  that  I  may  be  equally 
likely  to  guess  the  one  and  the  other.  No  one  will  say  it  is  an  even  chance  which  is  true ; 
but  It  really  is  an  even  chance  whether  my  guess  will  be  right.  The  chance  of my  giu.'ss- 
ing  in  the  negative  and  being  right,  is  \  of  a  very  small  chance,  nay,  perhaps  -^-5^15-^,  but 
the  chance  of  my  guessing  in  the  affirmative,  and  being  right,  is  \  of  the  remaining  yl^^-l^^ ; 
so  that  the  two  together  are  \.  When,  however,  I  have  guessed,  and  told  my  guess,  the 
even  chance  yvluch  of  the  two  I  should  .guess  is  converted  into  a  certainty,  li  1  have 
guessed  aye,  the  chance  that  I  am  right  is  xffT^^I :  i^  no>  i'  J^  only  rsWBTr- 


CALCULATION"  OF  CHANCES.  323 

some  of  its  consequences:  and  the  inquiry  hinges  upon  determining 
what  cause  is  mOv-^t  likely  to  have  produced  a  given  effect.  The  theo- 
rem applicable  to  such  investigations  is  the  Sixth  Principle  in  Laplace's 
Essai  Philo;sophiquc  sur  les  Frobahilif^s,  which  is  described  by  him  as 
"  tlie  fundamental  principle  of  that  branch  of  the  Analysis-  of  Chances, 
which  consists  in  ascending  from  e^•vnts  to  their  causes."* 

Given  an  effect  to  be  accounted  for,  and  there  being  several  causes 
which  might  have  produced  it,  but  of  the  presence  of  which,  in  the 
particular  case,  nothing  is  known  ;  the  probability  that  the  effect  was 
produced  by  any  one  of  these  causes-  is  as  the  antecedent  jnohahiUty 
of  the  cause,  >n/(/tij>/ied  by  the  probability  that  the  cause,  if  it  existed, 
would  have  produced  the  given  effect. 

Let  M  be  the  effect,  and  A,  13,  two  causes,  by  either  which  it  might 
have  been  produced.  To  find  the  probability  that  it  was  produced 
by  the  one  and  not  by  the  other,  ascertain  which  of  the  two  is  most 
likely  to  have  existed,  and  which  of  them,  if  it  did  exist,  was  most 
likely  to  produce  the  effect  M  :  the  probability  sought  is  a  compound 
of  these  two  probabilities.         ■    , 

Case  I.  Let  the  causes  be  both  alike  in  the  second  respect ;  either 
A  or  B,  when  it  exists,  being  supposed  equally  likely, (or  equally 
certain)  to  produce  M  ;  but  let  A  be  in  itself  twice  as  likely  as  B  to 
exist,  that  is,  twice  as  frequent  a  phenomenon.  Then  it  is  twice  as 
likely  to  have  existed  in  this  case,  and  to  have  been  the  cause  which 
produced  M. 

For,  since  A  exists  in  nature  twice  as  often  as  B ;  in  any  300  cases 
in  which  one  or  other  existed,  A  has  existed  200  times  and  B  100. 
But  either  A  or  B  must  have  existed  wherever  M  is  produced  :  there- 
fore in  300  times  that  M  is  produced,  A  was  the  producing  cause  20ft' 
times,  B  only  100,  that  is,  in  the  ratio  of  2  to  1.  Thus,  then,  if  the 
causes  are  alike  in  their  capacity  of  producing  the  effect,  the  proba- 
bility as  to  which  actually  produced  it,  is  in  the  ratio  of  their  arrtecedent 
probabilities.  "  ^  "^ 

Case  II.  Reversing  the  last  hypothesis,  let  us  suppose  that  the 
causes  are  equally  frequent,  equally  likely  to  have  existed,  but  not 
equally  hkely,  if  they  did  exist,  to  produce  M  :  that  in  throe  times  that 
A  occurs,  it  produces  that  effect  twice,  while  B,  in  three  times,  pro- 
duces it  only  once.  Since  the  two  causes  are  equally  frequent  in  their 
occuiTence ;  in  every  six  times  that  either  one  or  the  otlrer  eJcists,  A 
exists  tlu-ee  times  and  B  three  times.  A,  of  its  three  times,  produces 
M  in  two ;  B,  of  it*  three  times,  produces  M  in  one.  Thus,  in  the 
whole  six  times,  M  is  only  produced  thiice ;  but  of  that  thrice  it  is 
produced  twice  by- A,  once  only  by  B.  Consequently,  when  the  an- 
tecedent probabilities  of  the  causes  are  equal,  the  chances  that  the 
effect  was  produco<l  by  them  are  in  the  ratio  of  the  probabilities  that 
if  they  did  exist  they  would  produce  the  effect. 

Case  III.  The  third  cose,  that  in  which  the  causes  are  unlike  ia 
Doth  respects,  is  solved  by  what  ha.s  preceded.  For,  when  a  quantity 
depend;*  upon  two  other  quantities,  in  Such  a  manner  that  while  either 
of  them  remains  constant  it  is  proportional  to  the  other,  it  must  neces- 
sarily be  proportional  to  the  jiruduct  of  the  two  quantities,  tl»e  product 

♦  Pp.  18,  19.  The  theorem  is  not  slated  by  Laplaco  in  iHe  exact  terms  in  which  I  have 
stated  it ;  but  the  identity  of  import  of  the  two  modes  of  expression  is  easily  demonstrable. 


324  INDUCTION. 

beino-  the  only  function  of  the  two  which  obeys  that  particular  law  of 
Variation.^  Therefore,  the  probability  that  M  was  produced  by  either 
cause,  is  as  the  antecedent  probability  of  the  cause,  multiplied  by  the 
probability  that  if  it  existed  it  would  produce  M.  Which  was  to  bo 
demonstrated. 

Or  we  may  prove  the  third  case  as  we  proved  the  first  and  second. 
Let  A  be  twice  as  frequent  as  B ;  and  let  them  also  be  unequally  likely, 
when  they  exist,  to  produce  M :  let  A  produce  it  twice  in  four  times, 
B  thrice  in  four  times.  The  antecedent  probability  of  A  is  to  that  of. 
B  as  2  to  1 ;  the  probabilities  of  their  producing  M  are  as  2  to  3  ;  the 
product  of  these  ratios  is  the  ratio  of  4  to  3,  which,  therefore,  if  the 
theorem  be  true,  will  be  the  ratio  of  the  probabilities  that  A  or  B  was. 
the  producing  cause  in  the  given  instance.  And  such  will  that  ratio 
really  be.  For  since  A  is  twice  as  frequent  as  B,  out  of  twelve  cases  in 
which  one  or  other  exists,  A  exists  in  8  and  B  in  4,  But  of  its  eight 
cases.  A,  by  the  supposition,  produces  M  in  only  4,  while  B  of  its  four 
cases  produces  M  in  3.  M,  therefore,  is  only  produced  at  all  m 
seven  of  the  twelve  cases;  but  in  four  of  these  it  is  produced  by  A,  in 
three  by  B  ;  hence,  the  probabilities  of  its  being  produced  by  A  and 
by  B  are  as  4  to  3,  and  are  expressed  by  the  fractions  |  and  ^.  Which 
was  to  be  demonstrated. 

It  is  here  necessary  to  point  out  another  serious  oversight  in  La- 
place's theory.  When  he  first  introduces  the  foregoing  theorem,  he 
characterizes  it  correctly,  as  the  principle  for  determining  to  which  of 
several  causes  we  are  to  attribute  a  known  fact.  But  after  having  con- 
ceived the  principle  thus  accurately,  when  he  comes  to  its  applications 
he  no  longer  restricts  it  to  the  ascertainment  of  causes  alone,  but,  with- 
out any  previous  notice  substitutes  for  the  idea  of  causes  that  o^  hypo- 
theses, or  suppositions  of  any  kind.  In  this  extended  sense,  I  do  not 
cpnceive  the  proposition  to  be  tenable.  The  hypotheses  must  be  either 
causes,  or  at  least  signs  showing  the  existence  of  causes.  If  we  could 
be  permitted  to  substitute  mere  suppositions  affording  no  ground  for 
concluding  that  the  effect  would  be  produced,  in  the  room  of  causes 
capable  of  producing  it,  the  theorem  thus  extended  would  stand  as 
follows.  A  fact,  M,  having  happened,  the  probability  of  the  truth  of 
any  arbitrary  supposition  altogether  unconnected  with  M,  is  as  the 
antecedent  probability  of  the  supposition,  multiphed  by  the  probability 
that  if  the  supposition  was  true  M  would  happen ;  that  is,  multiplied 
by  the  antecedent  probability  of  M,  since  M  is  neither  more  nor  less 
probable  on  account  of  a  supposition  which  has  nothing  to  do  with  the 
causes  of  it.  Now  the  proposition  as  thus  stated,  is  an  absurdity.  The 
probability  that  when  M  happened  A  had  pre\aously  happened,  is  not 
the  antecedent  probability  of  M  multiplied  by  that  of  A,  but  the  ante- 
cedent probability  of  A  only.  The  antecedent  probabiUty  of  M  cannot 
be  an  element  of  a  question  into  which  the  occun'ence  of  M  enters  not 
as  a  contingency  but  as  a  certainty.  What  the  product  of  the  antece- 
dent probabilities  of  A  and  M  does  give,  is,  not  the  probability  of  the 
the  one  when  the  other  is  a  known  past  event,  but  the  antecedent  prob- 
ability of  the  two  together,  considered  as  fiiture  events. 

This  error  of  Laplace  has  not  been  harmless.  We  shall  see  here- 
after, in  ti-eating  of  the  Grounds  of  DisbeHef,  that  he  has  been  led  by 
it  into  serious  practical  mistakes  when  attempting  to  pronounce  upon 
the  circumstances  which  render  any  statement  incredible. 


CALCULATION  OF  CHANCES.  325 

§  4.  From  the  preceding  view  of  the  foundation  of  the  doctrine  of 
chances,  its  gcncnd  principlt^:?  may  bo  seen  to  be  appHcable  in  a  rough 
way  to  many  subjects  which  are  by  no  means  amenable  to  its  precise 
calculations.  To  ivnder  these  applicable,  there  must  be  numerical 
data,  derived  from  the  observation  of  a  vei-y  large  number  of  instances. 
The  probabilities  of  life  at  dillerent  ages,  or  in  different  climates;  the 
probabilities  of  recovery  from  a  particular  disease  ;  the  chances  of  the 
birtli  of  male  or  female  offspring ;  the  chances  of  the  loss  of  a  vessel 
in  a  particular  voyage ;  all  these  admit  of  estimation  sufficiently  pre- 
cise to  render  the  numerical  appreciation  of  their  amount  a  thing  of 
pnictical  value ;  because  there  are  bills  of  mortality,  returns  from 
hospitals,  registers  of  birtlis,  of  shipwrecks,  &c.,  founded  on  cases 
sufficiently  numerous  to  afford  average  proportions  which  do  not 
materially  vaiy  from  year  to  year,  or  from  ten  yeai's  to  ten  years.  But 
where  obser\'ation  and  experiment  have  not  afforded  a  set  of  instances 
sufficiently  numerous  to  eliminate  chance,  and  sufficiently  various  to 
eliminate  all  non-essential  specialities  of  circumstance,  to  attempt  to 
calcidate  chances  is  to  convert  mere  ignorance  into  dangerous  error 
by  clothing  it  in  the  garb  of  knowledge. 

It  remains  to  examine  the  bearing  of  the  doctrine  of  chances  upon 
the  peculiar  problem  for  the  sake  of  which  wo  have  on  this  occasion 
adverted  to  it,  namely,  how  to  distinguish  coincidences  wliich  are 
casual  from  those  which  are  the  result  of  law ;  from  those  in  which  the 
facts  which  accompany  or  follow  one  another  are  somehow  connected 
through  causation. 

§  o.  The  doctrine  of  chances  affords  means  by  which,  if  we  knew 
the  average  number  of  coincidences  to  be  looked  for  between  two 
phenomena  connected  only  casually,  we  could  determine  how  often 
any  given  deviation  from  that  average  will  occur  by  chance.     If  the 

probability  of  any  casual  coincidence,  considered  in  itself,  be  — ,  the 

m 
probability  that  the  same  coincidence  will  be  repeated  n  times  in  suc- 
cession is  — ^.     For  example,  in  one  throw  of  a  die  the  probability  of 

ace  being  — ;  the  probability  of'  throwing  ace  twice  in  succession  will 

.  .  1 

be  1  divided  by  the  square  of  6,  or  — ,     For  ace  is  thrown  at  the  first 

throw  once  in  six,  or  six  in  thirty-six  times ;  and  of  those  six,  the  die 
being  cast  again,  ace  will  be  thrown  but  once  j  being  altogether  Once 
in  thirty-six  times.  Tie  chance  of  the  same  cast  three  times  succes- 
sively ia,  by  a  similar  reasoning,  —^  or  — —  :  that  is,  the  event  will  hap- 
pen, on  a  lai'ge  average,  only  once  in  two  hundred  and  sixteen 
throws. 

We  have  thus  a  rule  by  which  to  estimate  the  probability  that  any- 
given  series  of  coincidences  arises  from  chance ;  provided  we  can 
measure  coiTectly  the  probability  of  a  single  coincidence.  If  we  could 
obtain  an  equally  })reci8e  expression  for  the  probability  that  the  same 
series  of  coincidences  arises  from  causation,  wo  should  only  have  to 
compare  the  numbers.     This,  however,  can  rarely  be  done.     Let  us 


326  INDUCTION. 

see  what  degree  of  approximation  can  practically  be  made  to  the 
necessary  precision. 

The  question  falls  within  Laplace's  sixth  principle,  of  which  a  short 
distance  back,  we  gave  the  demonstration.  The  given  fact,  that  is  to 
say,  the  series  of  coincidences,  may  have  originated  -either  in  a  causal 
conjunction  of  causes  or  in  a  law  of  nature.  The  probabilities,  there- 
fore, that  the  fact  originated  in  these  two  modes,  are  as  their  ante- 
cedent probabilities,  multiplied  by  the  probabilities  that  if  they  existed 
they  would  produce  the  effect.  But  the  particular  combination  of 
chances  if  it  occuiTed,  or  the  law  of  nature  if  real,  would  certainly 
produce  the  series  of  coincidences.  The  probabilities,  therefore, 
that  the  coincidences  are  produced  by  the  two  causes  in  question, 
are  as  the  antecedent  probabilities  of  the  causes.  ■  One  of  these,  the 
antecedent  probability  of  the  combination  of  mere  chances  which 
would  produce  the  given  result,  is  an  appreciable  quantity.  The 
antecedent  probability  of  the  other  supposition  may  be  susceptible 
of  a  more  or  less  exact  estimation,  according  to  the  nature  of  the 
case. 

;In  some  cases,  the  coincidence,  supposing  it  to  be  the  result  of 
causation  at  all,  must  be  the  result  of  a  knowTi  cause ;  as  the  suc- 
cession of  aces,  if  not  accidental,  must  arise  from  the  loading  of  the 
die.  In  such  cases  we  may  be  able  to  form  a  conjecture  as  to  the 
antecedent  probability  of  such  a  circumstance,  from  the  characters 
of  the  parties  concerned,  or  other  such  evidence ;  but  it  would  clearly 
be  impossible  to  estimate  that  probability  with  anything  like  numerical 
precision.  The  counter-probability,  however,  that  of  the  accidental 
ojigin  of  the  coincidence,  dwindling  so  rapidly  as  it  does  at  each  new 
trial ;  the  stage  is  soon  reached  at  which  the  chance  of  unfairness  in 
the  die,  however  small  in  itself,  must  be  greater  than  that  of  a  causal 
coincidence :  and  on  this  ground,  a  practical  decision  can  generally  be 
come  to  without  much  hesitation,  if  there  be  the  power  of  repeating  the 
experiment.  ■        ' 

When,  however,  the  coincidence  is  one  which  cannot  be  accounted 
for  by  any  knowTi  cause,  and  the  connexion  between  the  two  phenom- 
ena, if  produced  by  causation,  must  be  the  result  of  some  law  of  nature 
hitherto  unknown ;  which  is  the  case  we  had  in  view  in  the  last  chap- 
ter; then,  although  the  probability  of  a  casual  coincidence  may  he 
capable  of  appreciation,  that  of  the  counter-supposition,  the  existence 
of  an  undiscovered  law  of  nature,  is  clearly  unsusceptible  of  even  an 
approximate  evaluation.  In  order  to  have  the  data  which  such  a  case 
would  require,  it  would  be  necessary  to  know  what  proportion  of  aU 
the  individual  sequences  or  coexistences  occuiTing  in  nature  are  the 
result  of  law,  and  what  proportion  are  the  result  of  chance.  It  being 
evident  that  we  cannot  form  any  plausible  conjecture  as  to  this  propor- 
tion, much  less  appreciate  it  numerically,  we  cannot  attempt  any  pre- 
cise estimation  of  the  comparative  probabilities.  But  of  this  we  are 
sure,  that  the  detection  of  an  unknown  law  of  nature — ^of  some  previ- 
ously unrecognized  constancy  of  conjunction  among  phenomena — is 
no  uncommon  event.  If,  therefore,  the  number  of  instances  in  which 
a  coincidence  is  observed,  over  and  above  that  which  would  arise  on 
the  average  from  the  mere  concurrence  of  chances,  be  such  that  so 
great  an  amount  of  coincidences  from  accident  alone  would  be  an 
extremely  uncommon  event ;  we  have  reason  to  concludo  that  the  coiiv- 


EXTENSION  OF  LAWS  TO  ADJACENT  CASES.  327 

cidcnce  is  the  efibct  of  ciiusation,  and  may  be  received  (subject  to 
correction  from  further  expcvioucc)  as  an  empirical  law.  Further 
tliaii  this,  in  point  of  precision,  we  cannot  go  ;  nor,  in  most  cases,  is 
greater  precision  required  for  the  solution  of  any  practical  doubt. 


CHAPTER  XIX. 

OF  THE  EXTENSION  OF  DERIVATIVE  LAWS  TO  ADJACENT  CASES. 

§  1.  We  have  had  frequent  occasion  to  notice  the  inferior  generality 
of  derivative  laws,  compared  with  the  ultimate  laws  from  which  they 
are  derived.  This  inferiority,  which  att'ects  not  only  the  extent  of  the 
propositions  themselves,  but  their  degree  of  certainty  within  that  ox- 
tent,  is  most  conspicuous  in  the  uniformities  of  coexistence  and  secjucnce 
obtaining  between  effects  which  depend  ultimately  upon  different 
primeval  causes.  Such  uniformities  will  only  obtain  where  there 
exists  the  same  collocation  of  those  primeval  causes.  If  the  collo- 
cation varies,  though  the  laws  themselves  remain  the  same,  a  totally 
different  set  of  derivative  uniformities  may,  and  generally  will,  be  the 
result. 

Even  where  the  derivative  uniformity  is  between  different  effects  of 
the  same  cause,  it  will  by  no  means  obtain  as  universally  as  the  law  of 
the  cause  itself.  If  a  and  h  accompany  or  succeed  one  another  as 
effects  of  the  cause  A,  it  by  no  means  follows  that  A  is  the  only  cause 
which  can  produce  them,  or  that  if  there  be  another  cause,  as  B, 
capable  of  })roducing  a,  it  must  produce  h  likewise.  The  conjunction, 
therefore,  of  «  and  h,  perhaps  does  not  hold  universally,  but  only  in  the 
instances  in  which  a  arises  from  A.  When  it  is  produced  by  a  cause 
other  than  A,  a  and  h  may  be  dissevered.  Day  (for  example)  is  always 
in  our  experience  followed  by  night ;  but  day  is  not  the  cause  of  night; 
both  are  successive  effects  of  a  common  cause,  the  periodical  passage 
of  the  spectator  into  and  out  of  the  earth's  shatlow,  consequent  on  the 
earth's  rotation,  and  on  the  illuminating  property  of  the  sun.  If,  there- 
fore, day  is  ever  produced  by  a  different  cause  or  set  of  causes  fiom 
this,  day  will  not,  or  at  least  nniy  not,  be  followed  by  night.  On  the 
sun's  own  surface,  for  instance,  this  may  be  the  case. 

Finally,  even  when  the  derivative  uniformity  is  itself  a  law  of  causa- 
tion (resulting  from  the  combination  of  several  causes),  it  is  not  alto- 
gether independent  of  collocations.  If  a  cause  supervenes,  capable  of 
wholly  or  partially  counteracting  the  effect  of  any  one  of  the  conjoined 
causes,  the  effect  will  no  longer  conform  to  the  derivative  law.  Wliile, 
tlierefore,  each  ultimate  law  is  only  liable  to  fi-ustration  from  one  set  of 
counteracting  causes,  the  derivative  law  is  liable  to  it  from  several. 
Now,  the  possiliility  of  the  occurrence  of  counteracting  causes  which 
do  not  arise  from  any  of  the  conditions  involved  in  the  law  itself, 
depends  on  the  original  collocations. 

it  is  true  that  (as  we  formerly  remarked)  laws  of  causation,  whether 
ultimate  or  derivative,  are,  in  most  cases,  fulfilled  even  when  counter- 
acted ;  the  cause  produces  its  effect,  though  that  effect  is  destroyed  by 
something  else.     That  the  effect  may  be  frustrated,  is,  therefore,  no 


328  INDUCTION. 

objection  to  the  universality  of  the  law  of  causation.  But  it  is  an  ob- 
jection to  the  universality  of  the  sequences  or  coexistences  of  effects, 
which  compose  the  greater  part  of  the  derivative  laws  flowing  from 
laws  of  causation.  When,  from  the  law  of  a  certain  combination  of 
■  causes,  there  results  a  certain  order  in  the  effects ;  as  from  the  combi- 
nation of  a  single  sun  with  the  rotation  of  an  opaque  body  round  its 
axis,  there  results,  on  the  whole  surface  of  that  opaque  body,  an  alter- 
nation of  day  and  night ;  then  if  we  suppose  one  of  the  combined 
causes  counteracted,  the  rotation  stopped,  the  sun  extinguished,  or  a 
second  sun  su2ieradded,  the  truth  of  that  paiticular  law  of  causation  is 
in  no  way  affected  ;  it  is  still  true  that  one  sun  shining  upon  an  opaque 
revolving  body  will  alternately  produce  day  and  night ;  but  since  the 
sun  no  longer  does  shine  upon  such  a  body,  the  derivative  uniformity, 
the  succession  of  day  and  night  on  the  given  planet,  is  no  longer  true. 
Those  dej-ivative  uniformities,  therefore,  which  are  not  laws  of  causa- 
tion, are  (except  in  the  rare  case  of  their  depending  upon  one  cause 
alone,  not  upon  a  combination  of  causes),  always  more  or  less  contin- 
gent upon  collocations ;  and  are  hence  subject  to.  the  characteristic 
infirmity  of  empirical  laws,  that  of  being  admissible  only  where  the 
collocations  are  known  by  experience  to  be  such  as  are  requisite  for 
the  truth  of  the  law,  that  is,  only  within  the  conditions  of  time  and 
place  confirmed  by  actual  observation. 

§  2.  This  principle,  when  stated  in  general  terms,  seems  clear  and 
indisputable ;  yet  many  of  the  ordinary  judgments  of  mankind,  the 
propriety  of  which  is  not  questioned,  have  at  least  the  semblance  of 
being  inconsistent  with  it.  On  what  grounds,  it  may  be  asked,  do  we 
expect  that  the  sun  will  rise  to-morrow  1  Is  to-morrow  within  the 
limits  of  time  comprehended  in  our  observations  1  They  have  extended 
over  some  thousands  of  years  past,  but  do  they  include  the  future  ] 
Yet  we  infer  with  confidence  that  the  sun  will  rise  to-morrow ;  and 
nobody  doubts  that  we  are  entitled  to  do  so.  Let,  us  consider  what  is 
the  waiTant  for  this  confidence. 

In  the  example  in  question,  we  know  the  causes  upon  which  the 
derivative  uniformity  depends.  They  are,  the  sun  giving  out  light, 
the  earth  in  a  state  of  rotation  and  intercepting  light.  The  induction 
which  shows  these  to  be  the  real  causes,  and  not  merely  prior  effects 
of  a  common  cause,  being  complete  and  irrefr'agable ;  the  only  circum- 
stances which  could  defeat  the  derivative  law  are  such  as  would  de- 
stroy or  counteract  one  or  other  of  the  combined  causes.  While  the 
causes  exist,  and  are  not  counteracted,  the  effect  will  continue.  If 
they  exist  and  are  not  counteracted  to-morrow,  the  sun  will  rise  to- 
morrow. 

Since  the  causes,  namely,  the  sun  and  the  earth,  the  one  in  the  state 
of  giving  out  light,  the  other  in  a  state  of  rotation,  will  exist  until  some- 
thing destroys  them ;  all  depends  upon  the  probabilities  of  their  destruc- 
tion, and  upon  those  of  their  counteraction.  We  know  by  observation 
(omitting  the  inferential  proofs  of  an  existence  for  thousands  of  ages 
anterior),  that  these  phenomena  have  continued  for  five  thousand  years. 
Within  that  time  there  has  existed  no  cause  sufficient  to  diminish  them 
appreciably ;  nor  which  has  counteracted  their  effect  in  any  appreciable 
degree.  The  chance,  therefore,  that  the  sun  may  not  rise  to-morrow, 
amounts  to  the  chance  that  some  cause,  which  has  not  manifested  itself 


EXTENSION    OF    LAWS    TO    ADJACENT    CASES.  329 

in  the  smallest  dogroo  durinr^  five  thousand  years;  will  exist  to-moirow 
in  6uch  intensity  as  to  destroy  the  sun  or  the  earth,  the  sun's  light  or 
the  earth's  rotation,  or  to  produce  an  immense  disturbance  in  the  efluct 
resulting  from  those  causes. 

Now,  if  such  a  cause  will  exist  to-morrow,  or  at  any  future  time, 
some  cause,  proximate  or  remot-c,  of  ihat  cause  must  exist  noW;  and 
must  have  existed  during  the  whole  of  the  five  thousand  years.  If, 
therefore,  the  sun  do  liot  rise  to-morrow,  it  will  be  bocause  some  cause 
has  existed,  the  effects  of  which,  though  during  five  thousand  years  they 
have  not  amounted  to  a  perceptible  quantity,  will  in  one  day  become 
overwhelming.  Since  this  cause  has  not  been  recognized  during  such 
an  interval  of  time,  by  observers  stationed  on  our  earth,  it  must,  if  it 
exist,  be  citlier  some  agent  whose  effects  develop  themselves  gradually 
and  very  slowly,  or  one  which  existed  in  regions  beyond  our  observa- 
tion, and  is  now  on  the  point  of  arriving  in  our  part  of  the  universe. 
Now  all  causes  which  we  have  experience  of,  act  according  to  laws 
incompatible  with  the  supposition  that  their  effects,  after  accumulating 
so  slowly  as  to  be  imperceptible  for  five  thousand  years,  should  start 
into  immensity  in  a  single  day.  No  mathematical  law  of  proportion 
between  an  effect  and  the  quantity  or  relations  of  its  cause,  could  pro- 
duce Kuch  contradictory  results.  The  sudden  development  of  an  effect, 
of  which  there  was  no  previous  trace,  always  arises  from  the  coming 
together  of  several  distinct  causes,  not  previously  conjoined;  but  3 
such  sudden  conjunction  is  destined  to  take  place,  the  causes,  or  their 
causes,  must  have  existed  during  the  entire  five  thousand  years,  and 
their  not  having  once  come  together  during  that  period,  shows  how; 
rare  that  particular  combination  is.  We  have,  therefore,  the  warrant 
of  a  rigid  induction  fin*  considering  it  probable,  in  a  degree  undistin- 
guishable  from  certainty,  that  the  known  conditions  requisite  for  the 
sun's  rising  will  exist  to-morrow. 

§  3.  But  this  extension  of  derivative  laws,  not  causative,  beyond  the 
limits  of  observation,  can  only  be  to  adjacent  cases.  If  instead  of  to- 
morrow we  had  said  this  day  twemy  thousand  years,  the  inductions 
would  have  been  anything  but  conclusive.  That  a  cause  which,  in 
opposition  to  very  powerful  causes,  produced  no  perceptible  effect 
during  five  thousand  years,  should  produce  a  very  considerable  one  by 
the  end  of  twenty  thousand,  has  nothing  in  it  which  is  not  in  conformity 
with  our  experience  of  causes.  We  know  many  agents,  the  effect  of 
which  in  a  short  period  does  not  amount  to  a  perceptible  quantity,  but 
by  accumulating  for  a  much  longer  period  becomes  considerable. 
Besides,  looking  at  the  immense  multitude  of  the  licavenly  bodies,  their 
vast  distances,  and  the  rapidity  (jf  the  motion  of  such  of  them  as  are 
known  to  move,  it  is  a  supposition  not  at  all  contradictory  to  experi- 
enc-e  that  some  body  may  be  in  motion  towards  us,  or  we  towards  it, 
within  the  limits  of  whose  influence  we  have  not  come  during  five  thou- 
sand years,  but  which  in  twenty  thousand  more  may  be  ])roducing 
effects  upon  us  of  the  most  extraordinary  kind.  Or  the  fact  which  is 
capable  of  preventing  sunrise  may  be,  not  the  cumulative  effect  of  one 
cause,  but  some  new  combination  of  causes;  and  the  chances  favorable 
to  that  combination,  though  they  have  not  produced  it  once  in  five 
thousand  years,  may  produce  it  once  in  twenty  thousand.  So  that  the 
inductions  which  authorize  us  to  expect  future  events,  gi'ow  weaker 
Tx 


330  INDUCTION. 

and  weaker  the  further  we  look  into  the  future,  and  at  length  become 
inappreciable. 

We  have  considered  the  probabilities  of. the  sun's  rising  to-mor- 
row, as  derived  from  the  real  laws,  that  is,  from  the  laws  of  the  causes 
on  which  that  uniformity  is  dependent.  Let  us  now  consider  how  the 
matter  would  have  stood  if  the  uniformity  had  been  known  only  as  an 
empirical  law  ;  if  we  had  not  been  aware  that  the  sun's  light,  and  the 
earth's  rotation  (or  the  sun's  motion),  were  the  causes  on  wlrich  the 
periodical  occurrence  of  sunrise  depends.  We  could  have  extended 
this  empirical  law  to  cases  adjacent  in  time,  though  not  to  so  gi-eat  a 
distance  of  time  as  we  can  now.  Having  evidence  that  the  effects  had 
remained  unaltered  and  been  punctually  conjoined  for  five  thousand 
years,  we  could  infer  that  the  unknown  causes  on  which  the  conjunc- 
tion is  dependent  had  existed  undiminished  and  un counteracted  during 
the  same  peaiod.  The  same  conclusions,  therefore,  would  follow  as  in 
the  preceding  case  ;  except  that  we  should  only  know  that  during  five 
thousand  years  nothing  had  occurred  to  defeat  perceptibly  this  particu- 
lar eftect ;  while,  when  we  know  the  causes,  we  have  the  additional 
assurance,  that  during  that  interval  no  such  change  has  been  noticeable 
in  the  causes  themselves,  as  by  any  degree  of  multiplication  or  length 
of  continuance  could  defeat  the  effect. 

To  this  must  be  added,  that  when  we  know  the  causes,  we  may  be 
able  to  judge  whether  there  exists  any  known  cause  capable  of  coun- 
teracting them  :  while  as  long  as  they  are  unknown  we  cannot  be  sure 
but  that  if  we  did  know  them,  we  could  predict  their  destruction  from 
causes  actually  in  existence.  A  bedridden  savage,  who  had  never 
seen  the  cataract  of  Niagara,  but  who  lived  within  hearing  of  it,  might 
imagine  that  the  sound  he  heard  would  endure  for  ever ;  but  if  he 
knew  it  to  be  the  effect  of  a  rush  of  waters  over  a  banier  of  rock 
which  is  progi-essively  wearing  away,  he  would  know  that  within  a 
number  of  ages  which  may  be  calculated,  it  will  be  heard  no  more. 
In  proportion,  therefore,  to  our  ignorance  of  the  causes  on  which  the 
empirical  law  depends,  we  can  be  less  assured  that  it  will  continue  to 
hold  good  ;  and  the  further  we  look  into  futurity,  the  less  improbable 
is  it  that  some  one  of  the  causes,  whose  coexistence  gives  rise  to  the 
derivative  uniformity,  may  be  destroyed  or  counteracted.  With  every 
prolongation  of  time  the  chancesi  multiply  of  such  an  event,  that  is  to 
say,  its  non-occurrence  hitherto  becomes  a  less  guarantee  of  its  not 
occurring  within  the  given  time.  If,  then,  it  is  only  to  cases  which  in 
point  of  time  are  adjacent  (or  nearly  adjacent)  to  those- which  we  have 
actually  observed,  that  any  derivative  law,  not  of  causation,  can  be  ex- 
tended with  an  assurance  equivalent  to  certainty,  much  more  is  this 
true  of  a  merely  empirical  lavv^.  Happily,  for  the  purposes  of  life  it  is 
to  such  eases  alone  that  we  can  almost  ever  have  occasion  to  extend 
them. 

In  respect  of  place,  it  might  seem  that  a  merely  empirical  law  could 
not  be  extended  even  to  adjacent  cases  ;  that  we  could  have  no  assu- 
rance of  its  being  ti'ue  in  any  place  where  it  has  not  been  specially 
observed.  The  past  duration  of  a  cause  is  a  guarantee  for  its  future 
existence,  unless  something  occurs  to  destroy  it ;  but  the  existence  of 
a  cause  in  one  or  any  number  of  places,  is  no  guarantee  for  its  exist- 
ence in  any  other  place,  since  there  is  no  uniformity  in  the  collocations 
of  primeval  causes.     When,  th&refore,  an  empirical  law -is  extended 


EXTENSION    OF    LAWS    TO    ADJACENT    CASES.  331 

beyond  the  local  limits  within  which  it  has  been  fonnd  true  by  obser- 
vation, the  cases  to  which  it  is  thus  extended  must  be  such  as  are  pre- 
sumably within  the  influence  of  the  same  individual  agents.  If"  we 
discovered  a  now  planet  ^vithin  the  known  hounds  of  "the  solar  system 
(or  even  beyond  those  bounds,  but  indicating  its  comiexion  with  the 
system  by  revolving  round  the  sun),  we  might  conclude,  with  great  prob- 
ability, that  it  revolves  upon  its  axis.  For  all  the  known  planets  do  so  ; 
and  thi-s  uniformity  points  to  some  common  cause,  antecedent  to  the 
first  records  of  astronomical  observation:  and  although  the  nature  of 
this  cause  can  only  be  matter  of  conjecture,  yet  if  it  be,  as  is  not 
unlikely  (and  as  Laplace's  theory  suggests,)  one  and  the  same  indi- 
vidual impulse  given  to  all  the  bodies  at  once,  that  cause,  acting  at 
the  extreme  points  of  the  space  occupied  by  the  sun  and  planets, 
must,  unless  defeated  by  some  counteracting  cause,  have  acted  at 
every  intermediate  point,  and  probably  somewhat  beyond  :  and  there- 
fore acted,  in  all  probability,  upon  the  supposed  newly-discovered 
planet. 

When,  therefore,  effects  which  are  always  found  conjoined,  can  be 
traced  with  any  probability  to  an  identical  (and  not  merely  a  similar) 
origin,  we  may  with  great  probability  extend  the  empirical  law  of  their 
conjunction  to  all  places  within  the  extreme  local  boundaries  within 
which  the  fact  has  been  observed ;  subject  to  the  possibility  of  coun- 
teracting causes  in  some  portion  of  the  field.  Still  more  confidently 
may  we  do  so  when  the  law  is  not.  merely  empirical ;  when  the  ph-e- 
nomena  which  we  find  conjoined  are  effects  of  ascertained  causes, 
from  the  laws  of  which  the  conjunction  of  their  effects  is  deducible. 
In  that  case,  we  may  both  extend  the  derivative  uniformity  over  a 
larger  space,  and  with  less  deduction  for  the  chance  of  counteracting 
causes.  The  first,  because  instead  of  the  local  boundaries  of  our  ob- 
servation of  the  fact  itself^  we  may  include  the  extreme  boundaries  of 
the  ascertained  influence  of  its  causes.  Thus  the  succession  of  day  and 
night,  we  know,  holds  true  of  all  the  bodies  of  the  solar  system  except 
the  sun  himself;  but  we  know  this  only  because  we  are  acquainted 
with  the  causes:  if  we  were  not,  we  could  not  extend  the  proposition 
beyond  the  orbits  of  the  earth  and  moon,  at  bot"h  extremities  of  which 
we  have  the  evidence  of  observation  for  its  truth.  With  respect  to  the 
probability  of  counteracting  causes,  it  has  been  seen  that  this  calls  for 
a  greater  abatement  of  confidence,  in  proportion  to  our  ignorance  of 
the  causes  on  which  the  phenomena  depend.  On  both  accounts,  there- 
fore, a  derivative  law  which  we  know  how  to  resolve,  is  susceptible  of 
a  greater  extension  to  cases  adjacent  in  place,  than  a  merely  em- 
pirical law. 


332  INDUCTION. 

CHAPTER  XX. 

OF   ANALOGY. 

§  1.  The  word  Analogy,  as  the  name  of  a  mode  of  reasoning,  is  gen- 
erally taken  for  some  kind  of  argument  supposed  to  be  of  an  inductive 
nature,  but  not  amounting  to  a  complete  induction.  There  is  no 
word,  however,  which  is  used  more  loosely,  or  in  a  greater  variety  of 
senses  than  Analogy.  It  sometimes  stands  for  arguments  which  may 
be  examples  of  the  most  rigid  Induction.  Archbishop  Whately,  for 
instance,  following  Ferguson  and  other  Mriters,  defines  Analogy  con- 
formably to  its  primitive  acceptation,  that  which  was  given  to  it  by 
mathematicians,  Resemblance  of  Relations.  In  this  sense,  when  d 
country  which  has  sent  out  colonies  is  termed  the  mother  countiy,  the 
expression  is  analogical,  signifying  that  the  colonies  of  a  country  stand 
in  the  same  relation  to  her  in  which  children  stand  to  their  parents. 
And  if  any  inference  be  drawn  from  this  resemblance  of  relations,  as, 
for  instance,  that  the  same  obedience  or  affection  is  due  from  colonies 
to  the  mother  country  which  is  due  from  children  to  a  parent,  this  is 
called  reasoning  by  analogy.  Or  if  it  be  argued  that  a  nation  is  most 
beneficially  governed  by  an  assembly  elected  by  the  people,  from  the 
admitted  fact  that  other  associations  for  a  common  purpose,  such  as 
joint  stock  companies,  are  best  managed  by  a  committee  chosen  by  the 
parties  interested  ;  this  is  an  argument  from  analogy  in  Archbishop 
Whately's  sense,  because  its  foundation  is  not,  that  a  nation  is  like  a 
joint  stock  company,  or  Parliament  like  a  board  of  directors,  but  that 
Parliament  stands  in  the  same  relation  to  the  nation  in  which  a  board 
of  directors  stands  to  a  joint  stock  company.  Now,  in  an  argument  of 
this  nature,  there  is  no  inherent  inferiority  of  conclusiveness.  Like 
other  arguments  from  resemblance,  it  may  amount  to  nothing,  or  it 
may  be  a  perfect  and  conclusive  induction.  The  circumstance  in  which 
the  two  cases  resemble,  may  be  capable  of  being  shovra  to  be  the 
material  circumstance ;  to  be  that  on  which  all  the  consequences, 
necessary  to  be  taken  into  account  in  the  particular  discussion,  depend. 
In  the  case  in  question,  the  resemblance  is  one  of  relation  ;  ihefunda- 
mentmn  relationis  being  the  management,  by  a  few  persons,  of  affairs 
in  which  a  much  greater  number  are  interested  along  Avith  them. 
Now,  some  may  contend  that  this  circumstance  which  is  common  to 
the  two  cases,  and  the  various  consequences  which  follow  fi'om  it,  have 
the  chief  share  in  determining  all  those  effects  which  make  up  what  we 
term  good  or  bad  administration.  If  they  can  establish  this,  their 
argument  has  the  force  of  a  rigid  induction  :  if  they  cannot,  they  are 
said  to  have  failed  in  proving  the  analogy  between  the  two  cases ;  a 
mode  of  speech  which  implies  that  when  the  analogy  can  be  proved, 
the  argument  founded  upon  it  cannot  be  resisted. 

§  2.  It  is  on  the  whole  more  usual,  however,  to  extend  the  name  of 
analogical  evidence  to  arguments  from  any  sort  of  resemblance,  pro- 
vided they  do  not  amount  to  a  complete  induction  ;  without  peculiarly 
distinguishing  resemblance  of  relations.  Analogical  reasoning,  in  this 
sense,  may  be  reduced  to  the  following  formula :  Two  things  resemble 


ANALOGY.  333 

each  other  in  one  or  more  respects ;  a  certain  proposition  is  true  of  the 
one ;  therefore  it  is  true  of  the  other.  But  we  have  here  nothing  by 
which  to  discriminate  analogy  from  induction,  since  this  type  will  sei-ve 
for  all  reasoning  from  experience.  In  the  most  rigid  induction,  equally 
with  the  faintest  analogy,  we  conclude  because  A  resembles  B  in  one 
or  more  properties,  that  it  does  so  in  a  certain  other  property.  The 
difierence  is,  that  in  the  case  of  a  real  induction  it  has  been  previously 
shown,  by  due  comparison  of  instances,  that  there  is  an  invariable 
conjunction  between  the  former  property  or  properties  and  the  latter 
property  :  but  in  what  is  called  analogical  reasoning,  no  such  conjunc- 
tion has  been  made  out.  There  have  been  no  opportunities  of  putting 
in  practice  the  Method  of  Difierence,  or  even  the  Method  of  Agree- 
ment ;  but  we  conclude  (and  that  is  all  which  the  argument  of  analogy 
amounts  to)  that  a  fact  7n,  known  to  be  true  of  A,  is  more  likely  to  be 
true  of  B  if  B  agrees  with  A  in  some  of  its  properties  (even  though 
no  connexion  is  known  to  exist  between  m  and  those  properties),  than 
if  no  resemblance  at  all  could  be  traced  between  B  and  any  other  thing 
known  to  possess  the  attribute  m. 

To  tliis  argument  it  is  of  course  requisite,  that  the  properties  com- 
mon to  A  with  B  shall  be  merely  not  known  to  be  connected  wdth  m; 
they  must  not  be  properties  knowm  to  be  unconnected  with  it.  If, 
either  by  processes  of  elimination,  or  by  deduction  from  previous 
knowledge  of  the  laws  of  the  properties  in  question,  it  can  be  con- 
cluded that  they  have  nothing  to  do  with  in,  the  argument  of  analogy 
is  put  out  of  court.  The  supposition  must  be,  that  7n  is  an  effect, 
really  dependent  upon  some  property  of  A,  but  we  know  not  upon 
which.  We  cannot  point  out  any  of  the  properties  of  A,  which  is  the 
cause  of  m,  or  united  with  it  by  any  law.  After  rejecting  all  which 
we  know  to  have  nothing  to  do  with  it,  there  remain  several  between 
which  we  are  unable  to  decide  :  of  which  remaining  properties,  B 
possesses  one  or  more.  This,  accordingly,  we  consider  as  affording 
grounds,  of  more  or  less  weight,  for  concluding  by  analogy  that  B 
possesses  the  attribute  m. 

There  can  be  no  doubt  that  every  such  resemblance  which  can  be 
pointed  out  between  B  and  A,  affords  some  degree  of  probability, 
beyond  what  would  otherwise  exist,  in  favor  of  the  conclusion  drawn 
from  it.  If  B  resembled  A  in  all  its  ultimate  properties,  its  possessing 
the  attribute  m  would  be  a  certainty,  not  a  probability :  and  every  re- 
semblance which  can  be  shown  to  exist  between  them,  places  it  by  so 
much  the  nearer  to  that  point.  If  the  resemblance  be  in  an  ultimate 
property,  there  will  be  resemblance  in  all  the  derivative  properties 
dependent  on  that  ultimate  property,  and  of  these  vi  may  be  one.  If 
the  resemblance  be  in  a  derivative  property,  there  is  reason  to  expect 
resemblance  in  the  ultimate  property  on  which  it  depends,  and  in  the 
other  derivative  properties  dependent  upon  the  same  ultimate  property. 
Every  resemblance  which  can  be  shown  to  exist,  affords  gi-ound  for 
expecting  an  indefinite  number  of  other  resemblances ;  the  paiticular 
resemblance  sought  will,  therefore,  be  oftener  found  among  things 
thus  known  to  resemble,  than  among  things  between  which  we  know 
of  no  resemblance.* 

♦  There  was  no  greater  foundation  than  this  for  Newton's  celebrated  conjecture  that  the 
diamond  was  combustible.  He  grounded  his  guess  upon  the  very  high  refractnig  power  of 
the  diamond,  comparatively  to  its  density  ;  a  peculiarity  which  had  been  observed  to  exist 


334  INDUCTION. 

For  example,  I  might  infer  that  there  are  probably  inhabitants  in 
the  moon,  because  there  are  inhabitants  on  the  earth,  in  the  sea,  and  in 
the  air ;  and  this  is  the  evidence  of  analogy.  The  circumstance  of 
having  inhabitants  is  here  assumed  not  to  be  an  ultimate  property,  but 
(as  it  is  reasonable  to  suppose)  a  consequence  of  other  properties  ; 
and  depending,  therefore,  in  the  case  of  our  earth,  upon  some  of  its 
properties  as  a  portion  of  the  universe,  but  upon  which  of  those  prop- 
erties we. know  not.  Now,  the  moon  resembles  the  earth  in  being  a 
solid,  opaque,  nearly  spherical  substance ;  containing  active  volcanoes ; 
receiving  heat  and  light  from  the  sun,  in  about  the  same  quantity  as 
our  earth  ;  revolving  on  its  axis  ;  whose  materials  gravitate,  and  which 
obey  all  the  various  laws  resulting  from  that  property.  And  I  think 
no  one  will  deny  that  if  this  were  all  that  was  known  of  the  moon,  the 
existence  of  inhabitants  in  that  luminary  would  derive  from  these 
various  resemblances  to  the  earth,  a  greater  degree  of  probability 
than  it  would  otherwise  have  :  although  the  amount  of  the  augmenta- 
tion it  would  be  ridiculous  to  attempt  to  estimate. 

If,  however,  every  resemblance  proved  between  B  and  A,  in  any 
point  riot  known  to  be  immaterial  with  respect  to  m,  forais  some  addi- 
tional reason  for  presuming  that  B  has  the  attribute  in  ;  it  is  clear  e  con- 
tra, that  every  dissimilarity  which  can  be  proved  between  them,  fur- 
nishes a  counter-probability  of  the  same  nature  on  the  other  side.  It  is 
not  indeed  impossible  that  different  ultimate  properties  may,  in  some 
particular  instances,  produce  the  same  derivative  property;  but  on  the 
whole  it  is  certain  that  things  which  differ  in  their  ultimate  properties, 
will  differ  at  least  as  much  in  the  aggregate  of  their  derivative  proper- 
ties, and  that  the  differences  which  are  unknown  will  on  the  average 
of  cases  bear  some  proportion  to  those  which  are  known.  There  will, 
therefore,  be  a  competition  between  the  known  points  of  agreement 
and  the  known  points  of  difference  in  A  and  B ;  and  according  as  the 
one  or  the  other  are  deemed  to  preponderate,  the  probability  derived 
from  analogy  \n\\  be  for  or  against  B's  having  the  property  in.  The 
moon,  for  instance,  agrees  with  the  earth  in  the  circumstances  ah'eady 
mentioned;  but  differs  in  being  smaller,  in  having  its  surface  more 
unequal,  and  apparently  volcanic  throughout,  in  having  no  atmosphere 
sufficient  to  refract  light,  no  clouds,  and  therefore  (it  is  inferentially 
concluded)  no  water.  These  differences,  considered  merely  as  Such, 
might  perhaps  balance  the  resemblances,  so  that  analogy  would  afford 
no  presumption  either  way.  But  considering  that  some  of  the  circum- 
stances which  are  wanting  on  the  moon  are  among  those  which,  on  our 
earth,  are  found  to  be  indispensable  conditions  of  aniinal  life,  we  may 
conclude  that  if  that  phenomenon  does  exist  in  the  moon,  it  must  be  as 
the  effect  of  causes  totally  different  from  those  on  which  it  depends 
here ;  as  a  consequence,  therefore,  of  the  moon's  diffel-ences  fi-ora  the 
earth,  not  of  their  points  of  agreement.  Viewed  in  this  light,  all  the 
resemblances  which  exist  become  presumptions  against,  not  in  favor  of, 

in  combustible  substances  ;  and  on  similar  grounds  he  conjectured  that  water,  though  not 
combustible,  contained  a  combustible  ingredient.  Experiment  having  subsequently  shown 
that  in  both  instances  he  guessed  right,  the  prophecy  is  considered  to  have  done  great 
honor  to  his  scientific  sagacity;  but  it  is  to  this  day  uncertain  whether  the  praise  was 
merited  ;  whether  the  guess  was,  in  truth,  what  there  are  so  many  examples  of  in  the 
history  of  science,  a  far-sighted  anticipation  of  a  law  afterwards  to  be  discovered.  The 
progress  of  science  has  not  hitherto  shown  ground  for  believing  that  there  is  any  real  con- 
nexion between  combustibility  and  a  high  refracting  power. 


ANALOGY.  335 

her  being  inhabited.  Since  life  cannot  exist  there  in  the  manner  in 
which  it  exists  here,  the  greater  the  resemblance  of  the  lunar  world  to 
the  terrestrial  in  all  other  respects,  the  less  reason  we  have  to  bolievo 
tliat  it  can  contain  life. 

There  ai'e,  however,  other  bodies  in  our  system,  between  which  and 
the  earth  there  is  a  much  closer  resemblance;  which  possess  an  atmos- 
phere, clouds,  consequently  water  (or  some  fluid  analogous  to  it),  and 
even  give  strong  indications  of  snow  in  their  polar  regions ;  while  the 
cold,  or  heat,  though  differing  greatly  on  the  avcu'age  from  ours,  is,  in 
some  parts  at  least  of  those  planets,  jjossibly  not  more  extreme  than  in 
some  regions  of  our  own  wliich  are  habitubli;.  To  balance  these  agree-; 
ments,  the  ascertained  differences  are  chiefly  in  the  average  light  and 
heat,  velocity  of  rotation,  intensity  of  gravity,  and  similar  circumstances 
of  a  secondary  kind.  With  regard  to  these  planets,  therefore,  the  argu- 
ment of  analogy  gives  a  decided  preponderance  in  favor  of  their  resem- 
bling the  earth  in  any  of  its  derivative  properties,  such  as  that  of  having 
inliabitants :  though,  when  we  consider  how  immeasurably  multitudi- 
nous are  those  of  their  properties  which  we  are  entirely  ignorant  of, 
compared  with  the  few  wliich  we  know,  we  cannot  attach  more  than 
a  very  trifling  weight  to  any  considerations  of  resemblance  in  which 
the  known  elements  bear  so  inconsiderable  a  proportion  to  the  un- 
known. 

Besides  the  competition  between  analogy  and  diversity,  there  may 
be  a  competition  of  conflicting  analogies.  The  new  case  may  be  sim- 
ilar in  some  of  its  circumstances  to  cases  in  which  the  fact  m  exists, 
but  in  others  to  cases  in  which  it  is  known  not  to  exist.  Amber  has 
some  properties  in  common  with  vegetable,  others  with  mineral  pro- 
ducts. A  painting,  of  unknown  origin,  may  resemble,  in  certain  of  its 
characters,  known  works  of  a  particular  master,  but  in  others  it  may^ 
as  strikingly  resemble  productions  known  not  to  be  his.  A  vase  may 
bear  some  analogy  to  works  of  Grecian,  and  some  to  those  of  Etruscan 
or  Egyptian  art.  We  are  of  course  supposing  that  it  does  not  possess 
any  quality  which  has  been  ascertained,  by  a  sufficient  induction,  to  be 
a  conclusive  mark  either  of  the  one  or  of  the  other. 

§  3.  Since  the  value  of  an  analogical  argument  infen-ing  one  resem- 
blance from  other  resemblances  without  any  antecedent  evidence  of  a 
connexion  between  them,  depends  upon  the  extent  of  ascertained 
resemblance,  compared  first  with  the  amount  of  ascertained  difference, 
and  next  with  the  extent  of  the  unexplored  region  of  unascertained 
properties;  it  follows  that  where  the  resemblance  is  very  great,  the 
ascertained  difference  very  small,  and  our  knowledge  of  the  subject- 
matter  tolerably  extensive,  the  argument  from  analogy  may  approach, 
in  strength  very  near  to  a  valid  induction.  If,  after  much  observation 
of  B,  we  find  that  it  agrees  with  A  in  nine  out  of  ten  of  its  known 
properties,  we  may  conclude  with  a  probability  of  nine  to  one,  that  it 
will  possess  any  given  derivative  property  of  A.  If  we  discover,  for. 
example,  an  unknown  animal  or  plant,  resembling  closely  some  knovm 
one  in  the  greater  number  of  the  properties  we  observe  in  it,  but  dif- 
fering in  some  few,  we  may  reasonably  expect  to  find  in  the  unob- 
served remainder  of  its  properties,  a  general  agreement  with  those  of 
the  former ;  but  also  a  difference,  corresponding  proportionally  to  the 
amount  of  obseiTed  diversity. 


336  INDUCTION. 

It  thus  appears  that  the  conclusions  derived  from  analogy  are  only 
■of  any  considerable  value,  w^hen  the  case  to  which  we  reason  is  an  ad- 
jacent case;  adjacent,  not  as  before,  in  place  or  time,  but  in  circum- 
stances. In  the  case  of  effects  of  which  the  causes  are  impeiiectly  or 
not  at  all  known,  when  consequently  the  observed  order  of  their  oc- 
cuiTcnce  amounts  only  to  an  empirical  law,  it  often  happens  that  the 
conditions  which  have  coexisted  whenever  the  effect  was  observed,  have 
been  very  numerous.  Now  if  a  new  case  presents  itself,  in  which  all 
these  conditions  do  not  exist,  but  the  far  greater  part  of  them  do,  some 
one  or  a  few  only  being  wanting ;  the  inference  that  the  effect  wall 
occur  notwithstanding  this  deficiei>cy  of  complete  resemblance  to  the 
cases  in  which  it  has  been  observed,  may,  although  of  the  nature  of 
analogy,  possess  a  high  degi-ee  of  probability.  It  is  hardly  necessary 
to  add  that,  however  considerable  this  probability  may  be,  no  com- 
petent inquirer  into  nature  will  rest  satisfied  with  it  when  it  is  possible 
to  obtain  a  complete  induction ;  but  will  consider  the  analogy  as  a 
mere  guide-post,  pointing  out  the  direction  in  which  more  rigorous 
investigations  should  be  prosecuted. 

It  is  in  this  last  respect  that  considerations  of  analogy  have  the  high- 
est  philosophical  value.  The  cases  in  which  analogical  evidence 
affords  in  itself  any  very  high  degree  of  probability,  are,  as  we  have 
just  observed,  only  those  in  which  the  resemblance  is  very  close  and 
extensive;  but  there  is  no  analogy,  however  faint,  which  may  not  be 
of  the  utmost  value  in  suggesting  experiments  or  observations  that 
may  lead  to  more  positive  conclusions.  When  the  agents  and  their 
effects  are  out  of  the  reach  of  fiirther  observation  and  experiment,  as 
in  the  speculations  already  alluded  to  respecting  the  moon  and  planets, 
such  slight  probabilities  are  no  more  than  an  interesting  theme  for  the 
pleasant  exercise  of  imagination  ;  but  any  suspicion,  however  slight, 
that  sets  an  ingenious  person  at  Avork  to  contrive  an  experiment,  or 
that  affords  a  reason  for  trying  one  experiment  rather  than  another, 
may  be  of  eminent  service  to  philosophy. 

On  this  gi-ound,  notwithstanding  the  unfavorable  judgment  which  I 
have  concurred  with  M.  Comte  in  passing  upon  those  scientific  hypo- 
theses (when  considered  as  positive  doctrines)  which  are  unsusceptible 
of  being  ultimately  brought  to  the  test  of  actual  induction,  such  for  in- 
stance as  the  two  theories  of  light,  the  emission  theory  of  the  last  cen- 
tury, and  the  undulatory  theory  which  predominates  in  the  present ;  I 
am  yet  unable  to  agree  with  M.  Comte  in  considering  those  hypo- 
theses to  be  worthy  of  entire  disregard.  As  is  well  said  by  Hartley 
(and  concurred  in  by  a  philosopher  in  general  so  diameti-ically  opposed 
to  Hartley's  views  as  Dugald  Stewart),  "  any  hypothesis  that  has  so 
much  plausibility  as  to  explain  a  considerable  number  of  facts,  helps 
us  to  digest  these  facts  in  proper  order,  to  bring  new  ones  to  light, 
and  make  experivienta  crucis  for  the  sake  of  future  inquirers."*  If  an 
hypothesis  not  only  explains  known  facts,  but  has  led  to  the  prediction 
of  others  previously  unknown,  and  since  verified  by  experience,  the 
laws  of  the  phenomenon  which  is  the  subject  of  inquiry  must  bear  at 
least  a  great  similarity  to  those  of  the  class  of  phenomena  to  which  the 
hypothesis  assimilates  it;  and  since  the  analogy  which  extends  so  far 

*  Hartley'.s  Observations  on  Man,  vol.  i.,  p.  16.  The  passage  is  not  in  Priestley's  cur- 
tailed edition. 


EVIDENCE  OF  UNIVERSAL  CAUSATION.  337 

may  probably  extend  further,  nothing  is  more  Ukely  to  suggest  experi- 
ments tending  to  throw  light  upon  the  real  properties  of  the  phenom- 
enon, than  the  following  out  such  an  hypothesis.  But  to  this  end  it  is 
by  no  means  necessary  that  the  hypothesis  be  mistaken  for  a  scientific 
truth.  On  tlie  contrary,  that  illusion  is  in  this  respect,  as  in  every 
other,  an  impediment  to  the  progress  of  real  knowledge,-  by  leading 
men  to  restrict  themselves  arbitrarily  to  the  particular  hypothesis 
which  is  most  accredited  at  the  time,  instead  of  looking  out  for  evez'y 
class  of  phenomena  between  the  laws  of  which  and*  those  of  the  given 
phenomenon  any  analogy  exists,  and  trying  all  such  experiments  as 
may  tend  to  the  discovery  of  ulterior  analogies  pointing  in  the  same 
direction. 


CHAPTER  XXI. 

OF  THE  EVIDENCE   OF   THE   LAW  OF   UNIVERSAL  CAUSATION. 

§  1.  We  have  now  completed  our  review  of  the  logical  processes  by 
which  the  laws,  or  uniformities,  of  the  sequences  of  phenomena,  and 
those  uniformities  in  iheir  coexistence  which  depend  upon  the  laws  of 
their  sequence,  are  ascertained.  As  we  recognized  in  the  commence- 
ment, and  have  been  enabled  to  see  more  clearly  in  the  progress  of 
the  investigation,  the  basis  of  all  these  logical  operations  is  the  uni- 
versality of  the  law  of  causation.  The  validity  of  all  the  Inductive 
Methods  depends  upon  the  assumption  that  every  event,  or  the  begin- 
ning of  every  phenomenon,  must  have  some  cause  ;  some  antecedent, 
upon  the  existence  of  which  it  is  invariably  and  unconditionally  conse- 
quent. In  the  Method  of  Agreement,  this  is  obvious  ;  that  Method 
avowedly  proceeding  on  the  supposition,  that  we  have  found  the  true 
cause  so  soon  as  we  have  negatived  every  other.  The  assertion  is 
equally  true  of  the  Method  of  Difference.  That  Method  authorizes  us 
to  infer  a  general  law  from  two  instances ;  one,  in  which  A  exists  to- 
gether with  a  multitude  of  other  circumstances,  and  B  follows; 
another,  in  which,  A  being  removed,  and  all  other  circumstances 
remaining  the  same,  B  is  prevented.  What,  however,  does  this  prove  ? 
It  proves  that  A,  in  the  particular  instance,  cannot  have  had  any  other 
cause  than  B ;  but  to  conclude  fi-om  this  that  A  was  the  cause,  or  that 
A  will  on  other  occasions  be  followed  by  B,  is  only  allowable  on  the 
assumption  that  B  must  have  some  cause ;  that  among  its  antecedents 
in  any  single  instance  in  which  it  occurs,  there  must  bo  one  which  has 
the  capacity  of  producing  it  at  other  times.  This  being  admitted,  it  is 
seen  that  in  the  case  in  question  that  antecedent  can  be  no  other  than 
A ;  but,  that  if  it  be  no  other  than  A  it  must  be  A-,  is  not  proved,  by 
these  instances  at  least,  but  taken  for  granted.  Th(;re  is  no  need  to 
spend  time  in  proving  that  the  same  thing  is  true  of  the  other  Induc- 
tive Methods.  The  universality  of  tlie  law  of  causation  is  assumed  in 
them  all. 

But  is  this  assumption  warranted  ?  Doubtless  (it  may  be  said)  77iost 
phenomena  are  connected  as  effects  with  some  antecedent  or  cause, 
that  is,  are  never  produced  unless  sonje  assignable  fact  has  preceded 

U  U  VI  \o 


338  INDUCTION. 

them ;  but  the  very  circumstance  that  complicated  processes  of  induc- 
tion are  sometimes  necessary,  shows  that  cases  exist  in  which  this 
regular  order  of  succession  is  not  apparent  to  our  first  and  simplest 
apprehension.  If,  then,  the  processes  which  bring  these  cases  within 
the  same  category  with  the  rest,  require  that  we  should  assume  the 
universality  of  the  very  law  which  they  do  not  at  first  sight  appear  to 
exemplify,  is  not  this  a  real  petitio  principii  ?  Can  we  prove  a  propo- 
sition, by  an  argument  which  takes  it  for  granted "?  And  if  not  so 
proved,  on  what  evidence  does  it  rest  1 

For  this  difliculty,  which  I  have  purposely  stated  in  the  strongest 
terms  it  would  admit  of,  the  school  of  metaphysicians  who  have  long 
predominated  in  this  country  find  a  ready  salvo.  They  affirm,  that  the 
universality  of  causation  is  a  truth  which  we  cannot  help  believing ; 
that  the  belief  in  it  is  an  instinct,  one  of  the  laws  of  our  believing 
faculty.  As  the  proof  of  this,  they  say,  and  they  have  nothing  else  to 
say,  that  everybody  docs  believe  it ;  and  they  number  it  among  the 
propositions,  rather  nuinerous  in  their  catalogue,  which  may  be  logi- 
cally argued  against,  and  perhaps  cannot  be  logically  proved,  but  which 
are  of  higher  authority  than  logic,  and  which  even  he  who  denies  in 
speculation,  shows  by  his  habitual  practice  that  his  arguments  make 
no  impression  upon  himself 

I  have  no  intention  of  entering  into  the  merits  of  this  question,  as  a 
problem  of  transcendental  metaphysics.  But  I  must  renew  my  protest 
against  adducing  as  evidence  of  the  truth  of  a  fact  in  external  nature, 
any  necessity  which  the  human  mind  may  be  conceived  to  be  under  of 
believing  it.  It  is  the  business  of  the  human  intellect  to  adapt  itself  to 
the  realities  of  things,  and  not  to  measure  those  realities  by  its  own  capa- 
cities of  comprehension.  The  same  quality  which  fits  mankind  for  the 
offices  and  purposes  of  their  own  little  life,  the  tendency  of  their  belief 
to  follow  their  experience,  incapacitates  them  for  judging  of  what  lies 
beyond.  Not  only  what  man  can  know,  but  what  he  can  conceive, 
depends  upon  what  he  has  experienced.  Whatever  forms  a  part  of  all 
his  experience,  forms  a  part  also  of  all  his  conceptions,  and  appears  to 
.  him  universal  and  necessary,  though  z-eally,  for  aught  he  knows,  having 
no  existence  beyond  certain  nan-ow  limits.  The  habit,  however,  of 
philosophical  analysis,  of  Avhich  it  is  the  surest  effect  to  enable  the 
mind  to  command,  instead  of  being  commanded  by,  the  laws  of  the 
merely  passive  part  of  its  own  nature,  and  which,  by  showing  to  us 
that  things  are  not  necessarily  connected  in  fact  because  their  ideas 
are  connected  in  our  minds,  is  able  to  loosen  innumerable  associations 
which  reign  despotically  over  the  undisciplined  mind ;  this  habit  is  not 
without  power  even  over  those  associations  which  the  philosophical 
school  of  which  I  have  been  speaking,  regard  as  connate  and  instinc- 
tive. I  am  convinced  that  any  one  accustomed  to  abstraction  and 
analysis,  who  will  fairly  exert  his  faculties  for  the  purpose,  will,  when 
his  imagination  has  once  learnt  to  entertain  the  notion,  find  no  difficulty 
in  conceiving  that  in  some  one  for  instance  of  the  many  firmaments 
into  which  sidereal  astronomy  now  divides  the  universe,  events  may 
succeed  one  another  at  random,  without  any  fixed  law;  nor  can  any- 
thing in  our  experience,  or  in  our  mental  nature,  constitute  a  sufficient, 
or  indeed  any,  reason  for  believing  that  this  is  nowhere  the  case.  The 
grounds,  therefore,  which  waiTant  us  in  rejecting  such  a  supposition 
with  respect  to  any  of  the  phenomena  of  which  we  have  experience, 


EVIDENCE  OF  UNIVERSAL  CAUSATION.  339 

must  be  sought  elsewhere  than  in  any  supposed  necessity  of  our  intel- 
lectual faculties. 

As  was  observed  in  a  former  place,*  the  belief  we  entertain  in  the 
universality,  throughout  nature,  of  the  law  of  cause  and  effect,  is  itself 
an  instance  of  induction ;  and  by  no  means  one  of  the  eai'liest  which 
any  of  us,  or  which  mankind  in  general,  can  have  made.  We  arrive 
at  this  universal  law,  by  generalization  from  many  laws  of  inferior 
generality.  The  generalizing  propensity,  which,  instinctive  or  not,  is 
one  of  the  most  powerful  principles  of  our  nature,  does  not  indeed 
wait  for  the  period  when  such  a  generalization  becomes  strictly  legiti- 
mate. The  mere  unreasoning  propensity  to  expect  what  has  been 
often  experienced,  doubtless  led  men  to  believe  that  everythhig  had  a 
cause,  before  they  could  have  conclusive  evidence  of  that  truth.  But 
even  this  cannot  be  supposed  to  have  happened  until  many  cases  of 
causation,  or,  in  other  words,  many  partial  uniformities  of  sequence, 
had  become  familiar.  The  more  obvious  of  the  particular  uniformi- 
ties suggest  and  j^rQve  the  general  uniformity,  and  that  general  uni- 
formity, once'  established,  enables  us  to  prove  the  remainder  of  the 
particular  uniformities  of  which  it  is  made  up.  As,  however,  all  rigor- 
ous processes  of  induction  presuppose  the  general  uniformity,  ouf 
knowledge  of  the  particular  uniformities  from  which  it  was  first  in- 
ferred was  not,  of  course,  derived  from  rigid  induction,  but  from  the 
loose  and  uncertain  mode  of  induction  ^^er  enumcrationtm  simplicem ; 
and  the  law  of  universal  causation,  being  collected  from  results  so  ob- 
tained, cannot  itself  rest  upon  any  better  foundation. 

§  2.  This  opens  to  us  a  consideration  of  very  great  importance; 
namely,  that  induction  by  simple  enumeration,  or,  in  other  words,  gen- 
eralization of  an  observed  fact  from  the  mere  absence  of  any  known 
instances  to  the  contrary,  is  by  no  means  the  illicit  logical  j^rocess  in 
all  cases  which  it  is  in  most.  It  is  delusive  and  insufficient  exactly  in 
proportion  as  the  subject-matter  of  the  observation  is  special  and  lim- 
ited in  extent.  As  the  sphere  widens,  this  unscientific  method  becomes 
less  and  less  liable  to  mislead ;  and  the  most  universal  class  of  truths, 
the  law  of  causation  for  instance,  and  the  principles  of  number  and  of 
geometry,  are  duly  and  satisfactorily  proved  by  that  method  alone, 
nor  are  they  susceptible  of  any  other  proof 

With  respect  to  all  the  class  of  generalizations  of  which  we  have 
recently  treated,  the  unifonnities  which  depend  upon  causation,  the 
truth  of  the  remark  just  made  follows  by  obvious  inference  from  the 
principles  laid  down  in  the  preceding  chapters.  When  a  fact  has 
been  observed  a  certain  number  of  times  to  be  true,  and  is  not  in  any 
instance  known  to  be  false  ;  if  we  at  once  affinn  that  fact  as  an  uni- 
versal truth  or  law  of  nature,  without  testing  it  by  any  of  the  four 
methods  of  induction,  nor  deducing  it- by  reasoning  from  other  known 
laws,  we  shall  in  general  err  grossly :  but  wd  are  perfectly  justified  in 
affirming  it  as  an  empirical  law,  true  within  certain  limits  of  time, 
place,  and  circumstance,  provided  the  number  of  coincidOnces  is  greater 
than  can  with  any  probability  be  ascribed  to  chance.  The  reason  for 
not  extending  it  beyond  those  limits  is,  that  the  fact  of  its  holding  true 
within  them  may  be  a  consequence  of  collocations,  which  cannot  bo 
concluded  to  exist  in  one  place  because  they  exist  in  another ;  or  may 

*  Supra,  pp.  184-^. 


340  INDUCTION. 

be  dependent  upon  the  accidental  absence  of  counteracting  agencies, 
which  any  variation  of  time,  or  the  smallest  change  of  circumstances, 
may  possibly  bring  into  play.  If  we  suppose,  then,  the  subject  matter 
of  any  generahzation  to  be  so  widely  dittused  that  there  is  no  time,  no 
place,  and  no  combination  of  circumstances,  but  must  afford  an  exam- 
ple either  of  its  truth  or  of  its  falsity,  and  if  it  be  never  found  otherwise 
than  true,  its  truth  cannot  depend  upon  any  collocation  unless  such  as 
exist  at  all  times  and  places;  nor  can  it  be  frustrated  by  any  counter- 
acting agencies,  unless  by  such  as  never  actually  occur.  It  is,  therefore, 
an  empirical  law  coextensive  \vith  all  human  experience ;  at  which  point 
the  distinction  between  empirical  laws  and  lav/s  of  nature  vanishes,  and 
the  proposition  takes  its  place  in  the  highest  order  of  truths  accessible 
to  science.  Such  a  character  sti'ictly  belongs  to  the  law  of  universal 
causation,  and  to  the  ultimate  principles  of  mathematics.  The  induc- 
tion by  which  they  are  estabhshed  is  of  that  kind  which  can  -establish 
nothing  but  empirical  laws  ;  an  empirical  law,  however,  of  which  the 
truth  is  exemplified  at  every  moment  of  time  and  in  every  variety  of 
place  or  circumstance,  has  an  evidence  which  surpasses  that  of  the 
most  rigid  induction,  even  if  the  foundation  of  scientific  induction  were 
not  itself  laid  (as  we  have  seen  that  it  is)  in  a  generalization  of.  this 
very  description. 

§  3.  With  respect  to  the  general  law  of  causation,  it  does  appear 
that  there  must  have  been  a  time  when  the  universal  prevalence  of 
that  law  throughout  nature  could  not  have  been  affirmed  in  the  same 
confident  and  unqualified  manner  as  at  present.  There  was  a  time 
when  many  of  the  phenomena  of  nature  must  have  appeared  altogether 
capricious  and  in-egular,  not  governed  by  any  laws,  nor  steadily  con- 
sequent upon  any  causes.  Such  phenomena,  indeed,  were  commonly, 
in  that  early  stage  of  human  knowledge,  ascribed  to  the  direct  inter- 
vention of  the  will  of  some  supernatural  being,  and  therefore  still  to 
a  cause.  This  shows  the  strong  tendency  of  the  human  mind  to 
ascribe  every  phenomenon  to  some  cause  or  other ;  but  it  shows  also 
that  experience  had  not,  at  that  time,  pointed  out  any  regular  order  in 
the  occurrence  of  those  particular  phenomena,  nor  proved  them  to  be, 
as  we  now  know  that  they  are,  dependent  upon  prior  phenomeiia  as 
their  proximate  causes.  There  have  been  sects  of  philosophers  who 
have  admitted  what  they  teniied  Chance  as  one  of  the  agents  in  the 
order  of  nature,  by  which  certain  classes  of  events  were  entirely  regu- 
lated ;  which  could  only  mean  that  those  events  did  not  occur  in  any 
fixed  order,  or  depend  upon  imiform  laws  of  causation.  Finally,  there 
is  one  class  of  phenomena  which,  even  in  our  o-\\ni  day,  at  least  one- 
half  of  the  speculative  world  do  not  admit  to  be  governed  by  causes; 
I  mean  human  volitions.  These  are  believed,  by  the  metaphysicians 
who  espouse  the  fi-ee-wiU  doctrine,  to  be  self-determining,  self-causing; 
that  is,  not  caused  by  anything  external  to  themselves,  not  determined 
by  any  prior  fact.  It  is  true  that  the  real  opinion  of  these  philosophers 
does  not  go  quite  so  far  as  their  words  seem  to  imply ;  they  do  not  in 
reality  claim  for  this  class  of  phenomena  much  more  than  the  absence 
of  that  mystical  tie  which  the  word  necessity  seems  to  involve,  and  the 
existence  of  which,  even  in  the  case  of  inorganic  rtlatter,  is  but  an 
illusion  produced  by  language.  But  their  system  of  philosophy  does 
not  the  less  prove  that  the  existence  of  phenomena  wliich  are  not 


EVIDENCE  OF  UNIVERSAL,  CAUSATION.  341 

rigorously  consequent  upon  any  antecedents,  does  not  necessarily, 
even  in  the  present  state  of  our  experience,  appear  an  inadmissible 
paradt)x. 

The  truth  is,  as  M.  Comte  has  well  })ointod  out,  that  (although  the 
generalizing  propensity  must  have  prom})tcd  mankind  from  almost  the 
beginning  of  their  experience  to  ascribe  all  events  to  some  cause  more 
or  less  mysterious)  the  conviction  that  phcnomtnia  have  invariable  laws, 
and  follow  with  regularity  certain  antecedent  i)hcnomcna,  was  only 
acquired  gradually;  and  extended  itself,  as  knowledge  advanced,  from 
one  order  of  ])heuomena  to  another,  beginning  with  those  whose  laws 
were  most  accessible  to  observation.  This  progress  has  not  yet 
attained  its  ultimate  point;  there  being  still,  as  before  obser\'ed,  one 
cla^s  of  phenomena,  the  subjection  of  which  to  invariable  laws  is  not 
yet  universally  recognized.  So  long  as  any  doubt  hung  over  this 
fundamental  principle,  the  various  Methods  of  Induction  which  took 
that  principle  for  granted  could  only  afford  results  which  wei'e  admissi- 
ble conditionally ;  as  showing  what  law  the  phenomenon  under  inves- 
tigation must  follow  if  it  followed  any  fixed  law  at  all.  As,  however, 
when  the  rules  of  correct  induction  had  been  conformed  to,  the  result 
obtained  never  failed  to  be  verified  by  all  subsequent  experience ; 
every  such  inductive  operation  had  the  effect  of  extending  the  acknowl- 
edged dominion  of  general  laws,  and  bringing  an  additional  portion 
of  the  experience  of  mankind  to  strengthen  the  evidence  of  the  uni- 
versality of  the  law  of  causation :  until  now  at  length  we  are  fully 
waiTanted  in  considering  that  law,  as  applied  to  all  phenomena  within 
the  range  of  human  observation,  to  stand  on  an  equal  footing  in  respect 
to  evidence  with  the  axioms  of  geometiy  itself. 

§  4.  I  apprehend  that  the  considerations  which  give,  at  the  present 
day,  to  the  proof  of  the  law  of  uniformity  of  succession  as  true  of  all 
phenomena  without  exception,  this  character  of  completeness  and 
conclusiveness,  are  the  following  : — First ;  that  we  now  know  it  directly 
to  be  ti-ue  of  far  the  gi'eatest  number  of  phenomena ;  that  there  are 
none  of  which  we  know  it  not  to  be  true,  the  utmost  that  can  be  said 
being  that  of  some  we  cannot  positively  from  direct  evidence  affirm  its 
truth ;  while  phenomenon  after  phenomenon,  as  they  become  better 
known  to  us,  are  constantly  passing  from  the  latter  class  into  the 
former ;  and  in  all  cases  in  which  that  transition  has  not  yet  taken 
place,  the  absence  of  direct  proof  is  accounted  for  by  the  rarity  or  the 
obscurity  of  the  jjhenomena,  our  deficient  means  of  observing  them, 
or  the  logical  difficulties  arising  from  the  complication  of  the  circum- 
stances in  which  they  occur;  insomuch  that,  notwithstanding  as  rigid 
a  dependence  upon  given  conditions  as  exists  in  the  case  of  any  other 
phenomenon,  it  was  not  likely  that  we  should  l)e  better  acquainted 
vrith  those  conditions  than  we  are,  Jiesides  this  first  class  of  con-  , 
siderations  there  is  a  second,  which  still  further  corroborates  the 
conclusion,  and  from  the  recognition  of  which  the  com])lete  establish- 
ment of  the  universal  law  may  i-easonably  be  datcid.  Although  there 
are  phenomena,  the  ])roduction  and  changes  of  which  elude  all  our 
attempts  to  reduce  them  universally  to  any  ascertained  law ;  yet  in 
every  such  case,  the  phenomenrm,  or  the  objects  concerned  in  it,  are 
found  in  some  instances  to  obey  the  known  laws  of  nature.  The  wind, 
for  example,  is  the  type  of  uncertainty  and  caprice,  yet  we  find  it  in 


342  INDUCTION. 

some  cases  obeying  with  as  much  constancy  as  any  phenomena  in 
nature  the  law  of  the  tendency  of  fluids  to  distribute  themselves  so  as 
to  equalize  tlie  pressiu'e  on  every  side  of  each  of  their  particles ;  as 
in  the  case  of  the  trade  winds,  and  the  monsoons.  Lightning  might 
once  hav«  been  supposed  to  obey  no  laws;  but  since  it  has  been  ascer- 
tained to  be  identical  with  electricity,  we  know  that  the  very  same 
phenomenon  in  some  of  its  manifestations  is  implicitly  obedient  to  the 
action  of  fixed  causes.  I  do  not  believe  that  there  is  now  one  object 
or  event  in  all  our  experience  of  nature,  within  the  bounds  of  the  solar 
system  at  least,  which  has  not  either  been  ascertained  by  direct 
observation  to  follow  laws  of  its  Own,  or  been  proved  to  be  exactly 
similar  to  objects  and  events  which,  in  more  familiar  manifestations,  or 
on  a  more  limited  scale,  follow  strict  laws:  our  inability  to  trace  the 
same  laws  on  the  larger  scale  and  in  the  more  recondite  instances 
being  accounted  for  by  the  number  and  complication  of  the  modifying 
causes,  or  by  their  inaccessibility  to  observation. 

The  progress  of  experience,  therefore,  has  dissipated  the  doubt 
which  must  have  rested  upon  the  universality  of  the  law  of  causation 
while  there  were  phenomena  which  seemed  to  be  stii  generis,  not  sub- 
ject to  the  same  laws  with  any  other  class  of  phenomena,  and  not  a,s 
yet  ascertained  to  have  peculiar  laws  of  their  own.  This  great  gener- 
alization, however,  might  reasonably  have  been,  as  it  in  fact  was  by 
all  great  thinkers,  acted  upon  as  a  probability  of  the  highest  order,  be- 
fore there  were  sufficient  grounds  for  receiving  it  as  a  certainty.  For, 
whatever  has  been  found  true  in  innumerable  instances,  and  never 
found  to  be  false  after  due  examination  in  any,  we  are  safe  in  acting 
upon  as  universal  provisionally,  until-an  undoubted  exception  appears ; 
provided  the  nature  of  the  case  be  such  jhat  a  real  exception  could 
scarcely  have  escaped  our  notice.  When  every  phenomenon  that  we 
ever  knew  sufficiently  well  to  be  able  to  answer  the  question,  had  a 
cause  on  which  it  was  invariably  consequent,  it  was  more  rational  to 
suppose  that  our  inability  to  assign  the  causes  of  other  phenomena 
arose  from  our  ignorance,  than  that  there  were  phenomena  which  were 
uncaused,  and  Avhich  happened  accidentally  to  be  exactly  those  which 
we  had  hitherto  had  no  sufficient  opportunity  of  studying. 

§  5.  It  must,  at  the  same  time,  be  remarked,  that  the  reasons  for  this 
reliance  do  not  hold  in  circumstances  unknown  to  us,  and  beyond  the 
possible  range  of  our  experience.  In  distant  parts  of  the  stellar 
regions,  where  the  phenomena  may  be  entirely  unlike  those  with 
which  we  are  acquainted,  it  would  be  folly  to  affirm  confidently  dial 
this  general  law  prevails,  any  more  than  those  special  ones  which  we 
have  found  to.  hold  universally  on  our  own  planet.  The  uniformity  in 
the  succession  of  events,  otherwise  called  the  law  of  causation,  must  be 
received  not  as  a  law  of  the  universe,  but  of  that  portion  of  it  only 
which  is  within  the  range  of  our  means  of  sure  observation,  with  a 
reasonable  degree  of  extension  to  adjacent  cases.  To  extend  it 
further  is  to  make  a  supposition  without  evidence,  and  to  which  in 
the  absence  of  any  ground  from  experience  for  estimating  its  degi'ee 
of  probability,  it  would  be  ridiculous  to  affect  to  assign  any. 

But,  on  the  other  hand,  within  the  bounds  of  human  experience,  this 
fundamental  law,  though  itself  obtained  by  induction  from  particular 
laws  of  causation    cannot  be  deemed  less  certain,  but  on  the  contrary 


COEXISTENCES    rXDEPENDENT    OF    CAUSATION.  343 

more  so,  than  any  of  those  from  which  it  was  drawn.  It  adds  to  them 
as  much  proof  as  it  receives  from  them.  For  there  is  probably  no  ono 
even  of  the  best  estabHshed  hiws  of  causation  which  is  not  sometimes 
counteracted,  and  to  which,  therefore,  apparent  exceptions  do  not 
present  themselves,  which  would  have  necessarily  and  justly  shaken 
the  confidence  of  mankind  in  the  universality  of  those  laws,  if  inductive 
processes  founded  on  the  universal  law  had  not  enabled  us  to  refer  those 
exceptions  to  the  agency  of  counteracting  causes,  and  thereby  reconcile 
them  with  the  law  with  which  they  apparently  conflict.  Errors,  more- 
over, may  have  slipped  into  the  statement  of  any  one  of  the  special 
laws,  through  inattention  to  some  material  circumstance  ;  and  instead 
of  the  true  proposition,  another  may  have  been  enunciated,  false  as  an 
universal  law,  though  leading,  in  all  cases  hitlierto  observed,  to  the 
same  result.  But  the  general  law  of  causation  would  remahi  un- 
affected by  any  such  error.  The  law  of  cause  and  effect  is  therefore, 
not  without  reason,  placed,  in  point  of  certainty,  at  the  head  of  all  our 
inductions;  on  a  level  with  the  first  principles  of  mathematics,  which 
rest,  as  we  shall  see  presently,  upon  much  the  same  species  of  induc- 
tion as  itself. 


CHAPTER  XXII. 

OP  UNIFORMITIES   OF   COEXISTENCE   NOT  DEPENDENT  UPON   CAUSATION. 

§  1.  The  order  of  the  occurrence  of  phenomena  in  time,  is  either 
successive  or  simultaneous  ;  the  uniformities,  therefore,  which  obtain 
in  their  occuiTence,  are  either  uniformities  of  succession  or  of  coex- 
istence. Uniformities  of  succession  are  alb  comprehended  under  the 
law  of  causation  and  its  consequences.  Every  phenomenon  has  a 
cause,  which  it  invariably  follows  ;  and  from  this  are  derived  other 
invariable  sequences  among  the  successive  stages  of  the  -game  effect, 
as  well  as  between  the  effects  resulting  frorn  causes  whick  invariably 
succeed  one  another. 

In  the  same  manner  with  these  dei-ivative  uniformities  of  succession, 
a  great  variety  of  uniformities  of  coexistence  also  take  their  rise.  Co- 
ordinate effects  of  the  same  cause  naturally  coexist  with  one  another. 
High  water  at  any  point  on  the  earth's  surface,  and  high  water  at  the 
point  diametrically  opposite  to  it,  are  effects  uniformly  simultaneous, 
resulting  from  the  direction  in  which  the  combined  attraction  of  the 
sun  and  moon  act  upon  the  waters  of  the  ocean.  An  eclipse  of  the  sun 
to  us,  and  an  eclipse  of  the  earth  to  a  spectator  situated  in  the  moon, 
are  in  like  manner  phenomena  invariably  coexistent;  and  their  coex- 
istence can  equally  be  deduced  from  the  laws  of  their  production. 

It  is  an  obvious  question,  therefore,  whether  all  the  uniformities  of 
coexistence  among  phenomena  may  not  be  accounted  for  in  this  man- 
ner. And  it  cannot  be  doubted  that  between  phenomena  which  are 
themselves  effects,  the  coexistences  must  necessarily  depend  ujjon  the 
causes  of  those  phenomena.  If  they  are  effects  immediately  or  remote- 
ly of  the  same  cause,  they  cannot  coexist  except  by  virtue  of  some  laws 
or  properties  of  that  cause  :  if  they  are  effects  of  diffcjent  causes,  they 


344  INDUCTION. 

cannot  coexist  unless  it  be  because  their  causes  coexist ;  and  the  uni- 
formity of  coexistence,  if  such  there  be,  between  the  effects,  proves 
that  in  the  original  collocation  those  particular  causes,  within  the  limits 
of  our  observation,  have  uniformly  been  coexistent. 

§  2.  But  these  same  considerations  Compel  us  to  recognize  that  there 
must  be  one  class  of  coexistences  which  cannot  depend  upon  causation ; 
the  coexistences  between  the  ultimate  properties  of  things :  between 
those  properties  which  are  the  causes  of  all  phenomena,  but  are  not 
themselves  caused  by  any  phenomenon,  and  to  find  a  cause  for  which, 
we  must  ascend  to  the  origin  of  all  things.  Yet  among  these  ultimate 
properties  there  are  not  only  coexistences,  but  uniformities  of  coex- 
istence. General  propositions  may  be,  and  are  formed,  which  assert 
that  whenever  certain  properties  are  found,  certain  others  are  found 
along  v\dth  them.  We  perceive  an  object :  say,  for  instance,  water. 
We  recognize  it  to  be  water,  of  course,  by  certain  of  its  properties. 
Having  recognized  it,  we  are  able  to  affiiTn  of  it  innumerable  other 
properties ;  which  we  could  not  do  unless  it  were  a  general  ti'uth,  a 
law  or  uniformity  in  nature,  that  the  set  of  properties  by  which  we 
identified  the  substance  as  water,  always  have  those  other  properties 
conjoined  with  them. 

In  a  chapter  of  a  fonner  book,  it  has  been  explained  in  some  detail 
what  is  meant  by  the  Kinds  of  objects,*  those  classes  which  differ  from 
one  another  not  by  a  limited  and  definite,  but  by  an  indefinite  and  un- 
known, number  of  distinctions.  To  this  we  have  now  to  add,  that 
every  proposition  by  which  anything  is  asserted  of  a  Khid,  affirms  an 
unifoiTnity  of  coexistence.  Since  we  know  nothing  of  Kinds  but  their 
properties,  the  Kind,  to  us,  is  the  set  of  properties  by  which  it  is 
identified,  and  which  must  of  course  be  sufficient  to  distinguish  it  from 
every  other  Kind.t  In  affirming  anything,  therefore,  of  a  Kind,  we  are 
affirming  something  to  be  unifoiTnly  coexistent  with  the  properties  by 
which  the  Kind  is  recognized ;  and  that  is  the  sole  meaning  of  the 
assertion. 

Among  the  uniformities  of  coexistence  which  exist  in  nature,  may 
hence  be  numbered  all  the  properties  of  Kinds.  The  whole  of  these, 
however,  are  not  independent  of  causation,  but  only  a  portion  of  them. 
Some  are  ultimate  properties,  others  derivative ;  of  some,  no  cause 
can  be  assigned,  but  others  are  manifestly  dependent  upon  causes. 
Thus,  atmospheric  air  is  a  Kind,  and  one  of  its  most  unequivocal 
properties  is  its  gaseous  form  :  this  property,  however,  has  for  its 
cause  the  presence  of  a  certain  quantity  of  latent  heat;  and  if  that  heat 
could  be  taken  away  (as  has  been  done  from  so  many  gases  in  Mr. 
Faraday's  experiments),  the  gaseous  foi-m  would  doubtless  disappear, 
together  with  numerous  other  properties  which  depend  upon,  or  are 
caused  by,  that  property. 

*  Supra,  book  i.,  chap.  vii. 

t  In  some  cases,  a  Kind  is  sufficiently  identified  by  some  one  remarkable  property ;  but 
most  commonly  several  are  required ;  each  property,  considered  singly,  being  a  joint 
property  of  that  and  of  other  Kinds.  The  mere  color  and  brightness  of  the  diamond  are 
common  to  it  with  the  paste  from  which  false  diamonds  are  made  ;  the  double  refraction  is 
common  to  it  with  Iceland  spar,  and  many  other  stones ;  but  the  color  and  brightness 
and  the  double  refraction  together,  iclentify  its  Kind  ;  that  is,  are  a  mark  to  us  that  it  is 
combustible  ;  that  when  burnt  it  produces  carbonic  acid  ;  that  it  cannot  be  cut  with  any 
known  substance ;  together  with  many  other  ascertained  properties,  and  the  fact  that 
there  exist  an  indefinite  number  still  unascertained. 


COEXISTENCES    INDEPENDENT    OF    CAUSATION.  345 

In  regard  to  all  eubstances  which  are  ch'emicq,l  compoinids,  and 
which  tlierefore  may  be  regarded  a^  })i-oducts  of  the  juxtaposition  of 
substances  different  in  Kind  from  themsclvas,  there  is  considerable 
reason  to  })resume  that  the  specific  properties  of  the  compound  are 
conse(pient,  as  etiects,  upon  some  of  the  properties  of  the  elements, 
although  but  little  progTess  has  yet  been  made  in  tracing  any  invariable 
relation  between  the  latter  and  the  former.  Still  more  strongly  will  a 
similar  presumption  exist,  when  the  object  itself,  as  in  the  case- of 
organized  beings,  is  no  primeval  agent,  but  an  efllect,  which  depends 
upon»a  cause  or  causes  for  its  very  existence.  The  Kinds  therefor'e 
which  are  called  in  chemistry  simple  substances,  or  elementary  natural 
agents,  are  the  only  ones,  any  of  whose  properties  can  vvith  certainty 
be  considered  ultimate ;  and  of  these  the  ultimate  properties,  are 
probably  much  more  numerous  than  we  at  present  recognize,  since 
every  successful  instance  of  the  resolution  of  the  properties  of  their 
compounds  into  simpler  laws,  generally  leads  to  the  recognition  of 
propei'ties  in  the  elements  distinct  from  any  pi-eviously  known.  The 
resolution  of  the  laws  of  the  heavenly  motions,  established  the  pre- 
viously unknown  ultimate  property  of  a  mutual  attraction  between  all 
bodies  :  the  resolution,  so  far  as  it  has  yet  proceeded,  of  the  laws  of 
crystalization,  of  chemical  composition,  electricity,  magnetism,  &c., 
pouits  to  various  polarities,  ultimately  inherent  in  the  particles  of  which 
bodies  are  composed ;  the  comparative  atomic  weights  of  different 
kinds  of  bodies  were  ascertained  by  resolving,  into  more  general  laws, 
the  uniformities  observed  in  the  proportions  in  which  substances  com- 
bined with  one  another ;  and  so  forth.  Thus  although  every  resolution 
of  a  complex  uniformity  into  simpler  and  more  elementary  laws  has 
an  appai-ent  tendency  to  diminish  the  number  of  the  ultimate  properties, 
and  really  does  remove  many  properties  from  the  list;  yet  (since  the 
result  of  this  simplifying  process  is  to  trace  up  an  ever  greater  variety 
of  different  effects  to  the  same  agents,)  the  further  we  advance  in  this 
direction,  the  greater  number  of  distihct  properties  we  are  f(n"ced  to 
recognize^in  one  and  the  same  (object :  the  coexistences  of  which  prop- 
eities  must  accordingly  be  ranked  among  the  ultimate  generalities  of 
nature. 

§  3.  There  are,  therefore,  only  two  kinds  of  propositions  which  assert 
an  uniformity  of  coexistence  between  properties.  Either  the  properties 
depend  on  causes,  or  they  df)  not.  If  they  do,  the  proposition  which 
affirms  them  to  be  coexistent  is  a  derivative  law  of  coexistence  between 
effects,  and  until  resolved  into  the  laws  of  causation  upon  which  it 
depends,  is  an  empirical  law,  and  to  be  tried  by  the  princij)leH  of 
induction  to  which  such  laws  are  amenable.  If,  on  the  other  hand, 
the  properties  do  not  depend  upon  causes,  but  are  ultimate  properties; 
then  if  it  be  true  that  they  invariably  coexist,  they  must  both  be  ulti- 
mate properties  of  one  and  the  same  Kind  ;  and  it  is  of  these  only  that 
the  coexistences  can  be  classed  as  a  peculiar  sort  of  laws  of  nature. 

Wlien  we  affirm  that  all  crows  arc;  black,  or  that  all  negroes  have 
woolly  hair,  we  assert  an  uniformity  of  coexistence.  We  assert  that 
the  property  of  blackness,  or  of  having  woolly  hair,  invariably  coexists 
with  the  properties  which,  in  common  language,  or  in  the  scientific 
classification  that  we  adopt,  are  taken  to  constitute  the  class  crow,  or 
the  class  negro.  Now,  supposing  blackness  to  be  an  ultimate  property 
Xx 


346  INDUCTION. 

of  black  objects,  or  woolly  hair  an  ultimate  property  of  the  animals 
which  possess  it;  supposing  that  these  properties  are  not  results  of 
causation,  are  not  connected  with  antecedent  phenomena  by  any  law; 
then  if  all  crows  are  black,  and  all  negroes  have  woolly  hair,  those 
must  be  ultimate  properties  of  the  Kind  crow,  or  negro,  or  of  some 
Kind  which  includes  them.  If,  on  the  contrary,  blackness  or  woolly 
hair  be  an  effect  depending  on  causes,  these  general  propositions  are 
manifestly  empirical  laws ;  and  all  that  has  already  been  said  respect- 
ing that  class  of  generalizations  may  be  applied  without  modification 
to  these. 

Now,  we  have  seen  that  in  the  case  of  all  compounds — of  all  things, 
in  short,  except  the  elementary  substances  and  primary  powers  of 
nature — the  presumption  is,  that  the  properties  do  really  depend  upon 
causes  ;' and  it  is  impossible  in  any  case  whatever  to  be  certain  that 
they  do  not.  We  therefore  should  not  be  safe  in  claiming  for  any 
generalization  respecting  the  coexistence  of  properties,  a  degree  of 
certainty  to  which,  if  the  properties  should  happen  to  be  the  result  of 
causes,  it  would  have  no  claim.  A  generalization  respecting  coexist- 
ence, or  in  other  words  respecting  the  properties  of  Kinds,  may  be  an 
ultimate  truth,  but  it  may^  also,  be  merely  a  derivative  one  ;  and  since, 
if  so,  it  is  one  of  those  derivative  laws  which  are  neither  laws  of 
caUsation,  ndr  have  been  resolved  into  the  laws  of  causation  upon 
which  they  depend,  it  can  possess  no  higher  degree  of  evidence  than 
belongs  to  an  empirical' law. 

§  4.  This  conclusion  will  be  confirmed  by  the  consideration  of  one 
great  deficiency,  which  precludes  the  application  to  the  ultimate  uni- 
formities of  coexistence,  of  a  system  of  rigorous  and  scientific  induc- 
tion, such  as  the  uniformities  in  the  succession  of  phenomena  have 
been  found  to  be  susceptible  of.  The  basis  of  such  a  system  is  want- 
ing :  there  is  no  general  axiom,  standing  in  the  same  relation  to  the 
uniformities  of  coexistence  as  the  law  of  causation  does  to  those  of  suc- 
cession. The  Methods  of  Induction  applicable  to  the  ascertainment  of 
causes  and  effects,  are  grounded  upon  the  pz'inciple  that  everything 
which  has  a  beginning  must  have  some  cause  or  other  ;  that  among 
the  circumstances  which  actually  existed  at  the  time  of  its  commence- 
ment, there  is  certainly  some  one  or  more,  upon  which  the  effect  in 
question  is  unconditionally  consequent,  and  on  the  repetition  of  which 
it  would  certainly  again  recur.  But  in  an  inquiry  whether  some  kind 
(as  crow)  universally  possesses  a  certain  property  (as  blackness),  there 
is  no  room  for  any  assumption  analogous  to  this.  We  have  no  pre- 
vious certainty  that  the  property  must  have  something  which  constant- 
ly coexists  with  it ;  must  have  an  invariable  coexistent,  in  the  same 
manner  as  an  event  must  have  an  invariable  antecedent.  When  we 
feel  pain,  we  must  be  in  some  circumstances  under  which  if  exactly 
repeated  we  should  always  feel  pain.  But  when  we  are  conscious  of 
blackness,  it  does  not  follow  that  there  is  something  pi'escnt  of  which 
blackness  is  a  constant  accompaninient.  There  is,  therefore,  no  room 
for  elimination  ;  no  Method  of  Agreement  or  Difference,  or  of  Con- 
comitant Variations  (which  is  but  a  modification  either  of  the  Method 
of  Agreement  or  of  the  Method  of  Difference).  We  cannot  conclude 
that  the  blackness  we  see  in  crows  must  be  an  invariable  property  of 
crows,  merely  because  there  is  nothing  else  present  of  which  it  can  be 


COEXISTENCES  INDEPENDENT    OF    CAUSATION.  347 

an  invariable  property.  We  therefore  inquire  into  the  truth  of  a 
proposition  like  "All  crows  are  black,"  under  the  same  disadvantage 
as  if,  in  our  inquiries  into  causation,  we  wore  compelled  to  let  in,  as 
one  of  the  possibilities,"  that  the  effect  may  in  that  particular  instance 
have  arisen  without  any  cause  at  all. 

To  overlook  this  grand  distinction  was,  as  it  seems  to  me,  the  capital 
eiTor  in  Bacon's  view  of  inductive  philosophy.  The  principle  of  elim- 
ination, that  gi"eat  logical  instrument  which  he  had  the  immense  merit 
of  first  bringing  into  general  use,  ho  deemed  applicable  in  the  same 
sense  and  in  as  unqualified  a  manner,  to  the  investigation  of  the  coex- 
istences, as  to  that  of  the  successions  of  phenomena.  He  .seercts  to 
have  thought  that  as  every  event  has  a  cause,  or  invariable  antecedent, 
so  every  property  of  an  object  has  an  invariable  coexistent,  which  he 
called  its  Form  :  and  the  examples  he  chiefly  selected  for  the  applica- 
tion and  illustration  of  his  method,  were  inquiries  into  such  Forms; 
attempts  to  determine  in  what  else  all  those  objects  x'esembled,  which 
agreed  in  some  one  general  property,  as  hardness  or  softness,  dryness 
or  moistness,  heat  or  coldness.  Such  inquiries  could  lead  to  no  result. 
The  objects  seldom  have  any  such  circumstance  in  common.  They 
usually  agree  in  the  one  point  inquired  into,  and  in  nothing  else.  A 
great  proportion  of  the  properties  which,  so  far  as  we  can  conjecture, 
are  the  likeliest  to  be  really  ultimate,  would  seem  to  be  inherently 
properties  of  many  different  Kinds  of  things,  not  allied  in  any  other 
respect.  And  as  for  the  properties  which,  being  effects  of  causes,  we 
are  able  to  give  some  account  of,  they  have  generally  nothing  to  do 
with  the  ultimate  resemblances  or  diversities  in  the  objects  themselves, 
but  depend  upon  some  outward  circumstances,  under  the  influence  of 
which  any  objects  whatever  are  capable  of  manifesting  those  proper- 
ties :  as  is  emphatically  the  case  with  those  favorite  subjects  of  Bacon's 
scientific  inquiries,  hotness  and  coldness ;  as  well  as  with  hardness 
and  softness,  solidity  and  fluidity,  and  many  other  very  conspicuous 
qualities. 

In  the  absence,  then,  of  any  universal  law  of  coexistence,  similar 
to  the  universal  law  of  causation  which  regulates  sequence,  we  are 
thrown  back  upon  the  unscientific  induction  of  the  ancients,  per  enu- 
mcrationem  simplicem,  nhi  non  rcperitxir  instantia  contradict  or  ia.  The 
reason  we  have  for  believing  that  all  crows  are  black,  is  simply  that  we 
have  seen  and  heard  of  many  black  crows,  and  never  of  one  of  any 
other  color.  It  remains  to  be  considered  how  far  this  evidence  can 
reach,  and  how  we  are  to  measure  its  strength  in  any  given  case. 

§  5.  It  sometimes  hap])ens  that  a  mere  change  in  the  ,mode  of  ver- 
bally enunciating  a  question,  although  nothing  is  really  added  to  the 
meaning  expressed,  is  of  itself  a  considerable  step  towards  its  solution. 
This,  I  think,  happens  in  the  present  instance.  The  degree  of  cer-: 
tainty  of  any  generalization  which  rests  upon  no  other  evidence  than 
the  agreement,  so  far  as  it  goes,  of  all  past  observation,  is  but  another 
phrase  for  the  degi-ee  of  improbability  that  an  exception,  if  it  existed, 
could  have  hitherto  remained  unobserved.  The  reason  for  believing 
that  all  crows  are  black,  is  measured  by  the  improbability  that  crows 
of  any  other  color  should  have  existed  to  the  present  time  without  our 
being  aware  of  it.  Let  us  state  the  question  in  this  last  mode,  and 
coiisider  what  is  implied  in  the  supposition  that  there  raay  be  crows 


348  INDUCTION. 

which  are  not  black,  and  under  what  conditions  we  can  be  justified  in 
regarding  this  as  incredible. 

If  there  really  exist  crows  which  are  not  black,  one  of  two  things 
must  be  the  fact.  Either  the  circumstance  of  blackness,  in  all  crows 
hitherto  observed,  must  be,  as  it  were,  an  accident,  not  connected  with 
any  distinction  of  Kind ;  or  if  it  be  a  property  of  Kind,  the  crows 
•which  are  not  black  must  be  a  new  Kind,  a  Kind  hitherto  overlooked, 
though  coming  under  the  same  general  description  by  which  crows 
have  hitherto  been  characterized.  The  first  supposition  would  be 
jiroved  true  if  we  were  to  discover  casually  a  white  crow  among  black 
ones,  or  if  it  were  found  tha-t  black  crows  sometimes  turn  white.  The 
second  would  be  shown  to  be  the  fact  if  in  Australia  or  Central  Africa 
a  species  or  a  race  of  white  or  gi'ay  crows  were  found  to  prevail. 

§  6.  The  former  of  these  suppositions  necessarily  implies,  that  the 
color  is  an  effect  of  causation.  If  blackness,  in  the  crows  in  which  it 
has  been  observed,  be  not  a  property  of  Kind,  but  can  be  present  or  ab- 
sent without  any  difference,  generally,  in  the  properties  of  the  object ; 
then  it  is  not  an  ultimate  fact  in  the  individuals  themselves,  but  is  cer- 
tainly dependent  upon  a  cause.  There  are,  no  doubt,  many  properties 
which  vary  from  individual  to  individual  of  the  same  Kind,  even  the 
same  infima  species,  or  lowest  Kind.  A  flower  may  be  either  white 
or  red,  without  differing  in  any  other  respect.  But  these  properties 
are  not  ultimate ;  they  depend  on  causes.  So  far  as  the  properties  of 
a  thing  belong  to  its  own  nature,  and  do  not  arise  from  some  cause 
extrinsic  to  it,  they  are  always  the  same  in  the  same  Kind.*  Take, 
for  instance,  all  simple  substances  and  elementary  powers ;  the  only 
things  of  which  we  are  certain  that  some  at  least  of  the  properties  are 
really  ultimate.  Color  is  generally  esteemed  the  most  variable  of  all 
properties :  yet  we  do  not  find  that  sulphur  is  sometimes  yellow  and 
sometimes  white,  or  that  it  varies  in  color  at  all,  except  so  far  as  color 
is  the  effect  of  some  exti'insic  cause,  as  of  the  sort  of  light  thrown  upon 
it,  the  mechanical  arrangement  of  the  particles,  &c.  (as  after  fusion).. 
We  do  not  find  that  iron  is  sometimes  fluid  and  sometimes  solid  at  the 
same  temperature  ;  gold  sometimes  malleable  and  sometimes  brittle ; 
that  hydrogen  will  sometimes  combine  with  oxygen  and  sometimes 
not ;  or  the  like.  If  from  simple  substances  we  pass  to  any  of  their 
definite  compounds,  as  water,  lime,  or  sulphuric  acid,  there  is  the  same 
constancy  in  their  properties.  When  properties  vary  from  individual 
to  individual,  it  is  either  in  the  case  of  miscellaneous  aggregations, 
such  as  atmospheric  air  or  rock,  composed  of  heterogeneous  substances, 
and  not  constituting  or  belonging  to  any  real  Kind,  or  it  is  in  the  case 
of  organic  beings.  In  them,  indeed,  there  is  variability  in  a  high 
degree.  Animals  of  the  same  species  and  race,  human  beings  of  the 
same  age,  sex,  and  country,  will  be  most  different,  for  example,  in  face 
and  figure.  But  organized  beings  (from  the  extreme  complication  of 
the  laws  by  which  they  are  regulated)  being  more  eminently  modifi- 
able, that  is,  liable  to  be  influenced  by  a  greater  number  and  variety 
of  causes,  than  any  other  phenomena  whatever;  having,  moreover, 
themselves  had  al)eginning,  and  therefore  a  cause;  there  is  reason  to 

*  I  do  not  here  include  among  properties  the  accidents  of  quantity  and  local  position. 
Every  one  is  aware  that  no  distinctions  of  Kind  can  be  grounded  upon  these  ;  aud  that  they 
are  incident  equally  to  things  of  different  Kinds  and  to  things  of  the  same. 


COEXISTENCES    INDEPENDENT    OF    CAUSATION.  349 

believe  that  none  of  their  properties  are  ultimate,  but  all  of  them  deriv- 
ative, and  produced  by  causation.  And  the  presumption  is  confirmed 
by  the  fact  that  the  properties  which  vary  from  one  individual  to 
anotlun-,  also  generally  vary  more  or  less  at  diflerent  times  in  the  same 
individual ;  which  variation,  like  any  other  event,  su})poses  a  cause, 
and  implies,  consequently,  that  the  properties  arc  not  independent  of 
causation. 

If,  therefore,  blackness  be  mei'ely  accidental  in  crows,,  and  capable 
of  varying  while  the  Kind  remains  the  same,  its  presence  or  absence 
is  doubtless  no  ultimate  fact,  but  the  effect  of  somO  unknown  cause ; 
and  in  that  case  the  universality  of  the  experience  that  all  crows  are 
black  is  sufficient  proof  of  a  common  cause,  and  establishes  the  gener- 
alization as  an  empirical  law.  Since  there  are  innumerable  instances 
in  the  affirmative,  and  hitherto  none  at  all  in  the  negative,  the  causes 
on  which  the  property  depends  must  exist  everywhere  in  the  limits  of 
the  observations  which  have  been  made ;  and  the  proposition  may  be 
received  as  universal  within  those  limits,  and  with  the  allowable  degree 
of  extension  to  adjacent  cases. 

§  7.  If,  in  the  second  place,  the  property,  in  the  instances  in  which 
it  has  been  observed,  is  not  an  effi^ct  of  causation,  it  is  a  property  of 
Kind  ;  and  in  that  case  the  generalization  can  only  be  set  aside  by  the 
discovery  of  a  new  Kind  of  crow.  That,  however,  a  peculiar  Kind, 
not  hitherto  discovered,  should  exist  in  nature,  is  a  supposition  so  often 
realized,  that  it  cannot  be  considered  at  all  improbable.  We  have 
nothing  to  authorize  us  in  attempting  to  limit  the  Kinds  of  things  which 
exist  in  nature.  The  only  unlikelihood  would  be  that  a  new  Kind 
should  be  discovered  in  localities  which  there  was  previously  reason  to 
believe  had  been  thoroughly  explored ;  and  even  this  impi'obability 
depends  upon  the  degree  of  conspicuousness  of  the  diffei-ence  between 
the  newly  discovered  Kind  and  all  others,  since  new  Kinds  of  minerals, 
plants,  and  even  animals,  previously  overlooked  or  confounded  with 
known  species,  are  still  continually  detected  in  the  most  frequented 
situations.  On  this  second  ground,  therefore,  as  well  as  on  the  first, 
the  observed  uniformity  of  coexistence  can  only  hold  good  as  an  cm])ir- 
ical  law,  within  the  limits  not  only  of  actual  observation,  but  of  an 
observation  as  accurate  as  the  nature  of  the  case  required.  And  hence 
it  is  that  (as  remarked  in  an  early  chapter  of  the  present  Book)  we  so 
often  give  up  generalizations  of  this  class  at  the  first  summons.  If  any 
credible  wittiess  stated  that  he  had  seen  a  white  crow,  under  circum- 
stances which  made  it  not  incredible  that  it  should  have  escaped  notice 
previously,  we  should  give  full  credence  to  the  statement. 

It  appears,  then,  that  the  uniformities  which  obtain  in  the  coex- 
istence of  phenomena — those  which  wo  have  reason  to  consider  aa 
ultimate,  no  less  than  those  which  arise  from  the  laws  of  causes  yet 
undetected — are  entitled  to  reception  only  as  empirical  laws ;  are  not 
to  be  presumed  true  except  in  the  limits  of  time,  place,  and  circum- 
stance, in  which  the  observations  were  made,  or  except  in  cases  etrictly 
adjacent. 

§  8.  We  have  seen  in  the  last  chapter  that  there  is  a  point  of  gener- 
ality at  which  empirical  laws  become  as  certain  as  laws  of  nature,  or 
rather,  at  which  there  is  no  longer  any  distinction  between  empirical 


350  INDUCTION. 

laws  and  laws  of  nature.  As  empirical  laws  approach  this  point,  in 
other  words,  as  they  rise  in  their  degree  of  generality,  they  become 
more  certain  ;  their  universality  may  be  more  strongly  relied  upon. 
For,  in  the  first  place,  if  they  are  results  of  causation  (which,  even 
in  the  class  of  unifomiities  treated  of  in  the  present  chapter,  we  never 
can  be  certain  that  they  are  not)  the  more  general  they  are,  the  greater 
is  proved  to  be  the  space  over  which  the  necessary  collocations  pre- 
vail, and  within  which  no 'causes  exist  capable  of  coimteracting  the 
unknown  causes  upoii  which  the  empirical  law  depends.  To  say  that 
anything  is  an  invariable  property  of  some  very  limited  class  of  objects, 
is  to  say  that  it  invai'iably  accompanies  some  vei-y  numerous  and  com- 
plex gi-oup  of  distinguishing  properties ;  which,  if  causation  be  at  all 
concerned  in  the  matter,  argues  a  combination  of  many  causes,  and 
therefore  a  very  gi-eat  liability  to  counteraction;  while  the  compara- 
tively narrow  range  of  the  observations  renders  it  impossible  to  pre- 
dict to  what  extent  unknown  counteracting  causes  may  be  distributed 
throughout  nature.  But  when  a  generalization  has  been  found  to  hold 
good  of  a  very  large  proportion  of  all  things  whatever,  it  is  already 
proved  that  nearly  all  the  causes  which  exist  in  nature  have  no  power 
over  it;  that  very  few  changes  in  the  combination  of  causes  can  affect 
it;  since  the  greater  number  of  possible  combinations  must  have 
already  existed  in  some  one  or  other  of  the  instances  in  which  it  has 
been  found  true.  If,  therefore,  any  empiiical  law  is  a  result  of  causa- 
tion, the  more  general  it  is,  the  more  it  may  be  depended  upon.  And 
even  if  it  be  no  result  of  causation,  but  an  ultimate  coexistence,  the 
more  general  it  is,  the  greater  amount  of  experience  it  is  derived  from, 
and  the  gi-eater  therefore  is  the  probability  that  if  exceptions  had 
existed,  some  would  already  have  presented  themselves. 

For  these  reasons,  it  requires  much  more  evidence  to  establish  an 
exception  to  one  of  the  more  general  empirical  laws  than  to  the  more 
special  ones.  We  should  not  have  any  difficulty  in  believing  that  there 
might  be  a  new  Kind  of  crow  ;  or  a  kind  of  bird  resembling  a  crow  in 
the  properties  hitherto  considered  distinctive  of  that  Kind.  But  it 
would  require  stronger  proof  to  convince  us  of  the  existence  of  a  kind 
of  crow  having  properties  at  variance  with  any  generally  recognized 
universal  property  of  birds ;  and  a  still  higher  dcgi-ee  if  the  properties 
conflict  with  any  recognized  universal  property  of  animals.  And  this 
is  conformable  to  the  mode  of  judgment  recommended  by  the  common 
sense  and  general  practice  of  mankind,  who  are  more  incredulous  as  to 
any  novelties  in  nature,  according  to  the  degree  of  generality  of  the 
experience  which  these  novelties  seem  to  contradict. 

§  9-  Still,  however,  even  these  greater  generalizations,  which  em- 
brace comprehensive  Kinds,  containing  under  them  a  gi'eat  number 
and  variety  of  infimce  species,  are  only  empirical  laws,  resting  upon 
induction  by  simjjle  enumeration  merely,  and  not  upon  any  process  of 
elimination,  a  process  wholly  inapplicable  to  the  kind  of  case.  Such 
generalizations,  therefore,  ought  to  be  grounded  upon  an  examination 
of  all  the  inJlmcB  species  comprehended  in  them,  and  not  oi  a  portion 
only.  We  cannot  conclude,  merely  because  a  proposition  is  ti'ue  of  a 
number  of  things  resembling  one  another  only  in  being  animals,  that 
it  is  therefore  time  of  all  animals.  If,  indeed,  anything  be  true  of 
epecies  which  differ  more  from  one  another  than  either  differs  from  a 


APPROXIMATE    GENERALIZATIONS.  351 

thiitl,  (especially  if  that  third  species  occupies. in  most  of  its  known 
properties  a  position  between  the  two  former,)  there  is  some  proba- 
bility that  the  same  thing  will  also  be  true  of  that  intermediate  fepecies; 
for  it  is  often,  though  by  no  means  universally,  found,  that  there  is  a 
sort  of  parallelism  in  the  properties  of  diflbrent  kinds,  and  that  their 
degree  of  unlikeness  in  one  respect  bears  some  proportion  to  their 
unlikeness  in  others.  We  see  this  parallelism  in  the  properties  of  the 
different  metals ;  in  those  of  sulphur,  phosphorus,  and  carbon ;  of 
oxygen,  chlorine,  iodine,  and  brome  ;  in  the  natural  ordws  of  plants 
and  animals,  &c.  But  there  are  innumerable  anomalies  and  excep- 
tions to  this  sort  of  conformity,  or  rather  the.conformitv  itself  is  but  an 
anomaly  and  an  exception  in  nature. 

Universal  propositions,  therefore,  respecting  the  properties  of  su- 
perior Kinds,  unless  grounded  on  proved  or  presumed  connexion  by 
causation,  ought  not  to  be  hazarded  except  after  separately  examining 
evej-y  known  sub-kind  included  in  the  larger  Kind.  And  even  then 
such  generalizations  must  be  held  in  readiness  to  be  given  up  on  the 
occurrence  of  some  new  anomaly,  which,  when  the  uniformity  is  not 
derived  from  causation,  can  never,  even  in  the  case  of  the  most  general 
of  these  emjjirical  laws,  be  considered  very  improbable.  Thus  all  the 
universal  propositions  which  it  has  been  attempted  to  lay  down 
respecting  simple  substances,  or  concerning  any  of  the  classes  which 
have  been  formed  among  simple  substances  (and  the  attempt  has  been 
often  made)  have,  with  the  progress  of  experience,  either  faded  into 
inanity,  or  been  proved  to  be  erroneous;  and  each  Kind  of  simple 
substance  remains  with  its  own  collection  of  properties  apart  from  the 
rest,  saving  a  certain  parallelism  with  a  few  other  Kinds,  the  most 
similar  to  itself.  In  organized  beings,  indeed,  there  are  abundance  of 
propositions  ascertained  to  be  universally  true  of  superior  .genera,  to 
many  of  which  the  discovery  hereafter  of  any  exceptions  must  be 
regarded  as  supremely  improbable.  But  these,  as  already  observed, 
are,  we  have  every  reason  to  believe,  truths  dependent  upon  causation. 

Uniformities  of  coexistence,  then,  not  only  when  they  are  conse- 
quences .of  laws  of  succession,  but  also  when  they  are  ultimate  truths, 
must  be  ranked,  for  the  purposes  of  logic,  among  empirical  laws ;  and 
are  amenable  in  every  respect  to  the  same  rules  with  those  unresolved 
uniformities  which  are  known  to  be  dependent  upon  causation. 


CHAPTER  XXIII. 

OF  APPROXIMATE  GENERALIZATIONS,   AND  PROBABLE  EVIDENCE. 

§  1.  In  our  inquiries  into  the  nature  of  the  inductive  process,  we 
have  hitherto  confined  our  notic(?  to  such  generalizations  from  experi- 
ence as  profess,  to  be  universally  true,  We  indeed  recognized  a 
distinction  between  generalizations  which  are  certain  and  those  which 
are  only  probable  :  but  tho  propositions  themselves,  though  they 
differed  in  being  more  or  less  doubtful  in  tho  one  case,  and  not  at  all 
doubtful  in  the  other,  were  always  of  the  form.  Every  A  is  B ;  they 
claimed  nothing  less  than  universality,  whatever  might  be  the  com- 


352  INDUCTION. 

pleteness  or  tlie  incompleteness  of  our  assurance  of  their  truth.  There 
remain,  however,  a  class  of  propositions  avowedly  not  universal ;  in 
which  if  is  not  pretended  that  the  predicate  is  always  true  of  the 
subject;  but  the  value  of  which,  as  generalizations,  is  nevertheless 
extremely  sreat.  An  imj^ortant  portion  of  the  field  of  inductive 
knowledo-e  does  not  consist  of  universal  truths,  but  of  approximations 
to  such  truths ;  and  when  a  conclusion  is  said  to  rest  upon  probable 
evidence,  the  premisses  it  is  drawn  from  are  usually  generalizations  of 
this  sort.     ■ 

As  every  certain  inference  respecting  a  particular  case, -implies  that 
there  is  ground  for  a  general  proposition,  of  the  form,  Every  A  is  Bj 
so  does  every  probable  inference  suppose  that  there  is  ground  for  a 
proposition  of  the  form,  Most  A  are  B :  and  the  degree  of  probability 
of  the  inference  in  an  average  case,  will  depend  upon  the  proportion 
between  the  number  of  instances  existing  in  nature  which  accord  with 
the  generalization,  and  the  number  of  those  which  conflict  with  it. 

§  2.  Propositions  in  tlie  form,  Most  A  are  B,  are  of  a  very  different 
degree  of  importance  in  science,  and  in  the  practice  of  life.  To  the 
scientific  inquirer  they  ai"e  valuable  cliiefly  as  materials  for,  and  steps 
towards,  universal  truths.  The  discovery  of  these  is  the  proper  end 
of  science:  its  work  is  not  done  if  it  stops  at  the  proposition  that  a 
majority  of  A  are  B,  without  circumscribing  that  majoiity  by  some 
common  character,  fitted  to  distinguish  them  from  the  minority.  Inde- 
pendently of  the  inferior  precision  of  such  imperfect  generalizations, 
and  the  inferior  assurance  with  which  they  can  be  applied  to  individual 
cases,  it  is  plain  that,  compared  with  exact  generalizations,  they  are 
almost  .  useless  as  means  of  discovering  ulterior  truths  by  way  of 
deduction.  We  may,  it  is  true,  by  combining  the  proposition.  Most  A 
are  B,  with  an  universal  proposition,  Every  B  is  C,  anive  at  the  con- 
clusion that  most  A  are  G.  But  when  a  second  proposition  of  the 
approximate  kind  is  introduced  —  or  even  when  there  is  but  one,  if 
that  one  be  the  major  pi^miss — nothing  can  be  positively  concluded. 
When  the  major  is  Most  B  are  D,  then,  even  if  the  minor  be  Every  A 
is  B,  we  cannot  infer  that  most  A  are  D,  or  with  any  certainty  that 
even  some  A  are  D,  Though  the  majority  of  the  class  B  have  the 
attribute  signified  by  D,  the  whole  of  the  sub-class  A  may  belong  to 
the  minority. 

Though  so  little  use  can  be  made,  in  science,  of  approxin^iate  gen- 
'eralizations,  except  as  a  stage  on  the  road  to  something  better,  for 
practical  guidance  they  are  often  all  we  have  to  rely  ujjon.  Even 
when  science  has  really  determined  the  universal  laws  of  any  phe- 
nomenon, not  only  are  those  laws  generally  too  much  encumbered 
with  conditions  to  be  adapted  for  every-day  use,  but  the  cases  which 
present  themselves  in  life  are  too  complicated,  and  our  decisions 
require  to  be  taken  too  rapidly-,  to  admit  of  waiting  till  die  existence 
of  a  phenomenon  can  be  proved  by  what  have  been  scientifically 
ascertained  to  be  uinversal  marks  of  it.  To  be  indecisive  and 
reluctant  to  act,  because  we  have  not  evidence  of  a  perfectly  con- 
clusive character  to  act  upon,  is  a  defect  sometimes  incident  to  scientific 
minds,  but  which,  vvherever  it  exists,  renders  them  unfit  for  practical 
emergenpies.  If  we  would  succeed  in  action,  we  must  judge  by  indi- 
cations'whiph,  although  they  do  not  generally  mislead  us,  sometimes 


APPROXIMATE    GENERALIZATIONS.  353 

do;  aucl  must  make  up  as  far  as  possible  for  the  incomplete  conclusive- 
ness of  any  one  indication,  by  obtaining  others  to  corroborate  it.  The 
principles  of  induction  applicable  to  ap[)roxiniate  geiieiahzation  are 
therefore  a  not  loss  important  subject  of  iiujuiry,  than  the  rules  for  the  , 
investigation  of  universal  truths;  and  might  reasonably  be  ex[)ected 
to  detain  us  almost  as  long,  were  it  not  that  these  principles  are  mere 
GOrollanes  from  those  which  have  been  already  treated  of. 

§  3.  There  are  two  sorts  of  cases  in  which  we  arc  forced  to  guide 
ourselves  by  generalizations  of  the  imperfect  foi'm.  Most  A  are  B. 
The  first  is,  when  we  have  no  others ;  when  we  have  not  been  able  to 
carry  our  investigation  of  the  laws  of  the  phenomena,  any  further; 
as  in  the  following  propositions :  Most  dark-eyed  persons  have  dark 
hail- ;  Most  springs  contain  mineral  substances ;  Most  stratified  fijrma- 
tions  contain  fossils.  The  importance  of  this  class  of  generalizations  is 
not  very  gieat ;  for,  though  it  frequently  liappens  that  we  see  no  I'ea- 
son  why  that  which  is  true  of  most  individuals  of  a  class  is  not  true  of 
the  remainder,  nor  are  able  to  bring  the  former  under  any  general 
description  which  can  distinguish  them  from  the  latter,  yet  if  we  are 
willing  to  be  satisfied,  with  propositions  of  a  less  degi'ee  of  generality, 
and  to  break  down  the  class  A  into  sub-classes,  we  may  generally 
obtain  a  collection  of  propositions  exactly  true.  We  do  not  know  why 
most  wood  is  lighter  than  water,  nor  can  we  point  out  any  general 
property  which  discriminates  wood  that  is  lighter  than  water  from  that 
which  is  heavier.  But  we  know  exactly  what  species  are  the  one  and 
what  the  other.  And  if  we  meet  with  a  specimen  not  confoi'mable  to 
any  known  species  (the  only  case  in  which  our  previous  knowledge 
ciffbrds  no  other  guidance  than  the  approximate  generalization),  we 
can  generally  make  a  specific  experiment,  which  is  always  a  safer 
resource. 

It  oftener  happens,  however,  that  the  proposition.  Most  A  are  B,  is 
not  the  ultimatum  of  our  scientific  pi'ogress,  though  the  knowledge  we 
possess  beyond  it  cannot  conveniently  be  brought  to  bear  upon  the 
particular  instance.  In  such  a  case,  we  know  well  enough  what  cir- 
cumstances really  distinguish  the  portion  of  A  which  have  the  attribute 
B  from  the  portion  which  have  it  not,  but  have  no  means,  or  no  time, 
to  examine  whether  those  characteristic  circumstances  exist  or  not  in 
the  individual  case.  This  is  generally  the  situation  we  are  in  when 
the  in(|uiry  is  of  the  kind  called  moral,  that  is,  of  the  kind  which  have 
in  view  to  predict  human  actions.  To  enable  us  to  affirm  anything 
universally  concerning  the  actions  of  classes  of  men,  the  classification 
must  be  grounded  upon  the  circumstances  of  their  mental  cultm-e  and 
habits,  which  in  an  individual  case  are  seldom  exactly  known;  and 
classes  grounded  on  these  distinctions  would  never  precisely  accbi-d 
with  those  intcj  which  mankind  are  necessarily  divided  for  social 
purposes.  All  propositions  which  can  be  framed  respecting  the  actions 
of  men  as  ordinarily  classified,  or  as  classified  according  to  any  kind  of 
outward  indications,  are  merely  approximate.  We  can  only  say,  Most 
men  of  a  particular  age,  profession,  country,  or  rank  in  society,  have 
such  and  such  qualities,  or.  Most  persons  when  placed  in  certain  cir- 
cumstances act  in  such  and  such  a  way.  Not  that  we  do  not  in  general 
know  well  enough  upon  what  causes  the  qualities  depend,  or  what  sort 
of  persons  they  are  who  act  in  that  particular  way ;  but  we  have  sel- 

y  Y 


354  INDUCTION. 

dom  the  means  of  knowing  whether  any  individual  person  has  been 
under  the  influence  of  those  causes,  or  is  a  person  of  that  particular 
sort.  We  could  replace  the  approximate  generalizations  by  proposi- 
tions universally  true;  but  these  would  hardly  ever  be  capable  of 
beino-  applied  to  practice.  We  should  be  sure  of  om-  majors,  but  we 
shoutd  not  be  able  to  get  minors  corresponding  to  them :  we  are 
forced  therefore,  to  draw  our  conclusions  from  coarser  and  more  fallible 
indications. 

§  4.  Proceeding  now  to  consider,  what  is  to  be  regarded  as  suf- 
ficient evidence  of  an  approximate  generalization  ;  we  can  have  no 
difficulty  in  at  once  recognizing  that  when  admissible  at  all,  it  is  ad- 
missible only  as  an  empirical  law.  Propositions  of  the  form.  Every 
A  is  B,  are  not  necessarily  laws  of  causation,  or  ultimate  uniformities 
of  coexistence  ;  propositions  like  Most  A  are  B,  cannot  be  so.  Propo- 
sitions hitherto  found  true  in  every  observed  instance,  may  yet  be  no 
necessary  consequence  of  laws  of  causation  or  of  ultimate  uniformities, 
and  unless  they  are  so,  may,  for  aught  we  know,  be  false  beyond  the 
limits  of  actual  obsei^-ation  :  still  more  evidently  must  this  be  the  case 
with  propositions  which  are  only  true  in  a  mere  majority  of  the  ob- 
served instances. 

There  is  some  difference,  however,  in  the  degi'ee  of  certainty  of  the 
proposition.  Most  A  are  B,  according  as  that  approximate  generaliza- 
tion composes  the  whole  of  our  knowledge  of  the  subject,  or  not. 
Suppose,  first,  that  the  former  is  the  case.  We  know  only  that  most 
A  are  B,  not  why  they  are  so,  nor  in  what  respect  those  which  are, 
differ  from  those  which  are  not.  How  then  did  we  learn  that  most  A 
are  B  1  Precisely  in  the  manner  in  which  we  should  have  learnt,  had 
such  happened  to' be  the  fact,  that  all  A  are  B.  We  collected  a  num- 
ber of  instances  sufficient  to  eliminate  chance,  and  having  done  so, 
compared  the  number  of  instances  in  the  aflBrmative  with  the  number  in 
the  negative.  The  result,  like  other  unresolved  derivative  laws,  can  be 
rebed  on  solely  within  the  limits  not  only  of  place  and  time,  but  also  of 
circumstance,  under  which  its  truth  has  been  actually  observed ;  for 
as  we  are  supposed  to  be  ignorant  of  the  causes  which  make  the 
proposition  true,  we  cannot  tell  in  what  manner  any  new  circumstance 
might  perhaps  affect  it.  The  proposition.  Most  judges  are  inaccessi- 
ble to  bribes,  would  be  found  true  of  Englishmen,  Frenchmen,  Ger- 
mans, North  Americans,  and  so  forth  ;  but  if  on  this  evidence  alone  we 
extended  the  assertion  to  Orientals,  we  should  step  beyond  the  limits, 
not  only  of  place  but  of  circumstance,  within  which  the  fact  had  been 
observed,  and  should  let  in  possibilities  of  the  absence  of  the  deter- 
mining causes,  or  the  presence  of  counteracting  ones,  which  might  be 
fatal  to  the  approximate  generalization. 

In  the  case  where  the  approximate  proposition  is  not  the  ultimatum 
of  our  scientific  knowledge,  but  only  the  most  available  form  of  it  for 
our  practical  guidance  ;  where  we  know  not  only  that  most  A  have  the 
attribute  B,  but  also  the  causes  of  B,  or  some  properties  by  which  the 
portion  of  A  which  has  that  attribute  is  distinguished  from  the  portion 
which  has  it  not ;  we  are  rather  more  favorably  situated  than  in  the 
preceding  case.  For  we  have  now  a  double  mode  of  ascertaining 
whether  it  be  true  that  most  A  are  B  ;  the  direct  mode,  as  before, 
and  an  indirect  one,  that  of  examining  whether  the  proposition  admits 


APPROXIMATE    GENERALIZATIONS.  355 

of  being  Jeduced  from  the  known  cause,  or  from  the  known  criterion, 
of  B.  Let  the  question,  for  example,  be,  Whether  most  Scotchmen 
can  read  ?  We  may  not  have  observed,  or  received  the  testimony  of 
others  respecting,  a  sufficient  luimber  and  variety  of  Scotchmen  to 
ascertain  this  tact ;  but  when  we  consider  that  the  cause  of  being  able 
to  read  is  the  having  been  taught  it,  another  mode  of  determining  the 
question  presents  itself,  namely,  by  inquiring  whether  most  Scotchmen 
have  been  sent  to  schools  where  reading  is  effectually  taught.  Of 
these  two  modes,  sometimes  one  and  sometimes  the  other  is  the  more 
available.  In  some  cases,  the  frequency  of  the  effect  is  the  more  ac- 
cessible to  that  extensive  and  varied  observation  which  is  indispensable 
to  the  establishment  of  an  empirical  law;  at  other  times,  tlie  freipiency 
of  the  causes,  or  of  some  collateral  indications.  It  commonly  happens 
that  neither  is  susceptible  of  so  satisfactory  an  induction  as  could  be 
desired,  and  that  the  grounds  on  which  the  conclusion  is  received  are 
compounded  of  both.  Thus  a  man  may  believe  that  most  Scotchmen 
can  read,  because,  so  far  as  his  information  extends,  most  Scotch- 
men have  been  seat  to  school,  and  most  Scotch  schools  teach  reading 
effectually;  and  also  because  most  of  the  Scotchmen  whom  he  has 
known  or  heard  of,  could  read  ;  though  neither  of  these  two  sets  of 
observations  may  by  itself  fulfill  the  necessary  conditions  of  extent  and 
variety. 

Altliough  the  approximate  generalization  may  in  most  cases  be 
indispensable  for  our  guidance,  even  when  we  know  the  cause,  or 
some  certain  mark,  of  the  attribute  predicated;  it  needs  hardly  be 
obsei-ved  that  we  may  always  replace  the  uncertain  indication  by  a 
certain  one,  in  any  case  in  which  we  can  actually  recognize  the  ex- 
istence of  the  cause  or  mark.  For  example,  an  assertion  is  made 
by  a  witness,  and  the  question  is,  whether  to  believe  it.  If  we  do  not 
look  to  any  of  the  individual  circumstances  of  the  case,  we  have 
nothing  to  direct  us  but  the  approximate  generalization,  that  truth 
is  more  common  than  falsehood,  or,  in  other  words,  that  most  per- 
sons, on  most  occasions,  speak  truth.  But  if  we  consider  in  what 
circumstances  the  cases  when  truth  is  spoken  differ  from  those  in 
which  it  is  not,  we  find,  for  instance,  the  following:  the  witness's  being 
an  honest  man  or  not ;  his  being  an  accurate  observer  or  not ;  his 
having  an  interest  to  serve  in  the  matter  or  not.  Now,  not  only  may 
we  be  able  to  obtain  other  approximate  generalizations  respecting  the 
degi'ee  of  frequency  of  these  various  possibilities,  but  we  may  know 
which  of  them  is  positively  realized  in  tlie  individual  case.  That  the 
witness  has  or  has  not  an  interest  to  serve,  we  may  know  directly; 
and  the  other  two  points  indirectly,  by  means  of  marks ;  as,  for  ex- 
ample, fi'om  his  conduct  on  some  former  occasion  ;  or  fi-om  his  rep- 
utation, which,  though  not  a  sure  mark,  affords  an  a{)proximate 
generalization  (as,  for  instance.  Most  persons  who  are  reputed  honest 
by  those  with  whom  they  have  had  fi-equent  dealings,  arc  really  so,) 
which  approaches  nearer  to  an  universal  truth  than  the  ajiproximate 
general  proposition  with  which  we  set  out,  viz.,  Most  persons  on  most 
occasions  speak  truth. 

As  it  seems  unnecessary  to  dwell  any  further  upon  the  question  of 
the  evidence  of  approximate  generalizations,  we  shall  proceed  to  a  not 
less  important  topic,  that  of  the  cautions  to  be  observed  in  arguing 
from  these  incompletely  universal  propositions  to  particular  cases 


356  INDUCTION. 

§  5  So  far  as  regards  the  direct  application  of  an  approximate 
geneialization  to  an  individual  instance,  this  question  presents  no  diffi- 
culty. If  the  proposition,  Most  A  are  B,  has  been  established,  by  a 
sufficient  induction,  as  an  empirical  law,  we  may  conclude  that  any 
particular  A  is  B,  with  a  probability  proportioned  to  the  preponder- 
ance of  the  number  of  affirmative  instances  over  the  number  of  excep- 
tions. If  it  has  been  found  practicable  to  attain  numerical  precision 
in  the  data,  a  corresponding  degree  of  precision  may  be  given  to  the 
evaluation  of  the  chances  of  error  in  the  conclusion.  If  it  can  be 
established  as  an  empirical  law  that  nine  out  of  every  ten  A  are  B, 
there  will  be  one  chance  in  ten  of  eiTor  in  assuming  that  any  A,  not 
individually  known  to  us,  is  a  B  :  but  this  of  course  holds  only  within 
the  limits  of  time,  place,  and  circumstance,  embraced  in  the  observa- 
tions, and  therefore  cannot  be  counted  upon  for  any  sub-class  or  variety 
of  A  (or  for  A  in  any  set  of  external  circumstances)  which  were  not 
included  in  the  avei'age.  It  must  be  added,  that  we  can  only  guide 
ourselves  by  the  proposition.  Nine  out  of  every  ten  A  are  B,  in  cases 
of  which  we  know  nothing  except  that  they  fall  within  the  class  A. 
For  if  we  know,  of  any  particular  instance  i,  not  only  that  it  falls 
under  A,  but  to  what  species  or  variety  of  A  it  belongs,  we  shall 
generally  eiT  in  applying  to  i  the  average  struck  for  the  whole  genus, 
from  which  the  average  corresj^onding  to  that  species  alone  would,  in 
all  probability,  materially  differ.  And  so  if  /,  instead  of  being  a  par- 
ticular sort  of  instance,  is  an  instance  known  to  be  under  the  influence 
of  a  particular  set  of  circumstances.  The  presumption  drawn  from 
the  numerical  proportions  in  the  whole  genus  would  prcbably,  in  such 
a  case,  only  mislead.  A  general  average  should  only  be  applied  to  a 
case  which  is  neither  known,  nor  can  be  presumed,  to  be  other  than  an 
average  case.  Such  averages,  therefore,  are  commonly  of  little  use 
for  the  practical  guidance  of  any  affairs  but  those  which  concern  large 
numbers.  Tables  of  the  chances  of  life  are  useful  to  insurance  offices, 
but  they  go  a  very  little  way  towards  informing  any  one  of  the  chances 
of  his  own  life,  or  any  other  life  in  which  he  is  interested,  since  almost 
every  life  is  either  better  or  worse  than  the  average.  Such  averages 
can  only  be  considered  as  supplying  the  first  teiTn  in  a  series  of  ap- 
proximations;  the  subsequent  tenns  proceeding  upon  an  appreciation 
of  the  circumstances  belonging  to  the  particular  case. 

§  6.  From  the  application  of  a  single  approximate  generalization  to 
individual  cases,  we  proceed  to  the  application  of  two  or  more  of  them 
together  to  the  same  case. 

When  a  judgment  applied  to  an  individual  instance  is  grounded 
upon  two  approximate  generalizations  taken  in  conjunction,  the  prop- 
ositions may  cooperate  towards  the  result  in  two  different  ways.  In 
the  one,  each  proposition  is  separately  applicable  to  the  case  in  hand, 
and  our  object  in  combining  them  is  to  give  to  the  conclusion  in  that 
particular  case  the  double  probability  arising  from  the  two  propositions 
separately.  This  may  be  called  joining  two  probabilities  by  way  of 
Addition;  and  the  result  is  a  probability  gi-eater  than  either.  ^  The 
other  mode  is,  when  only  one  of  the  propositions  is  directly  applicable 
to  the  case,  the  second  being  only  applicable  to  it  by  virtue  of  the 
application  of  the  first.  This  is  joining  two  probabilities  by  way  of 
Deduction  ;  the  result  of  which  is  a  less  probability  than  either.     The 


APPROXIMATE    GENERALIZATIONS.  357 

type  of  llio  iii-st  argument  is,  Most  A  are  B ;  most  C  are  13 ;  this 
thing  is  both  an  A  and  a  C  ;  therefore  it  is  probably  a  B.  The  type 
of  the  second  is,  Most  A  are  B  ;  most  C  ai-e  A ;  this  is  a  C ;  therefore 
it  is  probably  an  A,  therefore  it  is  probably  a  B.  The  first  is  exem- 
plified when  we  prove  a  fact  by  the  testimony  of  two  unconnected 
witnesses ;  the  second,  when  we  adduce  only  the  testimony  of  one 
witness  that  he  has  heard  the  thing  asserted  by  another.  Or  again,  in 
the  first  mode  it  may  bo  argued  that  the  accused  committed  the  crime, 
because  he  concealed  himself,  and  because  his  clothes  wore  stained 
with  blood ;  in  the  second,  that  he  committed  it  because  he  washed  or 
burnt  his  clothes,  which  is  supposed  to  render  it  probable  that  they 
were  stained  with  blood.  Instead  only  oY  two  links,  as  in  these 
instances,  we  may  suppose  chains  of  any  length.  A  chain  of  tho 
former  kind  was  termed  by  Mr.  Bentham*  a  self-corroborative  chain 
of  evidence ;   the  second,  a  self-infiiTnative  chain. 

When  approximate  generalizations  are  joined  by  way  of  addition,  it 
is  easily  seen  from  the  theory  of  probabilities  laid  down  in  a  former 
chapter,  in  what  manner  each  of  them  adds  to  the  probability  of  a  con- 
clusion which  has  the  warrant  of  them  all.  If  two  of  every  three  A  are  B, 
and  three  of  every  four  C  are  B,  the  probability  that  something  which 
is  both  an  A  and  a  C  is  a  B,  will  be  more  than  two  in  three,  or  than 
three  in  four.  Of  every  twelve  things  which  are  A,  all  except  four 
are  B,  by  the  supposition ;  and  if  the  whole  twelve,  and  consequently 
those  four,  have  the  characters  of  C  likewise,  three  more  will  be  B  on 
that  ground.  Therefore,  out  of  twelve  which  are  both  A  and  C,  eleven 
are  B.  To  state  the  argument  in  another  way ;  a  thing  which  is  both 
A  and  C,  but  which  is  not  B,  is  found  in  only  one  of  three  sections 
of  the  class  A,  and  in  only  one  of  foui-  sections  of  the  class  C  ;  but  this 
fourth  of  C  being  spread  over  the  whole  of  A  indiscriminately,  only 
one-third  part  of  it  (or  one-twelfth  of  the  whole  number)  belongs  to  the 
third  section  of  A ;  therefore  a  thing  which  is  not  B  occurs  only  once, 
among  twelve  things  which  are  both  A  and  C  The  argument  would, 
in  the  language  of  the  doctrine  of  chances,  be  thus  expressed  : — the 
chance  that  an  A  is  not  B  is  i,  the  chance  that  a  C  is  not  B  is  ^,  hence 
if  the  thing  be  both  an  A  and  a  C  the  chance  is  i  of  i  =:=  j\. 

This  aigument  presupposes  (as  the  reader  will  doubtless  have  re- 
marked) that  the  probabilities  arising  from  A  and  C  are  independent 
of  one  another.  There  must  not  be  any  such  connexion  between  A 
and  C,  that  when  a  thing  belongs  to  the  one  class  it  will  therefore 
belong  to  the  other,  or  even  have  a  greater  chance  of  doing  so.  Else 
the  fourth  section  of  C,  instead  of  being  equally  distributed  over  the 
three  sections  of  A,  might  be  comprised  in  greater  proportion,  or  even 
wholly,  in  the  third  section ;  in  which  last  case  the  probability  arising 
from  A  and  C  together  would  be  no  greater  than  that  arising  from  A 
alone. 

Wlien  approximate  generalizations  are  joined  together  in  the  other 
mode,  that  of  deduction,  the  degree  of  probability  of  the  inference,  in- 
stead of  increasing,  diminishes  at  each  step.  From  two  such  prem- 
isses as  Most  A  are  B,  Most  B  are  C,  we  cannot  with  certainty  conclude 
that  even  a  single  A  is  C  ;  for  the  whole  of  the  portion  of  A  which  in 
any  way  falls  under  B,  may,  perhaps,  be  comprised  in  the  exceptional 

*  Rationale  of  Judicial  Evidence.    Book  v.    Circumstantial. 


358  INDUCTION. 

part  of  it.  Still,  the  two  propositions  in  question  afford  an  appreciable 
probability  that  any  given  A  is  C,  provided  the  average,  on  which  the 
second  proposition  is  grounded,  Was  taken  fairly  Avith  reference  to  the 
first ;  provided  the  proposition  Most  B  are  C  was  anived  at  in  a  man- 
ner leaving  no  suspicion  that  the  probability  arising  from  it  is  other- 
wise than  fairly  distributed  over  the  section  of  B  which  belongs  to  A. 
For  although  the  instances  which  are  A  7nay  be  all  in  the  minority, 
they  may,  also,  be  all  in  the  majority  ;  and  the  one  possibility  is  to  be 
set  against  the  other.  On  the  whole,  the  probability  arising  fi-om  the 
two  propositions  taken  together  will  be  correctly  measured  by  the 
probability  arising  from  the  one,  abated  in  the  ratio  of  that  arising 
from  the  other.  If  nine  out  of  ten  Swedes  have  light  hair,  and  eight 
out  of  nine  inhabitants  of  Stockholm  are  Swedes,  the  probability 
arising  from  these  two  propositions,  that  any  given  inhabitant  of  Stock- 
holm is  light-haired,  will  amount  to  eight  in  ten  ;  although  it  is  rigor- 
ously possible  (however  improbable)  that  the  whole  Swedish  popula- 
lation  of  Stockholm  may  belong  to  that  tenth  section  of  the  people  of 
Sweden  who  are  an  exception  to  the  rest. 

If  the  premisses  are  known  to  be  true  not  of  a  bare  majority,  but  of 
nearly  the  whole,  of  their  respective  subjects,  we  may  go  on  joining 
one  such  proposition  to  another  for  several  steps,  before  we  reach  a 
conclusion  not  presumably  true  even  of  a  majority.  The  en'or  of  the 
conclusion  will  amount  to  the  aggregate  of  the  eiTors  of  all  the  prem- 
isses. Let  the  proposition.  Most  A  are  B,  be  true  of  nine  in  ten  ;  Most 
B  are  C,  of  eight  in  nine  :  then  not  only  will  one  A  in  ten  not  be  C, 
because  not  B,  but  even  of  the  nine-tenths  which  are  B,  only  eight- 
ninths  will  be  C  :  that  is,  the  cases  of  A  which  are  C  will  be  only 
I  of  y9j,  or  fovir-fifths.  Let  us  now  add  Most  C  are  D,  and  suppose 
this  to  be  true  of  seven  cases  out  of  eight ;  the  proportion  of  A  which 
is  D  will  be  only  |-  of  -f  of  /^  >  ^^  Vo  •  Thus  the  probability  progressively 
dwindles.  The  experience,  however,  on  which  our  approximate  gen- 
eralizations are  groimded,has  so  rarely  laeen  subjected  to,  or  admits  of, 
accurate  numerical  estimation,  that  we  cannot  in  general  apply  any 
measurement  to  the  diminution  of  probability  which  takes  place  at 
each  illation;  but  must  be  content  with  remembering  that  it  does 
diminish  at  every  step,  and  that  unless  the  premisses  approach  veiy 
nearly  indeed  to  being  universal  truths,  the  conclusion  after  a  very  few 
steps  is  worth  nothing.  A  hearsay  of  a  hearsay,  or  an  argument  from 
presumptive  evidence  depending  not  upon  immediate  marks  but  upon 
marks  of  marks,  is  worthless  at  a  very  few  removes  from  the  first  stage. 

§  7.  There  are,  however,  two  cases  in  which  reasonings  depending 
upon  approximate  generalizations  may  be  carried  to  any  length  we 
please  with  as  much  assurance,  and  are  as  strictly  scientific,  as  if  they 
were  composed  of  universal  laws  of  nature.  Both  these  cases  are  ex- 
ceptions of  the  sort  which  are  currently  said  to  prove  the  rule.  The 
approximate  generalizations  are  as  suitable,  in  the  cases  in  question, 
for  purposes  of  ratiocination,  as  if  they  were  complete  generalizations, 
because  they  are  capable  of  being  transformed  into  complete  general- 
izations exactly  equivalent. 

First :  If  the  approximate  generalization  is  of  the  class  in  which  nur 
reason  for  stopping  at  the  approximation  is  not  the  impossibility,  but 
only  the  inconvenience,  of  going  further ;  if  we  are  cognizant  of  tho 


APPROXIMATE    GENERALIZATIONS.  359 

character  vvlilch  distinguishes  the  cases  that  accord  with  the  generali- 
zation from  those  which  are  exceptions  to  it;  we  may  then  substitute, 
for  the  approximate  proposition,  an  universal  proposition  with  a  pro- 
viso. The  proposition,  Most  persons  who  have  uncontrolled  power 
employ  it  ill,  is  a  generalization  of  this  class,  and  may  be  transformed 
intt)  the  lollownig  : — All  persons  vvho  have  uncontrt)lled  power  employ 
it  ill,  provhled  they  are  not  persons  of  unusual  strength  of  judgment 
and  will,  and  confirmed  habits  of  virtue.  The  proposition,  carrying 
the  hypothesis  or  proviso  with  it,  may  then  be  dealt  .with  no  longer  as 
an  ap2)roximate,  but  as  an  universal  proposition ;  and  to  whatever 
number  of  steps  the  reasoning  may  reach,  the  hypothesis,  being  carried 
forward  to  the  conclusion,  will  exactly  indicate  how  far  tJiat  conclusion 
is  from  being  applicable  universally.  If  in  the  course  of  the  argument 
other  approximate  generalizations  are  introduced,  each  of  them  being 
in  like  manner  expressed  as  an  universal  proposition  with  a  condition 
annexed,  the  sum  of  all  the  conditions  will  appear  at  the  end  as  the 
sum  of  all  the  errors  which  affect  the  conclusion.  Thus,  to  the  propo- 
sition last  cited,  let  us  add  the  following: — All  absolute  monarchs  have 
uncontrolled  power,  unless  their  position  is  such  that  they  need  the 
active  support  of  their  subjects  (as  was  the  case  with  Queen  Elizabeth, 
Frederick  of  Prussia,  and  others).  Combining  these  two  propositions 
we  can  deduce  from  them  an  universal  conclusion,  which  will  be  sub- 
ject to  both  the  hypotheses  in  the  premisses  :  All  absolute  monarchs 
employ  their  power  ill,  unless  their  position  makes  them  need  the 
active  support  of  their  subjects,  or  unless  they  are  persons  of  unusual 
strength  of  judgment  and  will,  and  confirmed  habits  of  virtue.  It  is  of 
no  consequence  how  rapidly  the  errors  in  our  premisses  accumulate, 
if  we  are  able  in  this  manner  to  record  each  eiTor,  and  keep  an  account 
of  the  aggregate  as  it  swells  up. 

Secondly:  there  is  a  case  in  wluch  approximate  propositions,  even 
without  our  taking  note  of  the  conditions  under  which  they  are  not 
ti-ue  of  individual  cases,  are  yet,  for  the  purposes  of  science,  universal 
ones ;  namely,  in  the  scientific  inquiries  which  relate  to  the  properties 
not  of  individuals,  but  of  multitudes.  The  principal  of  these  is  the 
ecience  of  politics,  or  of  human  society.  This  science  is  principally 
concerned  with  the  actions  not  of  solitary  individuals,  but  of  masses ; 
with  the  fortunes  not  of  single  persons,  but  of  communities.  For  the 
statesman,  therefore,  it  is  generally  enough  to  know  that  most  persons 
act  or  are  acted  upon  in  a  particular  way;  since  his  speculations  and 
bis  practical  arrangements  refer  almost  exclusively  to  cases  in  which 
the  whole  community,  or  some  large  portion  of  it,  is  acted  upon  at 
once,  and  in  which,  therefore,  what  is  done  or  felt  by  >nost  persons 
determines  the  result  pi-oduced  by  or  upon  the  body  at  large.  He  can 
get  on  well  enough  with  approximate  generalizations  on  human  nature, 
since  what  is  true  approximately  of  all  individuals  is  true  absolutely  of 
all  masses.  And  even  when  the  operations  of  individual  men  have  a 
part  to  play  in  his  deductions,  as  when  he  is  reasoning  of  kings,  or 
other  single  rulers,  still  as  he  is  providing  for  indefinite  duration,  in- 
volving an  indefinite  succession  of  such  individuals,  he  must  in  general 
both  reason  and  act  as  if  what  is  true  of  most  persons  were  true  of  all. 

The  two  kinds  of  considerations  above  adduced  are  a  sufficient 
refutation  of  the  popular  error,  that  speculations  on  society  and  govern- 
ment, as  resting  ujjon  merely  probable  evidence,  must  be  inferior  in 


360  INDUCTION. 

certainty  and  scientific  accuracy  to  the  conclusions  of  what  are  called 
the  exact  sciences,  and  less  to  he  relied  upon  in  practice.  There  are 
reasons  enough  why  the  moral  sciences  must  remain  inferior  to  at  least 
the  more  perfect  of  the  physical ;  why  the  laws  of  their  more  compli- 
cated phenomena  cannot  be  so  completely  deciphei'ed,  nor  the  phe- 
nomena predicted  with  the  same  degiee  of  assurance.  But  though  we 
cannot  attain  to  so  many  truths,  there  is  no  reason  that  those  we  can 
attain  should  deserve  less  reliance,  or  have  less  of  a  scientific  character. 
Of  this  topic,  however,  we  shaU  treat  more  systematically  in  the  con- 
cluding Book,  to  which  place  any  further  consideration  of  it  must  be 
deferred. 


CHAPTER  XXIV. 

OF    THE   REMALVING  LAWS    OF  NATURE. 

§  1.  In  the  First  Book  we  found  that  all  the  assertions  which  can  be 
conveyed  by  language,  express  some  one  or  more  of  five  different 
things:  Existence;  Order  in  Place;  Oi-der  in  Time;  Causation;  and 
Resemblance.*  Of  these.  Causation,  in  our  view  of  the  subject,  not 
being  fundamentally  different  from  Order  in  Time,  the  five  sjiecies  of 
possible  assertions  are  reduced  to  four.  The  propositions  which  affirm 
Order  in  Time,  in  either  of  its  two  modes.  Coexistence  and  Succession, 
have  foiined,  thus  far,  the  subject  of  the  present  Book.  And  we  have 
now  concluded  the  exposition,  so  far  as  it  falls  within  the  limits 
assigned  to  this  work,  of  the  nature  of  the  evidence  on  which  these 
propositions  rest,  and  the  processes  of  investigation  by  which  they  are 
discovered  and  proved.  There  remain  three  classes  of  facts :  Exist- 
ence, Oi-der  in  Place,  and  Resemblance ;  in  regard  to  which  the  same 
questions  are  now  to  be  resolved. 

Regarding  the  first  of  these,  very  little  needs  be  said.  Existence  in 
general,  is  a  subject  not  for  our  science,  but  for  the  higher  metaphysics. 
To  determine  what  things  can  be  recognized  as  really  existing,  inde- 
pendently of  our  own  sensible  or  other  impressions,  and  in  what  mean- 
ing the  tei-m  is,  in  that  case,  predicated  of  them,  belongs  to  the  con- 
sideration of  "  Things  in  themselves,"  from  which,  throughout  this 
work,  we  have  as  much  as  possible  kept  aloof  Existence,  so  far  as 
Logic  is  concerned  about  it, has  reference  only  to  phenomena  ;  to  actual, 
or  possible,  states  of  external  or  internal  consciousness,  in  ourselves  or 
others.  Feelings  of  sensitive  beings,  or  possibilities  of  having  such 
feelings,  are  the  only  things  the  existence  of  which  can  be  a  subject  of 
logical  induction,  because  the  only  things  of  which  the  existence  in 
individual  cases  can  be  a  subject  of  experience. 

It  is  true  that  a  thing  is  said  by  us  to  exist,  even  when  it  is  absent, 
and  therefore  is  not  and  cannot  be  perceived.  But  even  then,  its  exist- 
ence ia  to  us  only  another  word  for  our  conviction  that  we  should  per- 
ceive it  on  a  certain  supposition;  if  we  were  placed  in  the  needful 

*  Supra,  70. 


REMAINING    LAWS    OP    NATURE.  3G1 

circumstances  of  time  and  place,  and  endowed  with  the  needful  perfec- 
tion of  organs.  My  belief  that  the  Emperor  of  China  exists,  is  simply 
iny  belief  that  if  I  were  transported  to  the  imperial  palace,  or  somfe 
other  locality  in  Pckin,  I  should  see  him.  My  belief  that  Julius  Cee- 
sar  existed,  is  my  belief  that  I  should  have  seen  him  if  I  had  bec?i  pres- 
ent in  the  Held  of  Pharsalia,  or  in  the  senate-house  at  Rome.  When 
I  believe  that  stars  exist  beyond  the  utmost  range  of  my  vision,  though 
assisted  by  the  most  povvei-ful  telescopes  yet  invented,  my  belief,  philo- 
sophically expressed,  is,  that  with  still  better  telescopes,  if  such  existed, 
I  could  see  them,  or  that  they  may  be  perceived  by  beings  less  remote 
from  them  in  space,  or  whose  capacities  of  perception  are  superior  to 
mine. 

The  existence,  therefore,  of  a  phenomenon,  is  but  another  word  for 
its  being  perceived,  or  for  the  infeiTed  possibility  of  percei\'ing  it. 
"Wlien  the  phenomenon  is  within  the  range  of  present  observation,  by 
present  observation  we  assure  ourselves  of  its  existence ;  when  it  is 
beyond  that  range,  and  is,  therefore,  said  to  be  absent,  we  infer  its 
existence  from  marks  or  evidences.  But  what  can  these  evidences  be  ? 
Other  phenomena;  ascertained  by  induction  to  be  connected  with  the 
given  phenomenon,  either  in  the  way  of  succession  or  of  coexistence. 
The  simple  existence,  therefore,  of  an  individual  phenomenon,  when 
not  directly  perceived,  is  inferred  from  some  inductive  law  of  succes- 
sion or  coexistence :  and  is  consequently  not  amenable  to  any  peculiar 
inductive  principles.  We  prove  the  existence  of  a  thing,  by  proving  that 
it  is  connected  by  succession  or  coexistence  with  some  known  thing. 

With  respect  to  general  propositions  of  this  class,  that  is,  which  affirm 
the  bare  fact  of  existence,  they  have  a  peculiai'ity  which  renders  the 
logical  treatment  of  them  a  very  easy  matter ;  they  are  generalizations 
which  are  sufficiently  proved  by  a  single  instance.  That  ghosts,  or 
unicoi'ns,  or  sea-serpents  exist,  would  be  fully  established  if  it  could 
be  ascertained  positively  that  such  things  haid  been  even  once  seen. 
Whatever  has  once  happened,  is  capable  of  happening  again;  the  only 
question  relates  to  the  conditions  under  which  it  happens. 

So  far,  therefore,  as  relates  to  simple  existence,  the  Inductive  Logic 
has  no  knots  to  untie.  And  we  may  proceed  to  the  remaining  two  of 
the  great  classes  into  which  facts  have  been  divided  ;  Resemblance,  and 
Order  in  Sjjace. 

§  2.  Resemblance  and  its  opposite,  except  in  the  case  in  which  they 
assume  the  names  of  Equality  and  Inequality,  are  seldom  regarded  as 
objects  of  science  ;  they  are  supposed  to  be  perceived  by  simple  appre- 
hension ;  by  merely  applying  our  senses  or  directing  our  attonticjn  to 
the  two  objects  at  once,  or  in  immediate  succession.  And  this  simul- 
taneous or  virtually  simultaneous  application  of  our  faculties  to  the  two 
things  which  are  to  be  compai'ed,  docs  necessarily  constitute  the  ulti- 
mate appeal,  wherever  such  application  is  practicable.  But  in  most 
cases,  it  is  not  practicable  :  the  objects  cannot  be  brought  so  closely 
together  that  the  feeling  of  their  resemblance  (at  least  a  complete  feel- 
ing of  it)  directly  arises  in  the  mind.  We  can  only  compare  each  of  them 
with  some  third  object  capable  of  being  transported  from  one  to  the  otlier. 
And  besides,  even  when  the  objects  can  be  brought  into  immediate 
juxtaposition,  their  resemblance  or  difference  is  but  imperfectly  kno^vn 
to  us  unless  we  have  compared  them  minutely,  part  by  part.  Until 
Zz 


362  INDUCTION. 

this  has  been  done,  things  in  reality  very  dissimilar  often  appear  undis- 
guishably  alike.  Two  lines  of  very  unequal  length  will  appear  about 
equal  when  lying  in  different  directions ;  but  place  them  parallel,  with 
their  further  extremities  even,  and  if  you  look  at  the  nearer  extremities, 
their  inequality  becomes  a  matter  of  direct  perception. 

To  ascertain  whether,  and  in  what,  two  phenomena  resemble  or  dif- 
fer, is  not  always,  therefore,  so  easy  a  thing  as  it  might  at  first  appear. 
When  the  two  cannot  be  brought  into  juxtaposition,  or  not  so  that  the 
observer  is  able  to  compare  their  several  parts  in  detail,  he  must  em- 
ploy the  indirect  means  of  reasoning  and  general  propositions.  When 
we  cannot  bring  two  straight  lines  together,  to  determine  whether  they 
are  equal,  we  do  it  by  the  physical  aid  of  a  foot  rule  applied  first  to 
one  and  then  to  the  other,  and  the  logical  aid  of  the  general  proposition 
or  foiTuula,  "Things  which  are  equal  to  the  same  thing  are  equal  to 
one  another."  The  comparison  of  two  things  through  the  intervention 
of  a  third  thing,  when  their  direct  comparison  is  impossible,  is  the  ap- 
propriate scientific  process  for  ascertaining  resemblances  and  dissimi- 
larities, and  is  the  sum  total  of  what  Logic  has  to  teach  on  the  subject. 

An  undue  extension  of  these  views  induced  Locke  to  consider 
reasoning  itself  as  nothing  but  the  comparison  of  two  ideas  through 
the  medium  of  a  third,  and  knowledge  as  the  perception  of  the  agree- 
ment or  disagi-eement  of  two  ideas :  doctrines  which  the  Condillac 
school  blindy  adopted,  without  the  qualifications  and  distinctions  with 
which  they  were  studiously  guarded  by  their  illustrious  author. 
Where,  indeed,  the  agreement  or  disagi-eement  (otherwise  called  re- 
semblance or  dissimilarity)  of  any  two  things  is  the  very  matter  to  be 
determined,  as  is  the  case  particularly  in  the  sciences  of  quantity  and 
extension,  there  the  process  by  which  a  solution,  if  not  attainable  by 
direct  perception,  must  be  indirectly  sought,  consists  in  comparing 
these  two  things  through  the  medium  of  a  third.  But  this  is  far  from 
being  true  of  all  inquiries.  The  knowledge  that  bodies  fall  to  the 
ground  is  not  a  perception  of  agreement  or  disagreement,  but  of  a 
series  of  physical  occurrences,  a  succession  of  sensations.  Locke's  defi- 
nitions of  knowledge  and.  of  reasoning  required  to  be  limited  to  oui- 
knowledge  of,  and  reasoning  about,  Resemblances.  Nor,  even  when 
thus  restricted,  are  the  propositions  strictly  connect  ;  since  the  com- 
parison is  not  made,  as  he  represents,  between  the  ideas  of  the  two 
phenomena,  but  between  the  phenomena  themselves.  This  mistake 
has  been  pointed  out  in  an  earlier  patt  of  our  inquiry,*  and  we  traced 
it  to  an  imperfect  conception  of  what  takes  place  in  mathematics, 
where  very  often  the  comparison  is  really  made  between  the  ideas, 
without  any  appeal  to  the  outward  senses ;  only,  however,  because  in 
mathematics  a  comparison  of  the  ideas  is  strictly  equivalent  to  a  com- 
parison of  the  phenomena  themselves.  Wliere,  as  in  the  case  of  num- 
bers, lines,  and  figures,  our  idea  of  an  object  is  a  complete  picture  of 
the  object,  so  far  as  respects  the  matter  in  hand  ;  we  can  of  course 
learn  from  the  picture,  whatever  could  be  learnt  fi-om  the  object  itself 
by  mere  contemplation  of  it  as  it  exists  at  the  particular  instant  when 
the  picture  is  taken.  No  mere  contemplation  of  gunpowder  would 
ever  teach  us  that  a  spark  would  make  it  explode,  nor,  consequently, 
would  the  contemplation  of  the  idea  of  gunpowder  do  so  :  but  the  mere 

*  Supra,  pp.  59,  154. 


REMAINING  LAWS  OF  NATURE.  363 

contemplation  of  a  straight  line  shows  that  it  cannot  inclose  a  space ; 
accordingly  tlio  contemplation  of  the  idea  of  it  will  show  the  same. 
Wliat  takes  place  in  mathematics  is  tluis  no  argument  that  the  com- 
parison is  between  the  ideas  only.  It  is  always,  either  indirectly  or 
directly,  a  comparison  of  the  phenomena. 

In  cases  in  which  we  cannot  bring  the  phenomena  to  the  test  of  direct 
inspection  at  all,  or  not  in  a  matter  sufficiently  precise,  but  must  judge 
of  their  resemblance  by  inference  from  other  resemblances  or  dissim- 
ilarities more  accessible  to  observation,  we  of  course  require,  as  in  all 
cases  of  ratiocination,  generalizations  or  formulce  applicable  to  the 
subject.  We  must  reason  fi-om  laws  of  nature  ;  fi-om  the  uniformities 
which  are  observable  in  the  fact  of  likeness  or  unlikeness. 

§  3.  Of  these  laws  or  unifomiities,  the  most  comprehensive  are 
those  supplied  by  mathematics ;  the  axioms  relating  to  equality,  ine- 
quality, and  proportionality,  and  the  various  theorems  thereon  founded. 
And  these  are  the  only  Laws  of  Resemblance  which  require  to  be,  or 
which  can  be,  treated  apart.  It  is  true  there  are  innumerable  other 
theorems  which  affirm  resemblances  among  phenomena ;  as  that  the 
angle  of  the  reflexion  of  light  is  equal  to  it  sangle  of  incidence  (equality 
being  merely  exact  resemblance  in  magnitude).  Again,  that  the 
heavenly  bodies  describe  equal  areas  in  equal  times ;  and  that  their 
periods  of  revolution  ave  proportional  (another  species  of  resemblance) 
to  the  sesquiplicate  powers  of  their  distances  from  the  centre  of  force. 
These  and  similar  propositions  affirm  resemblances,  of  the  same  nature 
with  those  asserted  in  the  theorems  of  mathematics  :  but  the  distinction 
is,  that  the  propositions  of  mathematics  are  true  of  all  phcnomenft 
whatever,  or  at  least  without  distinction  of  origin ;  while  the  truths  in 
question  are  affirmed  only  of  special  phenomena,  which  originate  in  a 
certain  way ;  and  the  eqtialities,  proportionalities,  or  other  resemblances, 
which  exist  between  such  phenomena,  must  necessarily  be  either  de-' 
rived  fiom,  or  identical  with,  the  law  of  their  origin — the  law  of  caus- 
ation on  which  they  depend.  .  The  otjuality  of  the  areas  described  by 
the  planets,  is  derived  from  the  laws  of  the  causes ;  and,  until  its  deri- 
vation was  shown,  it  was  an  empirical  law.  The  equality  of  the  angles 
of  reflexion  and  incidence  is  identical  with  the  law  of  the  cause  ;  for 
the  cause  is  the  incidence  of  a  ray  of  light  upon  a  reflecting  surface, 
and  the  equality  in  question  is  the  very  law  according  to  which  that 
cause  produces  its  effects.  This  class,  therefore,  of  the  uniformities 
of  resemblance  between  phenomena,  is  inseparable,  in  fact  and  in 
thought,  from  the  laws  of  the  production  of  those  phenomena  ;  and  the* 
principles  of  induction  applicable  to  them  are  no  other  than  those 
of  which  we  have  treated   in  the  preceding  chapters  of  this  Book. 

It  is  otherwise  with  the  truths  of  mathematics.  The  laws  of  equality 
and  inequality  between  spaces,  or  between  numbers,  have  no  connexion 
with  laws  of  causation.  That  the  angle  of  reflexion  is  equal  to  the 
angle  of  incidence  is  a  statement  of  the  mode  of  action  of  a  particular 
cause  ;  but  that  when  two  straight  lines  intersect  each  other  the  oppo- 
site angles  are  equal,  is  true  of  all  such  lines  and  angles,  by  whatever 
cause  produced.  That  the  squares  of  the  periodic  times,  of  the  planets 
are  proportional  to  the  cubes  of  their  distances  from  the  sun,  is  an 
uniformity  derived  from  the  laws  of  the.  causes  which  produce  the 
planetary  motions,  namely,  the  central  and  the  tangential  force ;  but 


384  INDUCTION. 

that  the  square  of  any  number  is  four  times  the  square  of  half  the 
number,  is  true  independently  of  any  cause.  The  onlj  laws  of  resem- 
blance, therefore,  which  we  are  called  upon  to  consider  independently 
of  causation  belong  to  the  province  of  mathematics. 

§  4.  The  same  thing  is  evident  with  respect  to  the  only  remaining 
one  of  our  five  categories,  Order  in  Place.  The  order  in  place,  of  the 
effects  of  a  cause,  is  (like  everything  else  belonging  to  the  eftects)  a 
consequence  of  the  laws  of  that  cause.  The  order  in  place,  or,  as  we 
have  termed  it,  the  collocation,  of  the  primeval  causes  is  (as  well  as 
their  resemblance)  in  each  instance  an  ultimate  fact,  in  which  no  laws 
or  uniformities  are  traceable.  The  only  remaining  general  propo- 
sitions respecting  order  in  place,  and  the  only  ones  which  have  nothing 
to  do  with  causation,  are  some  of  the  truths  of  geometry  ;  laws  through 
which  we  are  able,  from  the  order  in  place  of  certain  points,  lines,  or 
spaces,  to  infer  the  order  in  place  of  others  which  are  connected  with 
the  former  in  some  known  mode ;  quite  independently  of  the  partic- 
ular nature  of  those  points,  lines,  or  spaces,  in  any  other  respect  than 
position  or  magnitude,  as  well  as  independently  of  the  physical  cause 
from  which  in  any  p'articular  case  they  happen  to  derive  their  origin. 

It  thus  appears  that  mathematics  is  the  only  department  of  science 
into  the  methods  of  which  it  still  remains  to  inquire.  And  there  is  the 
less  necessity  that  this  inquiry  should  occupy  us  long,  as  we  have  already 
in  the  second  Book,  made  considerable  progress  in  it.  We  there  re- 
marked, that  the  directly  inductive  truths  of  mathematics  are  few  in 
number ;  consisting  of  the  axioms,  together  with  certain  propositions 
■concerning  existence,  tacitly  involved  in  most  of  the  so-called  defi- 
nitions. And  we  proved,  at  such  length  as  makes  any  return  to  the 
subject  altogether  superfluous,  that  these  oi'iginal  premisses,  from 
which  the  remaining  truths  of  the  science  are  deduced,  are,  notwith- 
standing all  appearances  to  the  contrary,  results  of  observation  and  ex- 
perience ;  founded,  in  short,  on  the  evidence  of  the  senses.  That 
things  equal  to  the  same  thing  are  equal  to  anoXher,  or  that  two  straight 
lines  which  have  once  intersected  with  one  another  continue  to  diverge, 
are  inductive  truths  ;  resting  indeed,  like  the  law  of  universal  causation, 
only  upon  induction  -per  enumeratloncm  simplicem  ;  upon  the  fact  that 
they  have  been  perpetually  found  true  and  never  once  false.'  But  as 
we  have  seen  in  a  recent  chapter  that  this  evidence,  in  the  case  of  a 
law  so  completely  universal  as  the  law  of  causation,  amounts  to  the 
fullest  proof  attainable  by  the  human  faculties,  so  is  this  even  more 
evidently  true  of  the  general  propositions  to  which  we  are  now  ad- 
verting ;  because,  as  a  perception  of  their  truth  in  any  individual  case 
whatever,  requires  only  the  simple  act  of  looking  at  the  objects  in  a 
proper  position,  there  never  could  have  been  in  their  case  (what,  for  a 
long  period,  in  the  case  of  the"  law  of  causation,  there  were)  instances 
which  were  apparently,  though  not  really,  exceptions  to  them.  Their 
infallible  truth  was  recognized  from- the  very  dawn  of  speculation ;  and 
as  their  extreme  familiarity  made  it  impossible  for  the  mind  to  conceive 
the  objects  under  any  other  law,  they  were,  and  still  are,  generally  con- 
sidered as  truths  recognized  by  their  own  evidence,  or  by  instinct. 

§  5.  There  is  something  which  seems  to  require  explanation,  in  the 
fact  that  the  immense  multitude  of  truths  (a  multitude  still  as  far  from 


REMAINING    LAWS    OF    NATURE.  365 

being  exliausted  as  ever)  comprised  in  the  mathematical  sciences,  can 
be  elicited  from  so  small  a  number  of  elementary'  laws.  One  sees  not, 
at  first,  how  it  is  that  there  can  be  room  for  such  -an  infinite  variety  of 
true  propositions,  on  subjects  apparently  so  limited. 

To  begin  with  the  fvcience  of  immber.  The  elementary  or  ultimate 
truths  of  this  science  are  the  common  axioms  concerning  equality, 
namely,  "  Things  which  ai'e  equal  to  the  same  thing  are  equal  to  one 
another,"  and  "  Equals  added  to  equals  make  equal  sums,"  (no  other 
axioms  are  necessary,*)  together  with  the  definitions  of  the  various 
numbers.  Like  other  so-called  definiticms,  these  are  composed  of  two 
things,  the  explanation  of  a  name  and  the  assertion  of  a  fact :  of  which 
the  latter  alone  can  form  a  first  princi])le  or  premiss  of  a  science.  The 
fact  asserted  in  the  definition  of  a  number  is  a  physical  fact.  Each  of 
the  numbers  two,  three,  four,  &c.,  denotes  physical  phenomena,  and 
connotes  a  physical  property  of  those  phenomena.  Two,  for  instance, 
denotes  all  pairs  of  things,  ajid  twelve  all  dozens  of  things,  connoting 
what  makes  them  pairs,  or  dozens  ;  and  that  which  makes  them  so  is 
something  physical ;  since  it  cannot  be  denied  that  two  apples  are 
physically  distinguishable  from  tlixee  apples,  two  horses  from  one  horse, 
and  so  forth  :  that  they  are  a  different  visible  and  tangible  phenomenon. 
I  am  not  undertaking  to  say  what  the  difference  is ;  it  is  enough  that 
there  is  a  difference  of  which  the  senses  can  take  cognizance.  And 
although  an  hundred  and  two  horses  are  not  so  easily  distinguished 
from  an  hundred  and  three,  as  two  horses  are  from  three — though  in 
most  positions  the  senses  do  not  perceive  any  difference — yet  they  may 
be  so  placed  that  a  difference  will  be  perceptible,  or  else  we  should 
never  have  distinguished  them,  and  given  them  different  names. 
Weight  is  confessedly  a  physical  property  of  thiugs ;  yet  small  differ- 
ences between  great  weights  are  as  imperceptible  to  the  senses  in  most 
situations,  as  small  differences  between  gi'eat  numbers  ;  and  are  only 
put  in  evidence  by  placing  the  two  objects  in  a  peculiar  position, 
namely,  in  the  opposite  scales  of  a  delicate  balance. 

What,  then,  is  that  which  is  connoted  by  a  name  of  number  %  Of 
course  some  property  belonging  to  the  agglomeration  of  things  which 
we  call  by  the  name  ;  and  that  property  is,  the  chaructei'istic  manner 
in  which  the  agglomeration  is  made  up  of,  and  may  be  separated  into, 
parts.  We  will  endeavor  to  make  this  more  intelligible  by  a  few 
explanations. 

When  we  call  a  collection  of  objects  two,  tliree,  or  four,  they 
are  not  two,  three,  or  four  in  the  abstract  ;  they  are  two,  three,  or 
four  things  of  some  particular  kind  ;  pebbles,  horses,  inches,  pounds 
weight.  What  the  name  of  number  connotes  is,  the  manner  in 
which  single  objects  of  the  given  kind  must  be  put  together,  in  order 

*  The  axiom,  "  Equals  subtracted  from  equals  leave  equal  differences,"  may  be  demon- 
strated from  the  two  axioms  in  the  text.  If  A  =  a,  and  B=6,  A —  B=a  — 6.  For  if  not, 
let  A  —  B=a  —  b -\- c.  Then,  since  B  =  6,  adding  equals  to  equals,  A=a-j-c.  But 
k—a.     Therefore  a=a  +  c,  which  is  absurd. 

This  proposition  having'  been  demonstrated,  we  may,  by  means  of  it,  demonstrate  the 
following:  "If  equals  be  added  to  imequals,  the  sums  are  unequal."  If  A=a  and  B 
not  =  fc,  A  4-  B  is  not  equal  a-\-b.  For  suppose  it  to  be  so.  Then,  since  A  =  a  and  A  + 
B  =  a-1-  6,  subtracting  equals  from  equals,  B  =  6  ;  which  is  contrary  to  the  hypothesis. 

So  again,  it  may  be  proved  that  two  things,  one  of  which  is  equal  and  the  other  unequal 
to  a  third  thing,  are  unequal  to  one  another.  If  A  =  a  and  A  not  —  B,  neither  is  n  =  B. 
For  suppose  it  to  be  equal.  Then,  sitice  A.—  a  and  a  =  B,  and  since  things  equal  to  the 
same  thing  are  equal  to  one  another,  A  =  B ;  which  is  contrary  to  the  hypothesis. 


366  INDUCTION. 

to  produce  that  particular  aggregate.  If  the  aggregate  be  of  peb- 
bles, and  we  call  it  tivo,  the  name  implies  that  to  compose  the 
aggregate,  one  pebble  must  be  joined  to  one  pebble.  If  we  call  it 
three,  we  mean  that  one  and  one  and  one  pebble  must  be  brought  to- 
gether to  produce  it,  or  else  that  one  pebble  must  be  joined  to  an 
aggi'egate  of  the  kind  called  two,  already  existing.  The  aggregate 
which  we  call_/o«?"  has  a  still  greater  number  of  characteristic  modes 
of  formation.  One  and  one  and  one  and  one  pebble  may  be  brought 
together;  or  two  aggi'egates  of  the  kind  called  two  may  be  united  ;  or 
one  pebble  may  be  added  to  an  aggregate  of  the  kind  called  three. 
Every  succeeding  number  in  the  ascending  series,  may  be  formed  by 
the  junction  of  smaller  numbers  in  a  progressively  greater  variety  of 
ways.  Even  limiting  the  parts  to  two,  the  number  may  be  formed, 
and  consequently  may  be  divided,  in  as  many  different  ways  as  there 
are  numbers  smaller  than  itself;  and,  if  we  admit  of  threes,  fours,  &c., 
in  a  still  greater  variety.  Other  modes  of  arriving  at  the  same  aggre- 
gate present  themselves,  not  by  the  union  of  smaller,  but  by  the  dis- 
memberment of  larger  aggregates.  Thus,  three  pehhles  may  be  formed 
by  taking  away  one  pebble  from  an  .aggregate  of  four ;  tioo  2>ehbles,  by 
an  equal  division  of  a  similar  aggregate ;  and  so  on. 

Every  arithmetical  proposition  ;  every  statement  of  the  result  of  an 
arithmetical  operation  ;  is  a  statement  of  one  of  the  modes  of  the 
formation  of  a  given  number.  It  affinns  that  a  certain  aggregate 
might  have  been  formed  by  putting  together  certain  other  aggregates, 

by  vvithdrawing  certain  j^ortions  of  some  aggregate;  and  that,  by 
consequence,  we  might  reproduce  those  aggregates  from  it,  by  revers- 
ing the  process. 

Thus,  when  we  say  that  the  cube  of  12  is  1728,  what  we  affirm  is 
this :  That  if,  having  a  sufficient  number  of  pebbles  or  of  any  other 
objects,  we  put  them  together  in  the  particular  sort  of  parcels  or 
aggregates  called  twelve ;  and  put  together  these  twelves  again  into 
similar  collections  ;  and,  finally,  make  up  twelve  of  these  largest  par- 
cels; the  aggregate  thus  formed  will  be  such  a  one  as  we  call  1728; 
namely,  that  which  (to  take  the  most  familiar  of  its  modes  of  formation) 
may  be  made  by  joining  the  parcel  called  a  thousand  pebbles,  the  parcel 
called  seven  hundred  pebbles,  the  parcel  called  twenty  pebbles,  and  the 
parcel  called  eight  pebbles.  The  converse  proposition,  that  the  cube 
root  of  1728  is  12,  asserts  that  this  large  aggregate  may  again  be  decom- 
posed into  the  twelve  twelves  of  twelves  of  pebbles  which  it  consists  of. 

The  modes  of  formation  of  any  number  are  innumerable;  but  when 
we  know  one  mode  of  formation  of  each,  all  the  rest  may  be  deter- 
mined deductively.  If  we  know  that  a  is  formed  from  h  and  c,  h  from 
d  and  c,  c  from  d  and  f,  and  so  forth,  until  we  have  included  all  the 
numbers  of  any  scale  we  choose  to  select,  (taking  care  that  for  each 
number  the  mode  of  formation  is  really  a  distinct  one,  not  bring- 
ing us  round  again  to  the  former  numbers,  but  introducing  a  new 
number,)  we  have  a  set  of  propositions  fi'om  which  we  may  reason 
to  all  the  other  modes  of  formation  of  those  numbers  from  one 
another.  Having  established  a  chain  of  inductive  truths  connecting 
together  all  the  numbers  of  the  scale,  we  can  ascertain  the  formation 
of  any  one  of  those  numbers  from  any  other  by  merely  travelling 
from  the  one  to  the  other  along  the  chain.  Suppose  that  we  knew 
only  the  following  raode.sof  foraiation  :  6  =  4-|-2,  4  =  7  —  3,  7  =  5  +  2, 


REMAINING   LAWS   OF    NATURE.  307 

6  =  9  —  4.  We  could  determine  how  6  may  be  formed  from  9.  For 
6  =  4  +  2=7  —  3  +  2=5  4-2  —  3  +  2  =  9  —  4  +  2  —  3  +  2.  It  may 
therefore  be  formed  by  taking  away  4  and  3,  and  adding  2  and  2.  If 
we  know  besides  that  2  +  2  =  4,  we  obtain  6  from  9  in  a  simpler 
mode,  by  merely  taking  away  3. 

•  It  is  sufficient,  therefore,  to  select  one  of  the  various  modes  of  forma- 
tion of  each  number,  as  a  means  of  ascertaining  all  the  rest.  And 
since  things  which  are  uniform,  and  therefoi-e  simple,  are  most  easi^ 
received  and  retained  by  the  understanding,  there  is  an  obvious  ad- 
vantage in  selecting  a  mode  of  formation  which  shall  be  alike  for  all ; 
in  fixing  the  connotation  of  names  of  number  on  one  unifonn  principle. 
The  mode  in  which  our  existing  numerical  nomenclature  is  contrived 
possesses  this  advantage,  with  the  additional  one,  that  it  happily  con- 
veys to  the  mind  two  of  the  modes  of  formation  of  every  number. 
Each  number  is  cojisidercd  as  formed  by  the  addition  of  an  unit  to  the 
number  next  below  it  in  magnitude,  and  this  mode  of  formation  is  con- 
veyed by  the  place  which  it  occupies  in  the  sei'ics.  And  each  is  also 
considered  as  formed  by  the  addition  of  a  number  of  units  less  than 
ten,  and  a  number  of  aggregates  each  equal  to  one  of  the  successive 
powers  of  ten  :  and  this  mode  of  its  formation  is  expressed  by  its 
spoken  name,  and  by  its  numerical  character.- 

What  renders  ai'ithmetic  a  deductive  science,  is  the  fortunate  appli- 
cability to  it  of  a  law  so  comprehensive  as  "  The  sums  of  equals  are 
equals  :"  or  (to  express  the  same  principle  in  less  familiar  but  more 
characteristic  language),  Whatever  is  made  up  of  parts  is  made  up  of 
the  parts  of  those  parts.  This  truth,  obvious  to  the  senses  in  all  cases 
which  can  be  fairly  referred  to  their  decision,  and  so  general  as  to  be 
coextensive  with  nature  itself,  being  true  of  all  sorts  of  phenomena  (for 
all  admit  of  being  numbered),  must  be  considered  an  inductive  truth, 
or  law  of  nature,  of  the  highest  order.  And  every  arithmetical  opera- 
tion is  an  application  of  this  law,  or  of  other  laws  capable  of  being  de- 
duced from  it.  This  is  our  warrant  for  all  calculations.  We  believe 
that  five  and  two  are  equal  to  seven,  on  the  evidence  of  this  inductive 
law,  combined  with  the  definitions  of  those  numbers.  We  arrive  at 
that  conclusion  (as  all  know  who  remember  how  they  first  learned  it) 
by  adding  a  single  iinit  at  a  time  :  5  +  1  =  6,  therefore  5+1  +  1=6 
+  1=7:  and  again  2  =  1  +  1,  therefore  5  +  2  =  5  +  1  +  1  =  7. 

§  6.  Innumerable  as  are  the  true  propositions  which  can  be  formed 
concerning  particular  mimbers,  no  adequate  conception  could  be  gained, 
from  these  alone,  of  the  extent  of  the  truths  composing  the  science  of 
number.  Such  propositions  as  we  have  spoken  of  are  the  least  gen- 
eral of  all  numerical  truths.  It  is  true  that  even  these  are  coextensive 
^vith  all  nature :  the  properties  of  the  number  four  are  true  of  all  ob- 
jects that  are  divisible  into  four  equal  parts,  and  all  objects  are  either 
actually  or  ideally  so  divisible.  But  the  propositions  which  com])ose 
the  science  of  algebra  are  true,  not  of  a  particular  number,  but  of  all 
numbers  ;  not  of  all  things  under  the  condition  of  being  divided  in 
'  a  particular  way,  but  of  all  things  under  the  condition  of  being  divided 
in  any  way — of  being  designated  by  a  number  at  all. 

Since  it  is  impossible  for  different  numbers  to  have  any  of  their 
modes  of  formation  completely  in  common,  it  looks  like  a  paradox  to 
say,  that  all  propositions  which  can  be  made  concerning  numbers  relate 


368  INDUCTION. 

to  their  modes  of  formation  from  other  numbers,  and  yet  that  there 
are  propositions  which  are  true  of  all  numbers.  But  this  very  paradox 
leads  to  the  real  principle  of  generalization  concerning  the  properties 
of  numbers.  Two  different  numbers  cannot  be  formed  in  the  same 
manner  fi'om  the  same  numbers  ;  but  they  may  be  formed  in  the  same 
manner  from  different  numbers  ;  as  nine  is  formed  from  three  by  mul- 
Uplying  it  into  itself,  and  sixteen  is  formed  from,  four  by  the  same 
process.  Thus  there  arises  a  classification  of  modes  of  formation,  or, 
in  the  language  commonly  used  by  mathematicians,  a  classification  of 
Functions.  Any  number,  considered  as  formed  from  any  other  num- 
ber, is  called  a  function  of  it;  and  there  are  as  many  kinds  of  functions 
as  there  are  modes  of  formation.  The  simple  functions  are  by  no 
means  numerous,  most  functions  being  foiined  by  the  combination  of 
several  of  the  operations  which  form  simple  functions,  or  by  successive 
repetitions  of  some  one  of  those  operations.  The  simple  functions  of 
any  number  x  are  all  reducible  to  the  following  forms :  x-{-  a,  x  —  a, 

ax,  —,  x"',  ai  —  J  log.  X  (to  the  baso  a),  and  the  same  expressions 

a  V  X  ^ 

varied  by  putting  x  for  a  and  a  for  x,  wherever  that  substitution  would 
alter  the  value :  to  which  perhaps  we  ought  tO;  add  (with  M.  Comte) 
sin  X,  and  arc  (sin  =  x).  All  other  functions  of  x  are  formed  by 
putting  some  one  or  more  of  the  simple  functions  in  the  place  of  x 
or  a,  and  subjecting  them  to  the  same  elementary  operations. 

In  order  to  carry  on  general  reasonings  on  the  subject  of  Functions, 
we  require  a  nomenclature  enabling  us  to  express  any  two  numbers 
by  names  which,  without  specifying  what -]3articular  numbers  they  are, 
shall  show  what  fimction  each  is  of  the  other ;  or,  in  other  words,  shall 
put  in  evidence  their  mode  of  formation  from  one  another.  The  sys- 
tem of  general  language  called  algebraical  notation  does  this.  The 
expressions  a  and  a'^-\-3a  denote,  the  one  any  number,  the  other  the 
number  formed  from  it  in  a  particular  manner.  The  expressions 
.a,  h,  n,  and  [a  +  Z»)",  denote  any  three  numbers,  and  a  fourth  which  is 
formed  from  them  in  a  certain  mode. 

The  following  may  be  stated  as  the  general  problem  of  the  alge- 
braical calculus :  F  being  a  certain  function  of  a  given  number,  to  find 
what  function  F  will  be  of  any  function  of  that  number.  For  example, 
a  binomial  a-{-b  is  a  function  of  its  two  parts  a  and  b,  and  the  parts 
are,  in  their  turn,  functions  of  a  +  ^:  now  (a  +  J)"  is  a  certain  function 
of  the  binomial;  what  fimction  will. this  be  of  a  and  b,  and  the  two 
parts  %     The  answer  to  this  question  is  the  binomial  theorem.     The 

formula  {a  +  b)"  =  a"  -| a"~^b  ■\ — ^-5-  a"~^b'^  -{-,  &c.,  shows  in  what 

manner  the  number  which  is  formed  by  multiplying  a-{-b  into  itself 
n  times,  might  be  formed  without  that  process,  directly  fi-om  a,  b,  and  n. 
And  of  this  nature  are  all  the  theorems  of  the  science  of  number. 
They  assert  the  identity  of  the  result  of  different  modes  of  foimation. 
They  affirm  that  some  mode  of  formation  from  a-,  and  some  mode  of 
formation  from  a  certain  function  of  x,  produce  the  same  number. 

Besides  these  general  theorems  or  formulae,  what  remains  in  the 
algebraical  calculus  is  the  resolution  of  equations.  But  the  resolution 
of  an  equation  is  also  a  theorem.  If  the  equation  be  x^  +  ax  —  b,  the 
resolution  of  this  equation,  viz.,  x=  —  ^a±  '^   i«^  +  i,  isa  general 


REMAINING    LAWS    OF    NATURK.  369 

proposition,  which  may  be  rou;arded  a-s  an  ansvv(>r  to  the  question,  If  i 
is  a  certain  function  of  x  and  a  (nanielv  x^-{-ax),  wliat  function  is 
a;  of  b  and  a?  The  resolution  of  ciiimtions  is,  therefore,  a  mere 
variety  of  the, general  ])rol)lem  as  above  stated.  The  problem  is  — 
Given  a  function,  what  function  is  it  of  some  othei-  function  ?  And,  in 
the  resolution  of  an  equation,  the  question  is,  to  find  what  function  of 
one  of  its  own  functions  the  number  itself  is. 

Such  as  above  described,  is  the  aim  and  end  of  the  calculus.  As 
for  its  processes,  every  one  knows  that  they  are  simply  deductive.  In 
demonstrating  an  algebraical  theorem,  or  in  resolving  an  equation, 
we  travel  from  the  datum  to  the  qucesitum  by  pure  ratiocination ;  in 
which  the  only  premisses  introduced,  besides  the  original  hypotheses, 
are  the  fundamental  axioms  already  mentioned — that  things  equal  to 
the  same  thing  are  equal  to  one  another,  and  that  the  sums  of  equal 
things  are  equal.  At  each  step  in  the  demonstration  or  in  the  calcu- 
hition  we  apply  one  or  other  of  those  truths,  or  truths  deduced  from 
them,  as,  that  the  -differences,  products,  &c.,  of  equal  numbers  are 
equal.  .     .      • 

It  would  be  inconsistent  with  the  scale  of  this  work,  and  not  neces- 
sary to  its  design,  to  carry  the  analysis  of  the  truths  and  processes  of 
algebra  any  further ;  which  is  moreover  the  less  needful,  as  the  task 
has  been  recently  and  thoroughly  performed  by  other  writers.  Profes- 
sor Peacock's  Algebra,  and  ]N[r.  Whewell's  Doctrine  of  Limits,  should 
be  studied  by  every  one  who  desires  to  comprehend  the  evidence  of 
mathematical  truths,  and  the  meaning  of  the  obscurer  processes  of  the 
calculus;  while,  even  after  mastering  these  treatises,  the  student  will 
have  much  to  learn  on  the  subject  from  M.  Comte,  of  whose  admirable 
work  one  of  the  most  admirable  portions  is  that  in  which  he  may 
truly  be  said  to  have  created  the  philosophy  of  the  higher  mathe- 
matics.* 

§  7.  If  the  extreme  generality  and  remoteness,  not  so  much  from 
sense  as  from  the  visual  and  tactual  imagination,  of  the  laws  of  number, 
render  it  a  somewhat  difficult  effort  of  abstraction  to  conceive  those 
laws  as  being  in  reality  physical  truths  obtained  by  observation;  the 
same  difficulty  does  not  exist  with  regard  to  the  iaws  of  extension. 
The  facts  of  which  these  laws  are  expressions,  are  of  a  kind  peculiarly 
accessible  to  the  sense,  and  suggesting  eminently  distinct  images  to  the 
fancy.  That  geometry  is  a  strictly  physical  science  would  doubtless 
have  been  recognized  in  all  ag<.^s,  had  it  not  been  for  the  illusions  pro- 
duced by  two  causes.  One  of  these  is  the  characteristic  property, 
already  noticed,  of  the  facts  of  geometry,  that  they  may  be  collected 
from  our  ideas  or  mental  pictures  of  objects  as  effectually  as  from  the 
objects  themselves.  The  other  is,  the  demonstrative  character  of 
geometrical  truths ;  which  was  at  one  time  supposed  to  constitute  a 
radical  distinction  between  them  and  physical  truths,  the  latter,  as 
resting  on  merely  probable  evidence,  being  deemed  essentially  uncer- 

*  In  the  concluding  pages  of  his  Cows  de  Philosophie  Positive,  of  which  the  final  volume 
has  but  recently  appeared,  M.  Cointe  announces  the  intention  of  hereafter  producing  a 
special  and  systematic  work  on  the  Philosophy  of  Mathematics.  All  cninpetent  judges 
who  are  acquainted  with  what  M.  Comte  has  already  accomplished  in  that  great  depart- 
ment of  the  philosophy  of  the  sciences,  will  look  with  the  highest  expectations  to  this 
promised  treatise. 

3A 


370  INDUCTION. 

tain  and  unprecise.  The  advance  of  knowledge  has,  however,  made 
it  manifest  that  physical  science,  in  its  better  understood  branches,  is 
quite  as  demonstrative  as  geometry :  the  task  of  deducing  its  details 
from  a  few  comparatively  simple  principles  being  found  to  be  anything 
but  the  impossibility  it  was  once  supposed  to  be ;  and  the  notion  of 
the  superior  certainty  of  geometry  being  an  illusion  arising  from  the 
ancient  prejudice  which  in  that  science  mistakes  the  ideal  data  from 
which  we  reason,  for  a  peculiar  class  of  realities  while  the  correspond- 
in,f  ideal  data  of  any  deductive  physical  science  are  recognized  as 
what  they  really  are,  mere  hypotheses. 

Every  theorem  in  geometry  is  a  law  of  external  nature,  and  migtit 
have  been  ascertained  by  generalizing  from  observation  and  experi- 
ment, which  in  this  case  resolve  themselves  into'  comparison  and 
measurement.  But  it  was  found  practicable,  and  being  practicable, 
was  desirable,  to  deduce  these  truths  by  ratiocination  from  a  small 
number  of  general  laws  of  nature,  the  certainty  and  universality  of 
which  was  obvious  to  the  most  careless  observer,  and  which  compose 
the  first  principles  and  ultimate  premisses  of  the  science.  Among 
these  general  laws  must  be  included  the  same  two  which  we  have 
noticed  as  ultimate  principles  of  the  Science  of  Number  also,  and 
which  are  applicable  to  every  description  of  quantity:  viz.,  the  sums 
of  equals  are  equal,  and  things  which  are  equal  to  the  same  thing  are 
equal  to  one  another;  the  latter  of  which  may  be  expressed  in  a  manner 
more  suggestive  of  the  inexhaustible  multitude  of  its  consequences  by 
the  following  terms:  Whatever  is  equal  to  any  one  of  a  number  of 
equal  magnitudes,  is  equal  to  any  other  of  them.  To  these  two  must 
be  added,  in  geometry,  a  third  law  of  equality,  namely,  that  lines, 
surfaces,  or  solid  spaces,  which  can  be  so  applied  to  one  another  as  to 
coincide,  are  equal.  Some  writers  have  asserted  that  this  law  of  nature 
is  a  mere  verbal  definition :  that  the  expression  "equal  magnitudes" 
means  nothing  but  magnitudes  which  can  be  so  applied  to  one  another 
as  to  coincide.  But  in  this  opinion  I  cannot  agree.  The  equality  of 
two  geometrical  magnitudes  cannot  differ  fundamentally  in  its  nature 
from  the  equality  of  two  weights,  two  degrees  of  heat,  or  two  portions 
of  duration,  to  none  of  which  would  this  pretended  definition  of  equal- 
ity be  suitable.  None  of  these  things  can  be  so  apphed  to  one  another 
as  to  coincide,  yet  we  pertectly  understand  what  we  mean  when  we 
call  them  equal.  Things  are  equal  in  magnitude,  as  things  are  equal 
in  weight,  when  they  are  felt  to  be  exactly  similar  in  respect  of  the 
attribute  in  which  we  compare  them  :  and  the  application  of  the  ob- 
jects to  each  other  in  the  one  case,  like  t\ie  balancing  them  with  a  pair 
of  scales  in  the  other,  is  but  a  mode  of  bringing  them  into  a  position 
in  which  our  senses  can  recognize  deficiencies  of  exact  resemblance 
that  would  otherwise  escape  our  notice. 

Along  with  these  three  general  principles  or  axioms,  the  remainder 
of  the  premisses  of  geometry  consist  of  the  so-called  definitions,  that  is 
to  say,  propositions  asserting  the  real  existence  of  tho  various  objects 
therein  designated,  together  with  some  one  property  of  each.  In  some 
cases  more  than  one  property  is  commonly  assumed,  but  in  no  case  is 
more  than  one  necessary.  It  is  assumed  that  there  are  such  things  in 
natm'e  as  sti-aight  lines,  and  that  any  two  of  them  setting  out  from  the 
same  point,  diverge  more  and  more  without  limit.  This  assumption, 
(which  includes  and  goes  beyond  Euclid's  axiom  that  two  straight 


REMAINING    LAWS    OF    NATURE.  371 

linos  cannot  inclose  a  space,)  is  as  indispensable  in  geometry,  and  as 
evident,  resting  upon  as  simple,  familiar,  and  universal  observation,  as 
any  of  the  other  axioms.  It  is  also  assumed  that  straight  lines  diverge 
from  one  another  in  ditferent  degrees ;  in  other  words,  that  there  are 
such  things  as  angles,  and  that  they  are  capable  of  being  equal  or  un- 
equal. It  is  assumed  that  there  is  such  a  thing  as  a  circle,  and  that  all 
its  radii  are  equal ;  such  things  as  ellipses,  and  that  the  sums  of  the 
focal  distances  are  equal  for  t;very  point  in  an  ellipse  ;  such  things  as 
parallel  lines,  and  that  those  lines  are  everyw^here  equally  distant.* 

§  S.  It  is  a  matter  of  something  more  than  curiosity  to  consider  to 
w^hat  peculiarity  of  the  physical  truths  w^hich  are  the  subject  of  geom- 
etry, it  is  owing  that  they  can  all  bo  deduced  from  so  small  a  number  of 
original  premisses :  why  it  is  that  we  can  set  out  from  only  one  charac- 
teristic property  of  each  kind  of  phenomenon,  and  with  that  and  two 
or  tln'ee  general  truths  relating  to  equality,  can  travel  from  mark  to 
mark  until  we  obtain  a  vast  body  of  derivative  truths,  to  all  appear- 
ance extremely  unlike  those  elementary  ones. 

The  explanation  of  this  remarkable  fact  seems  to  lie  in  the  following 
circumstances.  Ih  the  first  place,  all  questions  of  position  and  figure 
may  be  resolved  into  questions  of  magnitude.  The  position  and  figure 
of  any  object  is  determined,  by  determining  the  position  of  a  sufficient 
number  of  points  in  it ;  and  the  position  of  any  point  may  be  deter- 
mined by  the  magnitude  of  three  rectangular  coordinates,  that  is,  of 
the  perpendiculars  drawn  from  the  point  to  three  axes  at  right  angles 
to  one  another,  arbitrarily  selected.  By  this  transformation  of  all  ques- 
tions of  quality  into  questions  only  of  quantity,  geometry  is  reduced  to 
the  single  problem  of  the  measurement  of  magnitudes,  that  is,  the 
ascertainment  of  the  equalities  which  exist  between  them.  Now  when 
we  consider  that  by  one  of  the  general  axioms,  any  equality,  when 
ascertained,  is  proof  of  as  many  other  equalities  as  there  are  other 
things  equal  to  either  of  the  two  equals;  and  that  by  another  of  those 
axioms,  any  ascertained  equality  is  proof  of  the  equality  of  as  many 
pairs  of  magnitudes  as  can  be  fi>rmed  by  the  numerous  operations  which 
resolve  themselves  into  the  addition  of  the  equals  to  themselves  or  to 
other  equals:  we  cease  to  wonder  that  in  proportion  as  a  science  is 
conversant  about  equality,  it  should  aflford  a  more  copious  supply  of 
marks  ;  and  that  the  sciences  of  number  and  extension,  which  are  con- 
versant with  little  else  than  equality,  should  be  the  most  deductive  of 
all  the  sciences. 

*  Geometers  have  usually  preferred  to  (lefinc  parallel  lines  by  the  property  of  being  in 
the  same  plane  and  never  meeting.  This,  however,  has  rendered  it  necess'iry  for  them  to 
assume,  as  an  a'dditional  axiom,  some  other  property  of  parallel  lines ;  and  the  unsatisfac- 
tory manner  in  which  properties  for  that  pur()Ose  have  been  selectetl  by  Euclid  and  others 
has  always  been  deemed  the  opprol)rium  of  elementary  geometry.  Even  as  a  verbal  delini- 
tion.  equi-distance  is  a  fitter  property  to  characterize  parallels  by,  since  it  is  the  attribute 
really  involved  in  the  signification  of  the  name.  If  to  be  in  the  same  plane  and  never  to 
meet  were  all  that  is  meant  by  being  parallel,  we  should  feel  no  incongruity  m  speaking  of 
a  curve  as  parallel  to  its  asymptote.  The  meaning  of  parallel  lines  is,  lines  which  pursue 
exactly  the  same  direction,  and  which,  therefore,  neither  approach  nearer  nor  go  further 
from  one  another ;  a  conception  suggested  at  once  by  the  contemplation  of  nature.  That 
the  lines  will  never  meet  is  of  course  implied  in  the  more  comprenensive  proposition  that 
they  are  everywhere  equally  distant.  And  that  any  straight  lines  which  are  in  the  same 
plane  and  not  equidistant  will  certainly  meet,  may  be  demonstrated  in  the  most  rigid 
manner  from  the  fundamental  property  of  straight  lines  assumed  in  the  text,  viz.,  that  if 
they  set  out  from  the  same  point  they  diverge  more  and  more  without  lijnit. 


372  INDUCTION. 

There  are,  moreover,  two  or  three  of  the  principal  laws  of  space  or 
extension  which  are  unusually  fitted  for  rendering  one  position  or 
magnitude  a  mark  of  another,  and  thereby  contributing  to  render  the 
science  largely  deductive.  First;  the  magnitudes  of  inclosed  spaces, 
whether  superficial  or  solid,  are  completely  determined  by  the  magni- 
tudes of  the  lines  and  angles  which  bound  them.  Secondly,  the  length 
of  any  line,  whether  straight  or  curve,  is  measured  (certain  other  things 
beino-  given,)  by  the  angle  which  it  subtends,  and  vice  versd.  Lastly, 
the  ano^le  which  any  two  straight  lines  make  with  each  other  at  an  inac- 
cessible point,  is  measured  by  the  angles  they  severally  make  with  any 
third  line  we  choose  to  select.  By  means  of  these  general  laws,  the 
measurement  of  all  lines,  angles,  and  spaces  whatsoever  might  be 
accomplished  (to  borrow  an  observation  from  M.  Comte),  by  measuring 
a  single  straight  line  and  a  sufficient  number  of  angles  ;  which  is,  indeed, 
the  plan  actually  pursued  in  the  trigonometrical  survey  of  a  country; 
and  fortunate  It  is  that  this  is  practicable,  the  exact  measurement  of 
straight  lines  being  difficult,  but  that  of  angles  very  easy.  Three  such 
generalizations  as  the  foregoing  affiard  such  facilities  for  the  indirect 
measurement  of  magnitudes,  (by  supplying  us  with  known  lines  or 
angles  which  are  marks  of  the  magnitude  of  unknown  ones,  and  thereby 
of  "the  spaces  which  they  inclose)  that  it  is  easily  conceivable  how  from 
a  few  data  we  can  go  on  to  ascertain  the  magnitude  of  an  indefinite 
multitude  of  lines,  angles,  and  spaces,  which  we  could  not  easily,  or 
could  not  at  all,  measure  by  any  more  direct  process. 

§  9.  Such  are  the  few  remarks  which  it  seemed  necessary  to  make 
in  this  place,  respecting  the  laws  of  nature  which  are  the  peculiar  sub- 
ject of  the  sciences  of  number  and  extension.  The  immense  part  which 
those  laws  take  in  giving  a  deductive  character  to  the  other  depart- 
ments of  physical  science,  is  well  known ;  and  is  not  surprising,  when 
we  consider  that  all  causes  operate  according  to  mathematical  laws. 
The  effect  is  always  dependent  upon,  or,  in  mathematical  language,  is 
a  function  of,  the  quantity  of  the  agent;  and  generally  of  its  position 
also.  We  cannot,  therefore,  reason  respecting  causation,  without  intro- 
ducing considerations  of  quantity  and  extension  at  every  step ;  and  if 
the  nature  of  the  phenomena  admits  of  our  obtaining  numerical  data  of 
sufficient  accuracy,  the  laws  of  quantity  become  the  grand  instruments 
for  calculating  forward  to  an  effect,  or  backward  to  a  cause.  That  in 
all  other  sciences,,  as  well  as  in  geometry,  questions  of  quality  are 
scarcely  ever  independent  of  questions  of  quantity,  may  be  seen  from 
the  most  familiar  phenomena.  Even  when  several  colors  are  mixed  on 
a  painter's  pallet,  the  comparative  quantity  of  each  entirely  deter- 
mines the  color  of  the  mixture. 

With  this  mere  suggestion  of  the  general  causes  which  render  math- 
ematical principles  and  processes  so  predominant  in  those  deductive 
sciences  which  afford  precise  numerical  data,  I  must,  on  the  present 
occasion,  content  myself;  refen'ing  the  reader  who  desires  a  thorough 
acquaintance  with  this  great  subject,  to  the  fii"st  two  volumes  of  M. 
Comte's  systematic  work. 

In  the  same  work,  and  more  particularly  in  the  third  volume,  are 
also  ftilly  discussed  the  necessary  limits  of  the  applicability  of  mathe- 
matical principles  to  the  improvement  of  other  sciences.  Such  prin- 
ciples are  manifestly  inapplicable,  where  tlie  causes  on  which  any  class 


REMAINING  LAWS  OP  NATURE.  373 

of  phenomena  depend  are  so  imperlectly  acxcssible  to  our  observation, 
that  we  cannot  ascertain,  by  a  proper  induction,  their  numerical  laws; 
or  where  the  causes  are  so  numerous,  and  intermixed  in  so  complex  a 
manner  with  one  another,  that  even  sujiposinir  their  laws  known,  the 
computation  of  the  ag^gi-egate  cftect  transcends  the  powers  of  the  cal- 
culus as  it  is,  or  as  it  is  ever  likely  to  be ;  or  lastly,  where  the  causes 
themselves  aro  in  a  state  of  perpetual  fluctuation,  as  in  physiology, 
and  still  more,  if  possible,  in  the  social  science.  As  M.  Comte*  well 
obsei'ves,  the  mathematical  solutions  of  physical  questions  become 
progressively  more  difficult  and  more  imperfect,  in  proportion  as  the 
questions  divest  themselves  of  their  abstract  and  hypothetical  character, 
and  approach  nearer  to  the  degree  of  complication  actually  existing  in 
nature;  insomuch  that  beyond  the  limits  of  astronomical  phenomena, 
and  of  those  most  nearly  analogous  to  them,  mathematical  accuracy  is 
generally  obtained  "  at  the  expense  of  the  reality  of  the  inquiry  :" 
while,  even  in  astronomical  questions,  "  notwithstanding  the  admirstble 
simplicity  of  their  mathematical  elements,  our  fc^eble  intelligence 
becomes  incapable  of  following  out  effectually  the  logical  combinations 
of  the  laws  on  which  the  phenomena  are  dependent,  as  soon  as  we 
attempt  to  take  into  simultaneous  consideration  more  than  two  or  three 
essential  influences."  Of  this,  the  problem  of  the  Three  Bodies  has 
already  been  cited  by  us,  more  than  once,  as  a  rcmarkalile  instance ; 
the  complete  solution  -of  so  comparatively  simple  a  question  having 
vainly  tried  the  skill  of  the  most  profound  mathematicians.  We  may 
conceive,  then,  how  chimerical  would  be  the  hope  that  mathematical 
principles  could  ever  be  advantageously  applied  to  phenomena  depen- 
dent upon  the  mutual  action  of  the  innumerable  minute  particles  of 
bodies,  as  those  of  chemistry,  and  still  more,  of  physiology  ;  and  for 
similar  reasons  those  principles  must  be  for  ever  inapplicable  to  the 
still  more  complex  inquiries,  the  subjects  of  which  are  phenomena  of 
society  and  government. 

The  value  of  mathematical  instruction  as  a  preparation  for  those 
more  difficult  investigations,  consists  in  the  applicability  not  of  its 
doctrines,  but  of  its  method.  Mathematics  will  ever  remain  the  most 
perfect  typo  of  the  Deductive  Method  in  general ;  and  the  applications 
of  mathematics  to  the  simpler  branches  of  physics,  furnish  the  only 
school  in  which  j)hilosophers  can  eff"ectually  learn  the  most  difficult  and 
important  portion  of  their  art,  the  employment  of  the  laws  of  simpler 
phenomena  for  explaining  and  predicting  those  of  the  more  complex. 
These  grounds  are  quite  sufficient  for  deeming  mathematical  training 
an  indispensable  basis  of  real  scientific  education,  and  regarding,  with 
Plato,  one  who  is  dyew/xt'rpT/Tor,  as  wanting  in  one  of  the  most  essential 
qualifications  for  the  successful  cultivation  of  the  higher  branches  of 
philosophy. 

*  Court  de  Philosophic  Positive,  iii.,  414-416. 


3*3^4  INDUCTION. 

CHAPTER  XXV. 

OF  THE  GROUNDS  OF   DISBELIEF. 

§  1.  The  method  of  aiTiving  at  general  truths,  or  general  propo- 
sitions fit  to  be  believed,  and  the  nature  of  the  evidence  on  which  they 
are  grounded,  have  been  discussed,  as  far  as  space  and  the  wiiter's 
faculties  permitted,  in  the  twenty-four  preceding  chapters.  But  the 
result  of  the  examination  of  evidence  is  not  always  belief,  nor  even 
suspension,  of  judgment;  it  is  sometimes  disbelief.  The  philosophy, 
therefore,  of  induction  and  experimental  inquiry  is  incomplete,  unless 
the  gi'ounds  not  only  of  belief,  but  of  disbelief,  are  treated  of;  and  to 
this  topic  we  shall  devote  one,  and  the  final  chapter. 

By  disbelief  is  not  here  to  be  understood  the  mere  absence  of  belief. 
I  The  ground  for  abstainmg  from  belief  is  simply  the  absence  or  in- 
sufficiency of  proof;  and  in  considering  what  is  sufficient  evidence  to 
support  any  given  conclusion,  we  have  already,  by  implication,  con- 
sidered what  evidence  is  not  sufficient  for  the  same  purpose.  By  dis- 
belief is  here  meant,  not  the  state  of  mind  in  which  we  are  ignorant, 
and  form  no  opinion  upon  a  subject,  but  that  in  which  we  are  fully 
persuaded  that  some  opinion  is  not  true ;  insomuch  that  if  evidence, 
even  of  great  strength,  (whether  grounded  on  the  testimony  of  others 
or  on  our  own  apparent  perceptions,)  were  produced  in  favor  of  the 
opinion,  we  should  believe  that  the  witnesses  spoke  falsely,  or  that 
they,  or  ourselves  if  we  were  the  direct  percipients,  were  mistaken. 

That  there  are  such  cases,  no  one  is  likely  to  dispute.  Assertions 
for  which  there  is  abundant  positive  evidence  are  often  disbelieved,  on 
account  of  what  is  called  their  improbability,  or  impossibility.  And 
the  question  for  consideration  is,  what,  in  the  present  case,  these  words 
mean,  and  how  far  and  under  what  circumstances  the  properties  which 
they  express  are  sufficient  grounds  for  disbelief 

§  2.  It  is  to  be  remarked  in  the  first  place,  that  the  positive  evidence 
produced  in  support  of  an  assertion  which' is  nevertheless  rejected  on 
the  score  of  impossibility  or  improbability,  is  never  such  as  amounts  to 
full  proof.  It  is  always  grounded  upon  some  approximate  generaliza- 
tion. The  fact  may  have  been  asserted  by  a  hundred  witnesses ;  but 
there  are  many  exceptions  to  the  universality  of  the  generalization 
that  what  a  hundred  witnesses  affirm  is  true.  We  may  seem  to  our- 
selves to  have  actually  seen  the  fact :  but,  that  we  really  see  what  we 
think  we  see,  is  by  no  means  an  universal  truth ;  our  organs  may  have 
been  in  a  morbid  state,  or  we  may  have  inferred  something,  and 
imagined  that  we  perceived  it.  The  evidence,  then,  in  the  affinnative, 
being  never  more  than  an  approximate  generalization,  all  will  depend 
upon  what  the  evidence  in  the  negative  is.  If  that  also  rests  upon  an 
approximate  generalization,  it  is  a  case  for  comparison  of  probabilities. 
If  the  approximate  generalizations  leading  to  the  affirmative  are,  when 
added  together,  less  strong,  or  in  other  woids,  further  removed  from 
universality,  than  the  approximate  generalizations  which  support  the 
negative  side  of  the  question,  the  proposition  is  said  to  be  improbable, 
and  is  to  be  disbelieved,  provisionally.     If,  however,  an  alleged  fact 


GROUNDS    OF    DISBELIEF.  375 

be  in  contratliction,  not  to  any  nnmber  of  approximate  generalizations, 
but  to  a  completed  generalization  grounded  upon  a  rigorous  induction, 
it  is  said  to  be  impossible,  and  is  to  be  disbelieved  totally. 

This  last  princi})le,  simple  and  evident  as  it  appears,  is  the  doctrine 
which,  on  the  occasion  of  an  attempt  to  apply  it  to  the  question  of  the 
credibility  of  miracles,  excited  so  violent  a  controversy.  Hume's  cele- 
brated principle,  that  nothing  is  credible  which  is  contradictory  to  ex- 
perience, or  at  variance  with  laws  of  nature,  is  merely  this  very  plain 
and  harmless  proposition,  that  whatever  is  contradictory  to  a  complete 
induction  is  incredible.  That  such  a  maxim  as  this  should  either  be 
accounted  a  dangerous  heresy,  or  mistaken  for  a  groat  and  recondite 
truth,  speaks  ill  for  the  state  of  philosophical  speculation  on  such  sub- 
jects. 

But  does  not  (it  may  be  asked)  the  very  statement  of  the  proposition 
imply  a  contradiction  ]  An  alleged  fact,  according  to  this  theory,  is 
not  to  be  believed  if  it  contradict  a  complete  induction.  But  it  is 
essential  to  the  completeness  of  an  induction  that  it  shall  not  contra- 
dict any  known  fact.  Is  it  not  then  a  yclitio  priucipii  to  say,  that  the 
fact  ought  to  be  disbelieved  because  the  induction  opposed  to  it  is  com- 
plete ?  How  can  we  have  a  right  to  declare  the  induction  complete, 
while  facts,  supported  by  credible  evidence,  present  themselves  in  op- 
position to  it  ? 

I  answer,  we  have  that  right  whenever  the  scientific  canons  of  in- 
duction give  it  to  us  ;  that  is,  whenever  the  induction  can  be  complete. 
We  have  it,  for  example,  in  a  case  of  ciiusation,  in  which  there  has 
been  an  experimentum  crucis.  If  an  antecedent  A,  superadded  to  a 
set  of  antecedents  in  all  other  respects  unaltered,  is  followed  by  an 
effect  B  which  did  not  exist  before,  A  is,  in  that  instance  at  least, 
the  cause  of  B,  or  a  necessary  part  of  that  cause ;  and  if  A  be  tried 
again  with  many  totally  different  sets  of  antecedents  and  B  still  fol- 
lows, then  it  is  the  whole  cause.  If  these  observations  or  experiments 
have  been  repeated  so  often,  and  by  so  many  persons,  as  to  exclude 
all  supposition  of  error  in  the  obsei-ver,  a  law  of  nature  is  established; 
and  so  long  as  this  law  is  received  as  such,  the  assertion  that  on  any 
particular  occasion  A  took  place,  and  yet  B  did  not  follow,  without 
anji  counteracting  cause,  must  be  disbelieved.  Such  an  assertion  is  not 
to  be  credited  upon  any  less  evidence  than  what  would  suffice  to 
overturn  the  law.  The  general  truths,  that  whatever  has  a  beginning 
has  a  cause,  and  that  when  none  but  the  same  causes  exist,  the  same 
effects  follow,  rest  upon  the  .strongest  hiductive  evidence  possible  ;  the 
proposition  that  things  affirmed  by  even  a  crowd  of  respectable  wit- 
nesses are  true,  is  but  an  approximate  generalization  ;  and — even  if 
we  fancy  we  actually  saw  or  felt  the  fact  which  is  in  contradiction  to 
the  law — what  a  human  being  can  see  is  no  more  than  a  set  of  appear- 
ances ;  from  which  the  real  nature  of  the  phenomenon  is  merely  an 
inference,  and  in  this  inference  approximate  generalizations  usually 
have  a  large  share.  If,  therefore,  we  make  our  election  to  hold  by. 
the  law,  no  quantity  of  evidence  whatever  ought  to  persuade  us  that 
there  has  occuiTed  anything  in  contradiction  to  it.  If,  indeed,  the  evi- 
dence produced  is  such  that  it  is  more  likely  that  the  set  of  observa- 
tions and  experimetits  upon  which  the  law  rests  should  have  been  in- 
accurately performed  or  incorrectly  interpreted,  than  that  the  evidence 
in  question  should  be  false,  we  may  believe  the  evidence  ;  but  then  we 


376  INDUCTION. 

must  abandon  the  law.  And  since  the  law  was  received  on  what 
seemed  a  complete  induction,  it  can  only  be  rejected  on  evidence 
equivalent ;  namely,  as  being  inconsistent  not  with  any  numbei-  of  ap- 
proximate generalizations,  but  with  some  other  and  better  established 
law  of  nature.  This  extreme  case,  of  a  conflict  between  two  supposed 
laws  of  nature,  has  probably  never  actually  occurred  where,  in  the 
process  of  investigating  both  the  laws,  the  true  canons  of  scientific  in- 
duction had  been  kept  in  view ;  but  if  it  did  occur,  it  must  terminate 
in  the  total  rejection  of  one  of  the  supposed  laws.  It  would  prove 
that  there  must  be  a  flaw  in  the  logical  process  by  which  either  one  or 
the  other  was  established ;  and  if  there  be  so,  that  supposed  general 
truth  is  no  truth  at  all.  We  cannot  admit  a  proposition  as  a  law  of 
nature,  and  yet  believe  a  fact  in  real  contradiction  to  it.  We  must  dis- 
believe the  alleged  fact,  or  believe  that  we  were  mistaken  in  admitting 
the  supposed  law. 

But  in  order  that  any  alleged  fact  should  be  contradictory  to  a  law  of 
causation,  the  allegation  must  be,  not  simply  that  the  cause  existed 
without  being  followed  by  the  effect,  for  that  would  be  no  imcommon 
occurrence  ;  but  that  this  happened  in  the  absence  of  any  adequate 
counteracting  cause.  Now  in  the  case  of  an  alleged  miracle,  the  asser- 
tion is  the  exact  opposite  of  this.  It  is,  that  the  effect  was  defeated, 
not  in  the  absence,  but  in  consequence,  of  a  counteracting  cause, 
namely,  a  direct  interposition  of  an  act  of  the  will  of  some  being  who 
has  power  over  nature  ;  and  in  particular  of  a  being,  whoso  will  having 
originally  endowed  all  the  causes  with  the  powers  by  which  they  pro- 
duce their  effects,  may  well  be  supposed  able  to  counteract  them.  A 
miracle  (as  was  justly  remarked  by  Brown*)  is  no  contradiction  to  the 
law  of  cause  and  effect ;  it  is  a  new  effi?ct,  supposed  to  be  produced  by 
the  introduction  of  a  new  cause.  Of  the  adequacy  of  that  cause,  if  it 
exist,  there  can  be  no  doubt ;  and  the  ouly  antecedent  improbability 
which  can  be  ascribed  to  the  miracle,  is  the  improbability  that  any  such 
cause  had  existence  in  the  case. 

All,  therefore,  which  Hume  has  made  out,  and  this  he  must  be  con- 
sidered to  have  made  out,  is,  that  no  evidence  can  be  sufficient  to  prove 
a  miracle  to  any  one  who  did  not  previously  believe  the  existence  of  a 
being  or  beings  with  supernatural  power  ;  or  who  believed  himself  to 
have  full  jjroof  that  the  character  of  the  Being  whom  he  recognizes,  is 
inconsistent  with  his  having  seen  fit  to  interfere  on  the  occasion  in 
question.  The  truth  of  this  (however  fatal  to  a  school  of  theology 
which  has  recently  been  revived  in  this  country,  and  which  has  the 
weakness  to  rest  all  the  evidences  of  religion  upon  tradition  and  tes- 
timony) may  be,  and  is,  admitted  by  all  defenders  of  revelation  who 
have  made  much  figure  as  such  during  the  present  century.  It  is  now 
acknowledged  by  nearly  all  the  ablest  writers  on  the  subject,  that 
natural  religion  is  the  necessary  basis  of  revealed;  that  the  proofs  of 
Christianity  presuppose  the  being  and  moral  attributes  of  God;  and 
that  it  is  the  conformity  of  a  religion  to  those  attributes  which  de- 
termines whether  credence  ought  to  be  given  to  its  external  evi- 
dences; that  (as  the  proposition  is  sometimes  expressed)  the  doctrine 
must  prove  the  miracles,  not  the  miracles  the  doctrine.  It  is  hardly 
necessary  to  point  out  the  complete  accordance  of  these  views  with 

*  See  the  two  very  remarkable  notes  (A)  and  (F),  appended  to  his  Inquiry  into  the  Rda- 
tion  of  Cause  and  Effect. 


GROUNDS    OF   DISBELIEF.  377 

the  opinions  which  (not  to  mention  otlicr  testimonies)  the  New  Testa- 
ment itself  shows  to  have  heen  generally  prevalent  in  the  apostolic 
age  ;  when  it  was  believed  intleeil  tliat  miracles  were  necessary  as  cre- 
dentials, and  tliat  whoever  was  sent  by  God  must  have  the  power  of 
working  them ;  but  no  one  dreamed  that  such  power  sufficed  by  itself 
as  proof  of  a  divine  mission,  and  St.  Paul  expressly  warned  the  churches, 
if  any  one  came  to  ihem  working  miracles,  to  observe  what  he  taught, 
and  unless  he  preached  "  Christ,  and  him  crucified,"  not  to  listen  to 
the  teaching.  There  is  no  reason,  therefore,  that  timid  Christians 
should  shrink  from  accepting  the  logical  canon  of  the  Grounds  of  Dis- 
belief And  it  is  not  hazarding  much  to  predict  that  a  schoitl  which 
peremptorily  rejects  all  evidences  of  religion,  except  such  as,  when  re-* 
lied  upon  exclusively,  the  canon  in  question  irreversibly  condemns  ; 
which  denies  to  mankind  the  right  to  judge  of  religious  doctrine,  and 
bids  them  depend  on  miracles  as  their  sole  guide ;  must,  in  the  present 
state  of  the  human  mind,  inevitably  fail  in  its  attempt  to  put  itself  at 
the  head  of  the  religious  feelings  and  convictions  of  this  country  :  by 
whatever  learning,  argumentative  skill,  and  even,  in  many  respects, 
comprehensive  views  of  human  affairs,  its  peculiar  doctrines  may  be 
recommended  to  the  acceptance  of  thinkers. 

§  3.  It  appears  from  what  has  been  said,  that  the  assertion  that  a  cause 
has  been  defeated  of  an  eflect  which  is  connected  with  it  by  a  completely 
ascertained  law  of  causation,  is  to  be  disbelieved  or  not,  according  to  the 
probability  or  improbability  that  there  existed  in  the  particular  instance 
an  adeipiate  counteracting  cause.  To  form  an  estimate  of  this,  is  not 
more  difficult  than  of  any  other  probability.  With  regard  to  all  known 
causes  capable  of  counteracting  the  given  causes,  we  have  generally 
some  previous  knowledge  of  the  frequency  or  rarity  of  their  occur- 
rence, from  whi(;h  we  may  draw  an  inference  as  to  the  antecedent 
improbability  of  their  having  been  present  in  any  particular  case. 
And  neither  in  respect  to  known  nor  unknown  causes  are  we  re<juired 
to  pronounce  upon  the  probability  of  their  existing  in  nature,  but  only 
of  their  having  existed  at  the  precise  time  and  place  at  which  the 
transaction  is  alleged  to  have  happened.  We  are  seldom,  therefore^, 
without  the  means  (when  the  circumstances  of  the  case  are  at  all 
known  to  us)  of  judging  how  far  it  is  likely  that  such  a  cause  should 
have  existed  at  tliat  time  and  place  without  manifesting  its  presence  by 
some  other  marks,  and  (in  the  case  of  an  unknown  cause)  without 
having  hitherto  manifested  its  existence  in  any  other  instance.  Ac-« 
cording  as  this  circumstance  or  the  falsity  of  the  testimony  appears 
more  improbable,  that  is,  conflicts  with  an  approximate  generalization 
of  a  higher  ordc'r,  we  behove  the  testimony,  or  disbelieve  it;  with  a 
stronger  or  a  wt^aker  degree  of  conviction,  according  to  the  prepon- 
derance :   at  least  until  we  have  sifted  the  matter  further. 

So  much,  th(Mi,  for  the  case  in  which  the  alleged  fact  conflicts,  or 
appears  to  conflict,  with  a  real  law  of  causation.  But  a  more  common 
case,  perhaps,  is  that  of  its  conflicting  with  uniformities  of  mere  co- 
existence, not  proved  to  be  dependent  on  causation  :  in  other  words, 
with  the  properties  of  Kinds.  It  is  with  these  uniformities  princi- 
pally, that  the  marvelous  stories  related  by  travolhjrs  are  apt  to  be  at 
variance  :  as  of  men  with  tails,  or  with  wings,  and  (until  confirmed  by 
experience)  of  flying  fish  ;  or  of  ice,  in  the  celebrated  anecdote  of  the 
3B 


378  INDUCTION. 

Dutch  travellers  and  the  King  of  Siam.  Facts  of  this  description, 
facts  previously  unheard  of,  but  which  could  not  from  any  known  law 
of  causation  be  pronounced  impossible,  are  what  Hume  characterizes 
as  not  contrary  to  experience,  but  merely  uncomfurmable  to  it ;  and 
Bentham,  in  his  treatise  on  Evidence,  denominates  them  facts  discon- 
formable  in  specie,  as  distinguished  from  such  as  are  disconformable 
in  toto  or  in  degree. 

In  a  case  of  this  description,  the  fact  asserted  is  the  existence  of  a 
new  Kind  ;  which  in  itself  is  not  in  the  slightest  degree  incredible, 
and  only  to  be  rejected  if  the  improbability  that  any  variety  of  object 
existing  at  the  particular  place  and  time  should  not  have  been  discov- 
ered sooner,  be  greater  than  that  of  error  or  mendacity  in  the  witnesses. 
Accordingly,  sucb  assertions,  when  made  by  credible  persons,  and  of 
unexplored  places,  are  not  disbelieved,  but  at  most  regarded  as  requiring 
confirmation  from  subsequent  observers  ;  unless  the  alleged  properties 
of  the  supposed  new  Kind  are  at  variance  with  known  properties  of 
some  larger  Kind  which  includes  it ;  or,  in  other  words,  unless,  in  the 
new  Kind  which  is  asserted  to  exist,  some  properties  are  said  to  have 
been  found  disjoined  from  others  which  have  always  been  known  to 
accompany  them  ;  as  in  the  case  of  Pliny's  men,  or  any  other  kind  oi 
animal  of  a  structure  diflierent  from  that  which  has  always  been  found 
to  coexist  with  animal  life.  On  the  mode  of  dealing  with  any  such 
case,  little  needs  be  added  to  what  has  been  said  on  the  same  topic  in 
the  twenty-second  chapter.*  When  the  uniformities  of  coexistence 
which  the  alleged  fact  would  violate,  are  such  as  to  raise  a  strong 
presumption  Of  their  being  the  result  of  causation,  the  fact  which 
conflicts  with  them  is  to  be  disbelieved,  at  least  provisionally,  and 
subject  t^  further  investigation.  When  the  presumption  amounts  to  a 
virtual  certainty,  as  in  the  case  of  the  general  structure  of  organized 
beings,  the  only  question  requiring  consideration  is  whether,  in  phenom- 
ena so  little  known,  there  may  not  be  liabilities  to  counteraction  from 
causes  hitherto  unknown  ;  or  whether  the  phenomena  may  not  be 
capable  of  originating  in  some  other  way,  which  would  produce  a 
different  set  of  derivative  uniformities.  Where  (as  in  the  case  of  the 
flying-fish,  or  the  ornithorhynchus)  the  generalization  to  which  the 
alleged  fact  would  be  an  exception  is  very  special  and  of  limited  range, 
neither  of  the  above  suppositions  can  be  deemed  very  improbable  ;  and 
it  is  generally,  in  the  case  of  such  alleged  anomalies,  wise  to  suspend 
our  judgment,  pending  the  subsequent  inquiries  which  will  not  fail  to 
confirm  the  assertion  if  it  be  true.  But  when  the  generalization  is  very 
comprehensive,  embracing  a  vast  number  and  variety  of  observations, 
and  covering  a  considerable  province  of  the  kingdom  of  nature  ;  then, 
for  reasons  which  have  been  fully  explained,  such  an  empirical  law 
comes  near  to  the  certainty  of  an  ascertained  law  of  causation  :  and 
any  alleged  exception  to  it  cannot  be  admitted,  unless  upon  the  evi- 
dence of  some  law  of  causation  proved  by  a  still  more  complete 
induction. 

Such  uniformities  in  the  course  of  nature  as  do  not  bear  marks  of 
being  the  results  of  causation,  are,  as  we  have  already  seen,  admissible 
as  universal  truths  with  a  degree  of  credence  proportioned  to  their 
generality.  Those  which  are  true  of  all  things  whatever,  or  at  least 
which  are  totally  independent  of  the  varieties  of  Kinds,  namely,  the 
*  Supra,  pp.  349-351. 


GROUNDS    OF    DISBELIEF.  379 

laws  of  number  and  oxtcnsidji,  to  which  we  may  add  the  law  of  causa- 
tion itself,  are  probably  the  only  ones,  an  exception  to  which  is  abso- 
lutely and  for  ever  incredible.  Accordingly,  it  is  to  assertions  supposed 
to  be  contradictory  to  these  laws,  or  to  some  others  coming  near  to 
them  in  generality,  that  tlie  word  impossibility  (at  least  absolute  impos- 
sibility) seems  to  l>e  generally  confined.  Violations  of  other  laws,  of 
special  laws  of  causation  for  instance,  are  said,  by  persons  studious  of 
accuracy  in  expression,  to  be  impossible  in  the  circumstances  of  the 
case ;  or  impossible  unless  some  cause  had  existed  which  did  not  exist 
in  the  particular  case.  Of  no  assertion,  not  in  contratKction  to  some 
of  these  very  general  laws,  will  more  than  improbability  be  asserted 
by  aTiy  cautious  person  ;  and  improbability  not  of  the  very  highest 
degree,  unless  the  time  and  place  in  which  the  fact  is  said  to  have 
occurred,  render  it  almost  certain  that  the  anomaly,  if  real,  could  not 
have  been  overlooked  by  other  observers.  Suspension  of  judgment  is 
in  all  other  cases  the  resource  of  the  judicious  inquirer ;  provided  the 
testimony  in  favor  of  the  anomaly  presents,  when  well  sifted,  no  sus- 
picious circumstances. 

But  the  testimony  is  scarcely  ever  found  to  stand  that  test,  in  cases 
in  which  the  anomaly  is  not  real.  In  the  instances  upon  record  in 
which  a  great  number  of  witnesses,  of  good  reputation  and  scientific 
acquirements,  have  testified  to  the  truth  of  something  which  has  turned 
out  untrue,  there  have  almost  always  been  circumstances  which,  to  a 
keen  observer  who  had  taken  due  pains  to  sift  the  matter,  would  have 
rendered  the  testimony  untrustworthy.  There  have  generally  been 
means  of  accounting  for  the  impression  upon  the  senses  or  minds  of 
the  alleged  percipients  by  fallacious  appearances ;  or  some  epidemic 
delusion,  propagated  by  the  contagious  influence  of  popular  feeling, 
has  been  concerned  in  the  case ;  or  some  strong  interest  has^  been 
implicated  —  religious  zeal,  party  feeling,  vanity,  or  at  least  the  passion 
for  the  marvelous,  in  persons  strongly  susceptible  of  it.  When  none 
of  these  or  similar  circumstances  exist  to  account  for  the  apparent 
strength  of  the  testimony :  and  where  the  assertion  is  not  in  contra- 
diction either  to  those  universal  laws  which  know  no  counteraction  or 
anomaly,  or  to  the  generalizations  next  in  comprehensiveness  to  them, 
but  would  only  amount,  if  admitted,  to  the  existence  of  an  unknown 
cause  or  an  anomalous  Kind,  in  ciroimstances  not  so  thoroughly 
explored  but  that  it  is  credible  that  things  hitherto  unknown  may  still 
come  to  light;  a  cautious  person  will  neither  admit  nor  reject  the;  testi- 
mony, but  will  wait  for  confirmation  at  other  times  and  from  otlier 
unconnected  sources.  Such  ought  to  have  been  the  conduct  of  the 
Kin"'  of  Siam  when  the  Dutch  travt^llers  affirmed  to  him  the  existence 
of  ice.  But  an  ignorant  person  is  as  obstinate  in  his  contcnnptnous 
incredulity  as  he  is  unreasonably  credulous.  Anything  unlike  liis  own 
narrow  experience  he  disbelieves,  if  it  flatter}?  no  propensity ;,  any 
nursery  tale  is  swallowed  implicitly  by  him  if  it  does. 

§  4.  Before  concluding  this  incjuiry,  we  must  advert  to  a  very  serious 
misapprehension  of  the  principh^s  of  the  subject,  which  has  been  com- 
mitted by  some  of  the  writers  against  Hume's  Essay  on  Miracles,  in 
their  anxiety  to  destroy  what  appeared  to  them  a  formidable  weapon 
of  assault  against  the  Christian  religion ;  and  to  which,  with  etifirely 
different  views  on  the  religious  question,  Laplaee,  in  his  Essay  on 


380  INDUCTION. 

Probabilities,  has  been  led  to  give  Lis  sanction  ;  the  effect  in  both  cases 
being,  entirely  to  confound  the  doctrine  of  the  Grounds  of  Disbelief. 
The  mistake  consists  in  overlooking  the  distinction  between  (what  may- 
be called)  improbability  before  the  fact,  and  improbability  after  it;  two 
different  properties,  the  latter  of  which  is  always  a'  gi-ound  of  disbelief; 
the  fonner  is  so  or  not,  as  it  may  happen. 

.  Many  events  are  altogether  improbable  to  us,  before  they  have 
happened,  or  before  we  are  informed  of  their  happening,  which  are 
not  in  the  least  incredible  when  we  are  informed  of  them,  because  not 
contrary  to  any,  even  approximate,  induction.  In  the  cast  of  a  per- 
fectly fair  die,  the  chances  are  five  to  one  against  throwing  ace,  that  is, 
ace  will  be  thrown  on  an  average  only  once  in  six  throws.  But  -this 
is  no  reason  against  believing  that  ace  was  thrown  on  a  given  occasion, 
if  any  credible  witness  asserts  it ;  since  although  ace  is  only  thrown 
once  in  six  times,  some  number  which  is  only  thrown  once  in  six  times 
must  have  been  thrown  if  the  die  was  thrown  at  all.  The  improba- 
bility, then,  or  in  other  words,  the  uruisualness,  of  any  fact,  is  no'reason 
for  disbelieving  it,  if  the  nature  of  the  case  renders  it  certain  that 
either  that  or  something  equally  improbable,  that  is,  equally  unusual, 
did  happen.  If  we  disbelieved  all  facts  which  had  the  chances  against 
them  beforehand,  we  should  believe  hardly  anything.  We  are  told 
that  A.  B.  died  yesterday  :  the  moment  before  we  were  so  told,  the 
chances  against  his  having  died  on  that  day  may  have  been  ten  thou- 
sand to  one ;  but  since  he  was  certain  to  die  at  some  time  or  other, 
and  when  he  died  must  necessarily  die  on  some  particular  day,  while 
the  chances  are  innumerable  against  every  day  in  particular,  experi- 
ence affords  no  ground  whatever  for  discrediting  any  testimony  which 
may  be  produced  to  the  event's  having  taken  place  on  a  given  day. 

Yet^it  has  been  considered,  by  Dr.  Campbell  and  others,  as  a  com- 
plete answer  to  Hume's  doctrine  (that  things  are  incredible  which  are 
contrary  to  the  unifoim  course  of  experience),  that  we  do  not  disbe- 
lieve, merely  because  the  chances  were  against  them,  things  in  strict 
conformity  to  the  unifonn  course  of  experience  ;  that  we  do  not  dis- 
believe an  alleged  fact  merely  because  the  combination  of  causes  upon 
which  it  depends  occurs  only  once  in  a  certain  number  of  times.  It  is 
evident  that  whatever  is  shown  by  experience  to  occur  in  a  certain 
proportion  (however  small)  of  the  whole  number  of  possible  cases,  is 
not  contraiy  to  experience ;  (though  we  are  right  in  disbelieving  it,  if 
some  other  supposition  respecting  the  matter  in  question  would  be  ti"ue 
in  a  greater  proportion  of  the  whole  number  of  cases.)  What  would 
really  be  contrary  to  experience,  would  be  the  assertion  that  the  event 
had  happened  more  frequently  in  some  large  number  of  times,  than 
the  same  combination  had  ever  been  known  to  occur  in  that  number 
of  times;  and. this  alone  it  is  which  is  improbable,  in  the  sense  of  in- 
credibility, or,  as  we  have  called  it,  improbability  after  the  fact. 

§  5.  While  the  defenders  of  Christianity  against  Hume  have  thus 
confounded  two  different  meanings  of  the  word  improbability,  con- 
tending that  because  improbability  of  the  one  kind  is  not  necessarily  a 
ground  of  disbelief,  neither  therefore  is  the  other,  and  that  nothing 
supported  by  credible  testimony  ought  ever  to  be  disbelieved  ;  La- 
place, again,  falling  into  the  same  confusion  between  the  two  meanings, 
contends,  on  the  contrary,  that  because  improbability  of  the  one  kind 


GROUNDS    OF    DISBELIEF.  381 

is  a  sufficient  ground  for  disbelief,  the  other  is  so  too ;  and  that  what 
is  improbable  before  the  fact,  is  therefore  (not  indeed  in  all  cases,  but 
in  a  peculiar  class  of  cases  which  I  am  about  to  specify),  incredible 
after  it.  , 

If,  says  Laplace,  there  are  one  thousand  tickets  in  a  box,  and  one 
only  has  been  drawn  out;  then  if  an  eye-witness  affirms  that  the 
number  drawji  was  79,  this,  though  the  chances  were  999  in  1000 
against  it,  is  not  incredible,  because  the  chances  wei-e  equally  great 
against  every  other  number.  But  (he  continues)  if  there  are  in  the 
box  999  black  balls  and  only  one  white,  and  the  witness  affirms  that 
the  white  ball  was  drawn,  this  is  incredible;  because  there  was  but 
one  chance  in  favor  of  white,  and  999  in  favor  of  some  black  ball. 

This  appears  to  me  entirely  fallacious.  It  is  evident,  both  from 
general  reasoning  and  specific  experience,  that  the  white  ball  will  be 
drawn  out  exactly  as  often,  in  any  large  number  of  trials,  as  the  ticket 
No.  79  will ;  the  two  assertions,  therefore,  are  precisely  on  the  same 
level  in  point  of  credibility.  There  is  one  way  of  putting  the  case 
which,  I  think,  must  carry  conviction  to  every  one.  Suppose  that  the 
thousand  balls  are  numbered,  and  that  the  white  ball  happens  to  be 
ticketed  79.  Then  the  drawing  of  the  white  ball,  and  the  drawing  of 
No.  79,  are  the  very  same  event;  how  then  can  the  one  be  credible, 
the  other  absolutely  incredible  ?  A  witness  sees  it  drawn,  and  makes 
his  report  to  us  :  if  he  says  that  No.  79  was  drawn,  according  to 
Laplace,  he  may  be  believed;  if  he  says  a  white  ball  was  drawn,  we 
are  bound  to  disbelieve  him.  Is  this  rational  ]  Is  it  not  clear,  on  the 
contrarr,  that  the  only  difference  there  could  be  in  the  credit  due  to 
him  would  arise  from  moral  causes,  namely,  from  the  influence  which 
(if  the  witness  knew  that  there  was  but  one  white  ball  in  a  thousand) 
might  be  assigned  to  the  greater  apparent  wonder  in  the  latter  case "? 
which  to  one  kind  of  person  would  be  a  temptation  to  deceive,  or  to 
take  up  a  hasty  impression,  while  to  another,  the  same  thing  would  be 
a  motive  for  assuring  himself  more  positively  of  the  fact,  and  would 
therefore  actually  increase  the  credit  due  to  his  testimony. 

The  mathematical  reas«jning  which  misled  Laplace  into  this  logical 
error,  is  too  long  to  be  here  quoted.  It  is  found  in  the  section  of  his 
Essai  Phiiosophique  stir  les  Probahilitcs,  entitled  Dc  la  Prohahilite  des 
Temoignages,  and  is  founded  upon  a  misapplication,  noticed  by  us  in 
a  former  place,  of  his  own  sixth  theorem  of  tlie  doctrince  of  chances;  a 
theorem  which  he  himself  desci'ibes  as  that  by  which  we  determine 
the  probability  tha^  a  given  effect  was  producecl  by  one  or  by  another 
of  several  causes  capable  of  producing  it.  The  substance  of  his  argu- 
ment may  be  briefly  stated  as  follows  :  Treating  the  assertion  of  the 
witness  as  the  effect,  lie  considers  as  its  two  possible  causes,  the  vera- 
city or  mendacity  of  the  witness  on  the  jjarticular  occasion,  that  is,  the 
truth  or  falsity  of  the  fact.  According  to  the  theorem,  the  probability 
that  the  effect  was  produced  by  a  particular  cause,  is  as  the  antecedent 
probability  of  the  cause,  muhiplied  by  the  probability  that  the  cause, 
if  it  existed,  would  produce  the  given  eflect.  Accordingly  (says 
Laplace)  in  the  case  of  the  thousand  tickets,  the  cause  mendacity  might 
produce  any  one  of  999  untrue  statements,  while  in  the  case  of  the 
balls,  there  being  only  two  statements  to  make,  viz.,  lohifc  or  black, 
and  one  of  these  being  true,  the  cause  mendacity  could  only  produce 
one  untrue  statement:  and  consequently  (the  antecedent  probabihty 


382  INDUCTION. 

of  mendacity  from  the  character  of  the  witness  being  supposed  the 
same  in  both  cases)  mendacity  was  999  times  less  likely  to  have  pro- 
duced the  particular  assertion  made,  and  is  therefore  999  times  less 
likely  to  have  existed,  in  the  former  case  than  in  the  latter. 

The  error  of  this  argument  seems  to  be  the  same  which  we  pointed 
out  in  a  former  chapter,*  that  of  applying  a  theorem,  only  true  of  the 
degrees  of  probability  of  causes,  to  the  probability  of  what  are  neither 
causes  nor  indications  of  causes,  nor  in  any  other  way  specially  con- 
nected with  the  effect.  The  point  in  question  is,  the  comparative 
probability  of  two  suppositions,  that  the  witness  lies,  and  that  he  speaks 
truth.  But  these  are  not  two  possible  causes  of  the  given  effect  (the 
witness's  assertion) ;  they  are  merely  two  possible  qualities  of  it.  The 
truth  of  the  assertion  is,  indeed,  on  the  supposition  of  veracity,  the 
cause  of  its  being  made  ;  but  the  falsity  of  it  is  not,  on  any  supposition, 
a  cause  of  its  being  made.  It  is  not  incompatible  with  the  dishonesty 
of  the  witness  that  he  should  have  spoken  the  truth  :  the  difl'erence  be- 
tween the  two  suppositions  of  honesty  and  dishonesty  is,  that  on  the  one 
he  would  certainly  speak  the  truth,  while  on  the  other  he  was  just  equal- 
ly likely  to  speak  that  or  anything  else.  If  the  falsity  of  the  proposition 
were  a  real  cause  for  his  asserting  it,  and  there  were  no  possible  mode 
of  accounting  for  a  false  assertion  but  by  supposing  that  it  is  made  pre- 
cisely because  of  its  falsity,  I  do  not  see  how  Laplace's  argument  could 
be  resisted.  The  case  where  there  arc  999  possible  false  assertions, 
and  that  in  which  there  is  but  one,  would  then  present  a  vast  differ- 
ence in  the  probability  that  the  assertion  actually  made  proceeded  trom 
falsity  ;  because  in  the  one  case  a  mendacious  witness  was  sure  to  as- 
sert the  one  false  fact,  in  the  other  there  would  be  an  equal  chance  of 
his  asserting  any  one  of  the  999.  But  as  it  is,  the  falsity  was  a  mere 
accident  of  the  assertion,  not  the  cause  of  it ;  and  even  on  the  suppo- 
sition of  dishonesty,  the  statement  is  as  likely  to  be  true  as  false,  while 
on  the  supposition  of  honesty  it  is  certain  to  be  true.  The  assertion, 
therefore,  is  credible. 

With  these  remarks  we  shall  close  the  discussion  of  the  Grounds  of 
Disbelief;  and  along  with  it,  such  exposition  as  our  space  admitted, 
and  as  the  wrriter  had  it  in  his  power  to  furnish,  of  the  Logic  of  Induc- 
tion. 

*  Supra,  p.  324. 


BOOK  IV. 

OF  OPERATIONS  SUBSIDIARY  TO  INDUCTION. 


*'  Clear  and  distinct  ideas  are  terras  which,  though  familiar  and  frequent  in  men's  mouths, 
I  have  reason  to  think  every  one  who  uses  does  not  perfectly  understand.  And  possibly  it 
is  but  here  and  there  one  who  gives  himself  the  trouble  to  consider  them  so  far  as  to  know 
what  he  himself  or  others  precisely  mean  by  them;  1  liave,  therefore,  in  most  places, 
chose  to  put  determinate  or  determmed,  instead  of  clear  and  distinct,  as  more  likely  ta 
direct  men's,  thoughts  to  my  meaning  in  this  matter." — Locke's  Ensay  on  the  Human  Un- 
derstandiiig  ;  Epistle  to  the  Reader. 

"  According  to  this  view  of  the  process  of  the  mind,  in  carrying  on  general  speculations, 
that  Idea  which  the  ancient  philosophers  considerea  as  the  essence  of  an  individual,  is 
nothing  more  than  the  particular  quality  or  qualities  in  which  it  resembles  other  imlividuals 
of  the  same  class;  and  in  consequence  of  which,  a  generic  name  is  applied  to  it." — D. 
Stewart,  Phil,  of  the  Human  Mind,  ch.  iv.,  sec.  2. 

"  Deux  grandes  notions  philosophiques  domiiient  la  theorip  fondamentale  de  la  methode 
naturelle  proprement  ditc,  savoir,  la  foimation  des  groupes  naturels,  et  ensuite  leur  suc- 
cession hierarchique." — Ccmte,  Cours  de  Philosophic  Positive,  42me  leqon 


CHAPTER  I. 

OP  OBSERVATION,  AND  DESCRIPTION. 


§  1.  The  inquiry  which  occupied  us  in  the  two  preceding  Books, 
has  conducted  us  to  what  appears  a  satisfactory  solution  of"  the  ])nncipal 
problem  of  Lot^c,  according  to  the  conception  I  have  formed  of  the 
science.  We  have  found,  that  the  mental  process  with  which  Logic 
is  conversant,  the  operation  of  investigating  truths  by  means  of  e\adence, 
is  always,  even  when  appearances  point  to  a  different  theory  of  it,  a 
process  of  induction.  And  we  have  particularized  tlie  various  modes 
of  induction,  and  obtained  a  clear  view  of  the  principles  to  which  it 
must  conform,  in  order  to  lead  to  results  which  can  be  relied  on. 

The  consideration  of  induction,  however,  does  not  end  with  the 
direct  rules  for  its  performance.  Something  must  be  said  of  those 
oth(!r  operations  of  the  mind,  which  are  either  necessarily  presupposed 
in  all  induction,  or  are  instrumental  to  the  more  difficult  and  compli- 
cated inductive  processes.  The  present  Book  will  be  devoted  to  the 
consideration  of  these  subsidiary  operations :  among  which  our  atten- 
tion must  first  be  given  to  those,  which  are  indispensable  preliminariea 
to  all  induction  whatsoever. 

Induction  being  merely  the  extension  to  a  class  of  cases,  of  some- 
thing which  has  been  observed  to  be  true  in  certain  individual  instances 
of  the  class;  the  fir.st  place  among  the  operations  subsidiary  to  induc- 
tion, is  claimed  l)y  Observation,  TliLs  is  oot,  however,  the  place  to 
lay  down  rules  for  making  good  ob.ser\-crs  ;  nor  is  it  within  the  com- 
petence of  Logic  to  do  so,  but  of  the  art  of  intellectual  Education. 
Our  business  with  Observation  is  only  in  its  connexion  with  the  ap- 


384  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

proprlate  problem  of  logic,  the  estimation  of  evidence.  We  have  to 
consider,  not~how  or  what  to  observe,  but  under  what  conditions  ob- 
servation is  to  be  relied  on;  what  is  needful,  in  order  that  the  fact, 
supposed  to  be  observed,  may  safely  be  received  as  true. 

§  2.  The  answer  to  this  question  is  very  simple,  at  least  in  its  first 
aspect.  The  sole  condition  is,  that  what  is  supposed  to  have  been 
observed  shall  really  have  been  observed ;  that  it  be  an  observation, 
not  an  inference.  For  in  almost  every  act  of  our  perceiving  faculties, 
observation  and  inference  are  intimately  blended.  What  we  are  said 
•o  obsetve  is  usually  a  compound  result,  of  which  one-tenth  may  be 
observation  and  the  remaining  nine-tenths  inference. 

I  affirm,  for  exariiple,  that  I  hear  a  man's  voice.  This  would  pass, 
in  common  language,  for  a  direct  perception.  All,  however,  wl^ich  is 
really  perception,  is  that  I  hear  a  sound.  That  the  sound  is  a  voice, 
and  that  voice  tiie  voice  of  a  rnan,  are  not  perceptions  but  inferences. 
I  affirm,  again,  that  I  saw  my  brother  at  a  certain  hour  this  moming. 
If  any  proposition  concerning  a  matter  of  fact  would  commonly  be 
said  to  be  knovsoi  by  the  direct  testimony  of  the  senses,  this  surely 
would  be  so.  The  truth,  however^  is  far  otherwise.  I  only  saw  a 
certain  colored  surface  ;  or  rather  I  had  the  kind  of  visual  sensations 
which  are  usually  produced  by  a  colored  surface ;  and  from  these 
as  marks,  known  to  be  such  by  previous  experience,  I  concluded  that  I 
saw  my  brother.  I  might  have  had  sensations  precisely  similar,  when 
my  brother  was  not  there.  I  might  have  seen  some  other  person 
so  nearly  resembling  him  in  appearance,  as,  at  the  distance,  and  with 
the  degree  of  attention  which  I  bestowed,  to  be  mistaken  for  him.  I 
might  have  been  asleep  and  have  dreamed  that  I  saw  him  ;  or  in  a 
state  of  nervous  disorder,  which  brought  his  image  before  me  in  a 
waking  hallucination.  In  all  these  modes  men  have  been  led  to  be- 
lieve that  they  saw  persons  well  known  to  them,  who  were  dead,  or 
far  distant.  If  any  of  these  suppositions  had  been  true,  the  affirmation 
that  I  saw  my  brother  would  have  been  eiToneous ;  but  whatever  was 
matter  of  direct  perception,  namely,  the  visual  sensations,  would  have 
been  real.  The  inference  only  would  have  been  ill  grounded ;  I 
should  have  ascribed  those  sensations  to  a  wrong  cause. 

Innumerable  instances  might  be  given,  and  analyzed  in  the  same 
manner,  of  what  are  vulgarly,  called  errors  of  sense.  There  are  none 
of  them  properly  eiTors  of  sense ;  they  are  eiToneous  inferences  from 
sense.  When  I  look  at  a  candle  through  a  multiplying  glass,  1-  seem 
to  see  a  dozen  candles  instead  of  one:  and  if  the  real -circumstances  of 
the  case  were  skillfully  disguised,  I  might  suppose  that  there  were  really 
that  number;  there  would  be  what  is  called  an  optical  deception.  In 
the  kaleidoscope  there  really  is  that  deception  :  when  I  look  through 
the  instrument,  instead  of  what  is  actually  there,  namely,  a  casual  ar- 
rangement of  colored  fragments  of  glass,  I  seem  to  see  the  same  com- 
bination several  times  repeated  in  symmetrical  arrangement  round  a 
point.  The  delusioii  is  of  course  eftected  by  giving  me  the  same  sen- 
sations, which  I  should  have  had  if  such  a  symmetrical  combination  had 
really  been  presented  to  me.  If  I  cross  two  of  my  fingers,  and  bring 
any  small  object,  a  niarble  for  instance,  into  contact  with  both,  at  points 
not  usually  touched  simidtaneously  by  one  object,  I  can  hai'dly,  if  my 
eyes  are  shut,  help  beheving  that  tiiere  are  two  marbles  instead  of  one. 


OBSERVATION    AND    DESCRIl'TION.  385 

But  it  is  not  my  toucli  in  this  case,  nor  my  sight  in  tlie  other,  whicli  is 
deceived  ;  the  deception,  whether  durable  or  only  momentary,  is  in 
my  judgment.  From  my  senses  I  have  only  the  sensations,  and  those 
are  genuine.  Being  accustomed  to  have  those  or  similar  sensations 
when,  and  only  when,  a  certain  arrangement  of  outward  objects  is 
present  to  my  organs,  I  have  the  habit  of  instantly,  when  I  experience 
the  sensations,  inferring  the  existence  of  that  state  of  outward  things. 
This  habit  has  become  so  powerful,  that  the  inference,  performed  with 
the  speed  and  certainty  of  an  instinct,  is  confounded  with  intuitive 
perceptions.  When  it  is  correct,  I  am  unconscious  that  it  ever  needed 
proof;  even  when  I  know  it  to  be  incorrect,  I  camiot  without  consid- 
erable effort  abstain  from  making  it.  In  order  to  be  aware  that  it  is 
not  made  by  instinct  but  by  an  acquired  habit,  I  am  obliged  to  reflect 
on  the  slow  process  by  which  I  learned  to  judge  by  the,  eyfe  of  many 
things  which  I  now  appear  to  perceive  directly  by  sight ;  and  on  the 
reverse  operation  performed  by  persons  learning  to  draw,  who  with 
difficulty  and  labor  divest  themselves  of  their  acquired  perceptions, 
and  learn  afresh  to  see  things  as  they  appear  to  the  eye,  instead  of  see- 
ing them  as  they  really  arc. 

It  would  be  easy  to  prolong  these  illustrations,  were  there  any  need 
to  expatiate  upon  a  topic  so  copiously  exemplified  in  various  popular 
works.  From  the  examples  already  given,  it  is  seen  sufficiently,  that 
the  individual  facts  from  which  we  collect  our  inductive  generalizations 
are  scarcely  ever  obtained  by  observation  alone.  Observation  extends 
only  to  the  sensations  by  which  we  recognize  objects;  but  the  propo- 
sitions which  we  make  use  of,  either  in  science  or  in  common  life, 
relate  mostly  to  the  objects  themselves.  In  every  act  of  what  is  called 
observation,  there  is  at  least  one  inference,  from  the  sensations  to  the 
presence  of  the  object ;  from  the  marks  or  diagnostics  to  the  entire 
phenomenon.  And  hence,  among  other  consequences,  follows  the 
seeming  paradox,  that  a  general  proposition  collected  from  particulars 
is  often  more  certainly  true  than  any  one  of  the  particular  propositions 
from  which,  by  an  act  of  induction,  it  was  infeiTed.  For,  each  of  those 
particular  (or  rather  singular)  propositions  involved  an  inference,  from 
the  impression  on  the  senses  to  the  fact  which  caused  that  impression  : 
and  this  inference  may  have  been  erroneous  in  any  one  of  the  instances^ 
but  cannot  well  have  been  erroneous  in  all  of  them,  provided  their 
number  was  sufficient  to  eliminate  chance.  The  conclusion,  therefore, 
that  is,  the  general  proposition,  may  deserve  more  complete  reliance 
than  it  would  be  safe  to  repose  in  any  one  of  the  inductive  premisses. 

The  logic  of  observation,  then,  consists  solely  in  a  correct  discrimi- 
nation between  that,  in  a  result  of  obsei-vation,  which  has  really  been 
perceived,  and  that  which  is  an  inference;  from  the  perception.  What- 
ever portion  is  inference,  is  amenable  to  the  rules  of  induction  already 
treated  of,  and  requires  no  further  notice  here :  the  question  for  us  in 
this  place  is,  when  all  which  is  inference  is  taken  away,  what  remains'? 
There  remain,  in  the  first  place,  the  mind's  own  feelings  or  states  of 
consciousness,  namely,  its  outward  feelings  or  sensations,  and  its  inward 
feelings  —  its  thoughts,  emotions,  and  volitions.  Whether  anything  else 
remains,  or  all  else  is  inference  from  this  ;  whether  the  mind  is  capable 
of  directly  perceiving  or  apprehending  anything  except  states  of  its 
own  consciousness  —  is  the  peculiar  problem  of  the  higher  or  trans- 
cendental metaphysics.  But  after  excluding  all  questions  on  which 
3C 


386  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

metaphysicians  differ,  it  remains  true  that  for  most  purposes  the  dis- 
crimination we  are  called  upon  practically  to  exercise  is  between 
sensations  or  other  feelings,  of  our  own  or  of  other  people,  and  infer- 
ences drauTi  from  them.  And  on  the  theory  of  Obsers'ation  this  is  all 
which  seems  necessary  to  be  said  in  this  place. 

§  3.  If,  in  the  simplest  observation,  or  in  what  passes  for  such,  there 
is  a  laro-e  part  which  is  not  observation  but  something  else ;  so  in  the 
simplest  description  of  an  observation,  there  is,  and  must  always  be, 
much  more  asserted  than  is  contained  in  the  perception  itself  We 
cannot  describe  a  fact  without  implying  more  than  the  fact.  The  per- 
ception is  only  of  one  individual  thing ;  but  to  describe  it  is  to  affirm 
a  connexion  between  it  and  every  other  thing  which  is  either  denoted 
or  connoted  by  any  of  the  terms  used.  To  begin  with  an  example, 
than  which  none  can  be  conceived,  more  elementary :  I  have  a  sensa- 
tion of  sight,  and.  I  endeavor  to  describe  it  by  saying  that  I  see  some- 
thing white.  In  saying  this,  I  do  not  solely  affinn  my  sensation ;  I 
also  class  it.  I  asseit  a  resemblance  between  the  thing  I  see,  and  all 
things  which  I  and  others  are  accustomed  to  call  wliite.  I  assert  that 
it  resembles  them  in  the  circumstance  in  which  they  all  resemble  one 
another,  in  that  which  is  the  ground  of  their  being  called  by  the  name. 
This  is  not  merely  one  way  of  describing  an  observation,  but  the  only 
way.  If  I  would  either  register  my  observation  for  my  own  future 
use,  or  make  it  known  for  the  benefit  of  others,  I  must  assert  a  resem- 
blance between  the  fact  which  I  have  observed  and  something  else. 
It  is  inherent  in  a  description,  to  be  the  statement  of  a  resemblance, 
or  reseinblances. 

These  resemblances  are  not  always  apprehended  directly;  by  merely 
comparing  the  object  obseived  with  some  other  present  object,  or  with 
our  recollection  of  an  object  which  is  absent.  They  are  often  ascer- 
tained through  immediate  marks,  that  is,  deductively.  In  describing 
some  new  kind  of  animal,  suppose  me  to  say  that  it  measures  ten  feet  in 
length,  from  the  forehead  to  the  extremity  of  the  tail.  I  did  not  ascer- 
tain this  by  the  unassisted  eye.  I  had  a  two-foot  rule  which  I  applied 
to  the  object,  and,  as  we  commonly  say,  measured  it;  an  operation 
which  was  not  wholly  manual,  but  partly  also  mathematical,  involring 
the  two  propositions.  Five  times  two  is  ten,  and  Things  which  are 
equal  to  the  same  thing  are  equal  to  one  another.  Hence,  the  fact 
that  the  animal  is  ten  feet  long  is  not  an  immediate  perception,  but  a 
conclusion  from  reasoning  ;  the  minor  premisses  alone  being  furnished 
by  observation  of  the  object.  But  this  does  not  hinder  it  from  being 
rightly  called  a  description  of  the  animal. 

To  pass  at  once  from  a  very  simple  to  a  very  complex  example :  I 
affirm  that  the  earth  is  globular.  The  assertion  is  not  grounded  upon 
direct  perception  ;  for  the  figure  of  the  earth  cannot,  by  us,  be  directly 
perceived,  although  the  assertion  would  not  be  true  unless  circum- 
stances could  be  supposed  under  which  its  truth  could  be  so  perceived. 
That  the  forni  of  the  earth  is  globular,  is  infeiTed  from  certain  marks, 
as  for  instance  from  this,  that  its  shadow  throwai  upon  the  moon  is  cir- 
cular ;  or  this,  that  on  the  sea,  or  any  extensive  plain,  our  horizon  is 
always  a  circle  ;  either  of  which  marks  is  incompatible  with  any  other 
than  a  globular  form.  I  assert  further,  that  the  earth  is  that  particular 
kind  of  globe  wliich  is  termed  an  oblate  spheroid ;  because  it  is  found 


OBSERVATION    AND   DESCRIPTION.  387 

by  measurement  In  the  direction  of  the  meridian,  that  the  length  on  the 
surface  of  the  earth  which  subtends  a  given  angle  at  its  centre,  dimin- 
ishes as  we  recede  from  the  equator  and  apju'oach  the  poles.  Bui 
these  propositions,  that  the  earth  is  glo!)ul;ir,  and  that  it  is  an  oblate 
spheroid,  assert,  each  of  them,  one  individual  fact;  in  its  own  nature 
capable  of  being  perceived  by  the  senses  when  the  requisite  organs 
and  the  necessary  position  are  supposed,  and  only  hot  actually  per- 
ceived because  these  organs  and  that  position  are  wanting.  That 
which,  if  the  fact  could  have  been  seen,  would  have  been  called  a  de- 
scription of  the  figure  of  the  earth,  may  without  impropriety  be  so 
called  when  instead  of  being  seen  it  is  inferred.  But  we  could  not 
■vdthout  impropriety  call  either  of  these  assertions  an  induction  from 
facts  respecting  the  earth.  They  arc  not  general  propositions  collected 
from  particular  facts,  but  particular  facts  deduced  from  general  prop- 
ositions. They  are  conclusions  obtained  deductively,  from  premisses 
originating  in  deduction ;  but  of  these  premisses  some  were  not  ob- 
tained by  observation  of  the  earth,  nor  had  any  peculiar  reference  to  it. 
If,  then,  the  truth  respecting  the  figure  of  the  earth  is  not  an  induc- 
tion, why  should  the  truth  respecting  the  figure  of  the  earth's  orbit  be 
so  ?  Mr.  Wliewell  contends  that  it  is ;  although  the  two  cases  only 
differ  in  this,  that  the  form  of  the  orbit  was  not,  like  the  form  of  the 
earth  itself,  deduced  by  ratiocination  fi-om  facts  which  were  marks  of 
ellipticity,  but  was  got  at  by  boldly  guessing  that  the  path  was  an 
ellipse,  and  finding  afterwards,  on  examination,  that  the  observations 
were  in  harmony  with  the  hy])othesis.  Not  only,  according  to  Mr. 
Wliewell,  is  this  process  of  guessing  and  verifying  our  guesses  induc- 
tion, but  it  is  the  whole  of  induction  :  no  other  exposition  can  be  given 
of  that  logical  operation.  That  he  is  \vi'ong  in  the  latter  assertion,  the 
whole  of  the  preceding  Book  has,  I  hope,  sufl'iciently  proved  ;  and  that 
even  the  former  of  the  two  contains  a  large  dose  of  eiTor  with  but  a 
small  portion  of  truth,  was  attemjited  to  be  shov  n  in  the  second  chap- 
ter of  the  same  Book.*  We  ai-e  now,  however,  prepared  to  go  more 
into  the  heart  of  the  question  than  at  that  earlier  period  of  our  inquiry, 
and  a  few  words  will,  I  think,  suffice  to  dispel  all  remaining  obscurity. 

§  4.  We  observed,  in  the  second  chapter,  that  the  proposition  "  the 
earth  moves  in  an  ellipse,"  so  far  as  it  only  serves  for  the  colligation  or 
connecting  together  of  actual  observ^ations,  (that  is,  as  it  only  affirms 
that  the  observed  positions  of  the  earth  may  be  coiTectly  represented 
by  as  many  points  in  the  circumference  of  an  imaginary  ellipse,)  is  not 
an  induction,  but  a  description  :  it  is  an  induction  only  when  it  affirms 
that  the  intermediate  positions,  of  which  there  has  been  no  direct 
observation,  would  be  found  to  correspond  to  the  remaining  points  of 
the  same  elliptic  circumference.  Now,  although  this  real  induction  is 
one  thing,  and  the  description  another,  we  are  in  a  VQry  different  con- 
dition for  making  the  induction  after  we  have  obtained  the  description, 
and  before  it.  For  inasmuch  as  the  description,  like  all  other  descrip- 
tions, contains  the  assertion  of  a  resemblance  between  the  phenomenon 
described  and  something  else ;  in  pointing  out  something  which  the 
series  of  observed  places  of  a  planet  resembles,  it  points  out  something 
in  which  the  several  places  themselves  agree.     If  the  series  of  places 

♦  Supra,  pp.  177-183. 


388  OPERATIONS    SVBSIDIARY    TO    INDUCTION. 

corresponds  to  as  many  points  of  an  ellipse,  the  places  themselves 
agree  in  being  situated  in  that  ellipse.  We  have,  therefore,  by  means 
of  the  description,  obtained  the  requisites  for  an  induction  by  the 
Method  of  Agreement.  The  successive  observed  places  of  the  earth 
beino-  considered  as  effects,  and  its  motion  as  the  cause  w^hich  produces 
them,  we  find  that  those  effects,  that  is,  those  places,  agree  in  the  cir- 
cumstance of  being  in  an  ellipse.  We  conclude  that  the  remaining 
effects,  the  places  which  have  not  been  observed,  agree  in  the  same 
circumstance,  and  that  the  laiv  of  the  motion  of  the  earth  is  motion  in 
an  ellipse. 

The  Colligation  of  Facts,  therefore,  by  means  of  hypotheses,  or,  as 
Mr.  Whewell  prefers  to  say,  by  means  of  Conceptions,  instead  of  being, 
as  he  supposes.  Induction  itself,  takes  its  proper  place  among  opera- 
tions subsidiary  to  Induction.  All  Induction  supposes  that  we  have 
previously  compared  the  requisite  number  of  individual  in^ances,  and 
ascertained  in  what  circumstances  they  agree  ;  the  Colligation  of  Facts 
is  no  other  than  this  preliminaiy  operation :  and  the  proper  office  of 
"  clear  and  appropriate  ideas,"  on  the  necessity  of  which  Mr.  Whewell 
has  said  so  much,  is  to  enable  us  to  perform  this  operation  correctly. 
When  Kepler,  after  vainly  endeavoring  to  connect  the  observed  places 
of  a  planet  by  various  hypotheses  of  circular  motion,  at  last  tried  the 
hypothesis  of  an  ellipse  and  found  it  answer  to  the  phenomena,  what 
he  really  attempted,  first  unsuccessfully  and  at  last  successfully,  was  to 
discover  the  circumstance  in  which  all  the  observed  positions  of  the 
planet  agreed.  And  when  he  in  like  manner  connected  another  set  of 
obsei'ved  facts,  the  periodic  times  of  the  different  planets,  by  the  prop- 
osition that  the  squares  of  the  times  are  proportional  to  the  cubes  of 
the  distances,  what  he  did  was  simply  to  ascertain  the  property  in 
which  the  periodic  times  of  all  the  different  planets  agreed. 

Since,  therefore,  all  that  is  true  and  to  the  pui-pose  in  Mr.  Whewell's 
doctrine  of  Conceptions  might  be  fully  expressed  by  the  more  familiar 
term  Hypothesis  ;  and  since  his  Colligation  of  Facts  by  means  of  ap- 
propriate Conceptions,  ic  but  the  ordinary  process  of  finding  by  a 
comparison  of  phenomena,  in  what  consists  their  agreement  or  resem- 
blance ;  I  would  willingly  have  confined  myself  to  those  better  under- 
stood expressions,  and  persevered  to  the  end  in  the  same  abstinence 
which  I  have  hitherto  observed  from  all  ideological  discussions  ;  con- 
sidering the  mechanism  of  our  thoughts  to  be  a  topic  distinct  from  and 
irrelevant  to  the  principles  and  rules  by  which  the  ti'ustworthiness  of 
the  results  of  thinking  is  to  be  estimated.  Since,  however,  a  work  of 
such  high  pretensions,  and,  it  must  also  be  said,  of  so  much  real  merit, 
has  rested  the  whole  theory  of  Induction  upon  such  ideological  con- 
siderations, it  seems  necessary  for  others  who  follow,  to  claim  for 
themselves  and  their  doctrines  whatever  position  may  properly  belong 
to  them  on  the  same  metaphysical  gioujid.  And  this  is  the  object  of 
the  succeeding  chapter. 


ABSTRACTION. 


CHAPTER  11. 

OF  ABSTRACTION,   OR  THE   FORMATION   OF   CONCEPTIONS. 

§  1.  The  metaphysical  inquiry  into  tlie  nature  and  composition  of 
what  have  been  called  Abstract  Ideas,  or  in  otlier  words,  of  the  notions 
which  answer  in  the  mnid  to  classes  and  to  general  names,  belongs  not 
to  Logic,  but  to  a  dift'erent  science,  and  our  purpose  does  not  require 
that  we  should  enter  upon  it  here.  We  are  only  concerned  with  the 
universally  aclcnowledged  fact,  that  such  general  notions  or  concep- 
tions do  exist.  The  mind  can  conceive  a  multitude  of  individual  things 
as  one  assemblage  or  class  ;  and  general  names  do  really  sug<»-est  to  us 
certain  ideas  or  mental  representations,  otherwise  we  could  not  use  the 
names  with  consciousness  of  a  meaning.  Whether  the  idea  called  up 
by  a  general  name  is  composed  of  the  various  circumstances  in  which 
all  the  individuals  denoted  by  the  name  ?igree,  and  of  no  others, 
(which  is  the  doctrine  of  Locke,  Brown,  and  the  Conceptualists) ;  or 
whether  it  be  the  idea  of  some  one  of  those  individuals,  clothed  in  its 
individualizing  peculiarities,  but  with  the  accompanying  knowledo-e 
that  those  peculiarities  are  not  properties  of  the  class,  (which  is  the 
doctrine  of  Berkeley,  Dugald  Stewart,  and  the  modern  Nominalists); 
or  whether  (as  held  by  Mr.  Mill),  the  idea  of  the  class  is  that  of  a 
miscellaneous  assemblage  of  individuals  belonging  to  the  class  ;  or 
whether,  finally,  (what  appears  to  be  the  truest  opinion)  it  be  any  one 
or  any  other  of  all  these,  according  to  the  accidental  circumstances  of 
the  case ;  certain  it  is,  that  some  idea  or  mental  conception  is  suggested 
by  a  general  name,  whenever  we  either  hear  it  or  employ  it  with  con- 
sciousness of  a  meaning.  And  this,  which  we  may  call  if  we  please  a 
general  Idea,  rejrresents  in  our  minds  the  whole  class  of  things  to  which 
the  name  is  applied.  Whenever  we  think  or  reason  concerniu"-  the 
class,  we  do  so  by  means  of  this  idea.  And  the  voluntary  power 
which  the  mind  has,  of  attending  to  one  part  of  what  is  present  to  it 
at  any  moment,  and  neglecting  another  part,  enables  us  to  keep  our 
reasonings  and  conclusions  respecting  the  class  unaffected  by  anything 
in  the  idea  or  mental  image  which  is  not  really,  or  at  least  which  we 
do  not  really  believe  to  be,  common  to  the  whole  class. 

We  have,  then,  general  conceptions:  we  can  conceive  a  class  as  a 
class.  But  this  appears  to  me  to  be  a  fact  which  Logic,  as  such,  may 
fairly  be  permitted  to  take  for  granted,  without  any  particular  exami- 
nation into  the  manner  of  it.  Logic  is  concerned  with  what  we  carr 
know,  and  with  what  we  can  assert,  but  not  with  what  we  can  con- 
ceive. We  can  speak  and  reason  of  a  number  of  objects  as  a  class, 
and  we  can  know  them  to  bo  a  class,  and  know  what  makes  them  so; 
and  it  is  enough  for  Logic  to  und<!rstand  this,  and  to  know  that  the 
mind  has  whatever  powers  this  implies,  without  incjuiring  what  powers 
these  are.  However,  if  we  are  forced  to  enter  upon  this  foreign 
ground,  it  cannot  but  be  admitted  that  there  are  such  things  as  general 
conceptions,  and  that  when  we  form  a  set  of  phenomena  into  a  class, 
that  is,  when  we  compare  them  with  one  another  to  ascertain  in  what 
they  agree,  some  general  conception  is  implied  in  this  mental  opera- 
tion.    And  inasmuch  as  such  a  compaiison  is  a  necessary  preHminary 


390  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

to  Induction,  it  is  most  true  that  Induction  could  not  go  on  without 
general  conceptions. 

§  2.  But  it  does  not  therefore  follow  that  these  general  conceptions 
must  have  existed  in  the  mind  previously  to  the  comparison.  It  is  not 
(as  Mr.  Whewell  seems  to  suppose,)  a  law  of  our  intellect,  that  in 
comparing  things  with  each  other  and  taking  note  of  their  agreement 
we  merely  recognize  as  realized  in  the  outward  world  something  that 
we  already  had  in  our  minds.  The  conception  originally  found  its 
way  to  us  as  the  result  of  such  a  comparison.  It  was  obtained  (in 
metaphysi.^al  phrase,)  by  abstraction  from  individual  things.  These 
things  may  be  things  which  we  perceived  or  thought  of  on  former 
occasions,  but  they  may  also  be  the  things  which  we  are  perceiving  or 
thinking  of  on  the  very  occasion.  When  Kepler  compared  the  observed 
places  of  the  planet  Mars,  and  found  that  they  agreed  in  being  points 
of  an  elliptic  circumference,  he  applied  a  general  conception  which 
was  already  in  his  mind,  having  been  derived  from  his  former  experi- 
ence. But  this  is  by  no  means  the  universal  case.  When  we  compare 
several  objects  and  find  them  to  agree  in  being  white,  or  when  we 
compare  the  various  species  of  ruminating  animals  and  find  them  agree 
in^being  cloven-footed,  we  have  just  as  much  a  general  conception  in  our 
minds  as  Kepler  had  in  his  :  we  have  the  conception  of  "  awhite  thing," 
or  the  conception  of  "  a  cloven-footed,  animal."  But  no  one  supposes 
that  we  necessarily  bring  these  conceptions  with  us,  and  superinduce 
them  (to  adopt  Mr.  Whewell's  expression*)  upon  the  facts :  because  in 
these  simple  cases  everybody  sees  that  the  very  act  of  comparison  which 
ends  in  our  connecting  the  facts  by  means  of  the  conception,  may  be  the 
source  from  which  we  derive  the  conception  itself.  If  we  had  never 
seen  any  white  object  or  had  never  seen  any  cloven-footed  animal  before, 
we  should  at  the  same  time  and  by  the  same  mental  act  acquire  the  idea, 
and  employ  it  for  the  colligation  of  the  observed  phenomena.  Kepler, 
on  the  contrary,  really  had  to  bring  the  idea  with  him,  and  superinduce 
it  upon  the  facts  ;  he  could  not  evolve  it  out  of  them  :  if  he  had  not 
already  had  the  idea,  he  would  not  have  been  able  to  acquire  it  by  a 
comparison  of  the  planet's  positions.  But  this  inability  was  a  mere 
accident  :  the  idea  of  an  ellipse  could  have  been  acquired  from  the 
paths  of  the  planets  as  effectually  as  from  anything  else,  if  the  paths 
had  not  happened  to  be  invisible.  If  the  planet  had  left  a  visible 
track,  and  we  had  been  so  placed  that  we  could  see  it  at  the  proper 
angle,  we  might  have  abstracted  our  original  idea  of  an  ellipse  from 
the  planetary  orbit.  Indeed,  every  conception  which  can  be  made  the 
instrument  for  connecting  a  set  of  facts,  might  have  been  originally 
evolved  from  those  very  facts.  The  conception  is  a  conception  of 
something ;  and  that  which  it  is  a  conception  of,  is  really  in  the  facts, 
and  might,  under  some  supposable  circumstances,  or  by  some  suppo- 
sable  extension  of  the  faculties  which  we  actually  possess,  have  been 
detected  in  them.  And  not  only  is  this  always  in  itself  possible,  but 
it  actually  happens,  in  almost  all  cases  in  which  the  obtaining  of  the 
right  conception  is  a  matter  of  any  considerable  difficulty.  For  if  there 
be  no  new  conception  required ;  if  one  of  those  ali-eady  familiar  to 
mankind  will  serve   the   purpose,  the  accident  of  being  the  first  to 

*  Philosophy  of  the  Inductive  Sciences,  i.,  42. 


ABSTRACTION.  391 

whom  the  right  one  occurs,  may  happen  to  ahnost  anybody  ;  at  least 
in  the  case  of  a  set  of  phenomena  which  the  "whole  scientific  world 
are  engaged  in  attempting  to  connect.  The  honor,  in  Kepler's  case, 
was  that  of  the  accurate,  j)atient,  autl  toilsome  calculations  by  which 
he  compared  the  results  that  followed  from  his  dilferent  guesses,  with 
the  observations  of  Tycho  Bralie  ;  but  llu;  merit  was  very  small  of 
guessing  an  ellipse :  the  only  wonder  is  that  men  had  not  guessed  it 
before,  nor  could  they  have  failed  to  do  so  if  there  had  not  existed  an 
obstinate  a  2>riori  j^rt^udice  that  the  heavenly  bodies  must  move,  if  not 
in  a  circle,  in  some  combination  of  circles. 

The  really  difficult  cases  arc  those  in  which  the  conception,  that  is 
to  create  light  and  order  out  of  darkness  and  confusion,  has  to  be  sought 
for  among  the  very  phenomena  which  it  afterwards  serves  to  arrange. 
Why,  according  to  Mr.  Whewell  himself,  did  the  ancients  fail  in  dis- 
covering the  laws  of  mechanics,  that  is,  of  ecjuilibrium  and  of  the  com- 
munication of  motion  1  Because  they  had  not,  or  at  least  had  not 
clearly,  the  ideas  or  conceptions,  of  pressure  and  resistance,  momen- 
tum, and  uniform  and  accelerating  force.  And  whence  could  they 
have  obtained  these  ideas,  except  from  the  very  facts  of  equilibrium  and 
motion  ?  The  tardy  development  of  several  of  the  j)hysical  sciences, 
for  example  of  optics,  electricity,  magnetism,  and  the  higher  generali- 
zations of  chemistry,  Mr.  Whewell  ascribes  to  the  fact  that  mankind 
had  not  yet  possessed  themselves  of  the  Idea  of  Polarity,  that  is,  the 
idea  of  opposite  properties  in  opposite  directions.  But  what  was  there 
to  suggest  such  an  idea,  until,  by  a  separate  examination  of  several  of 
these  different  branches  of  knowledge,  it  was  shown  that  the  facts  of 
each  of  them  did  present,  in  some  instances  at  least,  the  curious  phe- 
nomenon of  opposite  properties  in  opposite  directions  ?  The  thing 
w-as  superficially  manifest  only  in  two  cases,  those  of  the  magnet,  and 
of  electrified  bodies;  and  there  the  conception  was  encumbered  with 
the  circumstance  of  material  poles,  or  fixed  points  in  the  body  itself,  in 
which  points  this  opposition  of  properties  seemed  to  be  inherent.  The 
first  comparison  and  abstraction  had  led  only  to  this  conception  of  poles ; 
and  if  anything  corresponding  to  that  conception  had  existed  in  the 
phenomena  of  chemistry  or  optics,  the  difficulty  which  Mr.  Whewell 
justly  considers  as  so  great,  would  have  been  extremely  small.  The 
obscurity  arose  from  the  fact,  that  the  polarities  in  chemistry  and  optics 
were  distinct  species,  though  of  the  same  genus,  with  the  polarities  in 
electricity  and  magnetism  :  and  that  in  order  to  assimilate  the  phe- 
nomena to  one  another,  it  was  necessary  to  compare  a  polarity  without 
poles,  such  for  instance  as  is  exemplified  in  the  polarization  of  light, 
and  the  polarity  w'ith  poles,  which  we  see  in  the  magnet :  and  to  recog- 
nize that  these  polarities,  while  different  in  many  other  respects,  agi"ee 
in  the  one  character  which  is  exj)ressed  by  the  phrase,  opposite  prop- 
erties in  opposite  directions.  From  the  result  of  such  a  comparison  it 
was  that  the  minds  of  scientific  men  formed  this  new  general  concep- 
tion ;  between  which,  and  the  first  confused  ftHsling  of  an  analogy 
between  some  of  the  phenomena  of  light  and  those  of  electiicity  and 
magnetism,  there  is  a  long  intenal,  filled  up  by  the  labors  and  more 
or  less  sagacious  suggestions  of  many  superior  minds. 

The  conceptions,  then,  which  we  emj)loy  for  the  colligation  and 
methodization  of  facts,  do  not  develop  themselves  from  within,  but  are 
impressed  upon  the  mind  from  without;  tliey  arc  never  obtained  other- 


"92  OPERATIONS    SUBSIDARY    TO    INDUCTION. 

wise  than  by  way.  of  comparison  and  abstraction,  and,  in  the  most 
important  and  the  most  numerous  cases  are  evolved  by  abstraction 
from  the  very  phenomena  which  it  is  their  office  to  colligate.  I  am  far 
from  wishing  to  imply  that  it  is  not  often  a  very  difficult  thing  to  per- 
form this  process  of  abstraction  well,  or  that  the  success  of  an  induc- 
tive operation  does  not,  in  many  cases,  principally  depend  upon  the 
skill  with  which  we  perform  it.  Bacon,  in  his  forcible  manner,  desig- 
nated as  one  of  the  principal  obstacles  to  good  induction,  general  con- 
ceptions wrongly  formed,  "  notiones  temere  a  rebus  abstractas:"  to 
which  Mr.  Whewoll  adds,  that  not  only  does  bad  abstraction  make  bad 
induction,  but  that  in  order  to  perform  induction  well,  we  must  have 
abstracted  well :  our  general  conceptions  must  be  "  clear"  and  "  appro- 
priate" to  the  matter  in  hand.  Nor  can  it  be  doubted  that,  in  what 
they  thus  said,  both  Bacon  and  Mr.  Whewell,  though  they  expressed 
their  meaning  vaguely,  had  a  meaning,  and  a  highly  important  one. 

§  3.  In  attempting  to  show  what  the  difficulty  in  this  matter  really 
is,  and  how  it  is  surmounted,  I  must  beg  the  reader,  once  for  all,  to 
bear  this  in  mind :  That  although  in  discussing  Mr,  Whewell's  opin- 
ions I  am  willing  to  adopt  his  language,  and  to  speak,  therefore,  of 
connecting  facts  through  the  instrumentality  of  a  conception,  this  tech- 
nical phraseology  means  neither  more  nor  less  than  what  is  commonly 
called  comparing  the  facts  with  one  another  and  determining  in  what 
they  agree.  Nor  has  the  technical  expression  even  the  advantage  of 
being  metaphysically  correct.  The  facts  are  not  connected;  they 
remain  separate  facts  as  they  were  before.  The  ideas  of  the  facts  may 
become  connected,  that  is,  we  may  be  led  to  think  of  them  together; 
but  this  consequence  is  no  more  than  what  may  be  produced  by  any 
casual  association.  What  really  takes  place,  is,  I  conceive,  more  phi- 
losophically expressed  by  the  common  word  Coinparison,  than  by  the 
phrases  "to  connect"  or  "to  superinduce."  For,  as  the  general  con- 
ception is  itself  obtained  by  a  comparison  of  particular  phenomena,  so, 
when  obtained,  the  mode  in  which  we  apply  it  to  other  phenomena  is 
again  by  comparison.  We  compare  phenomena  wdth  each  other  to  get 
the  conception,  and  we  then  compare  those  and  other  phenomeiia  witJi 
the  conception.  We  get  the  conception  of  an  animal  (for  instance)  by 
comparing  different  animals,  and  when  we  afterwards  see  a  creature 
resembling  an  animal,  we  compare  it  with  our  general  conception  of 
an  anin>al ;  and  if  it  agi'ees  with  that  general  conception,  we  include  it 
in  the  class.      The  conception  becomes  the  type  of  comparison. 

And  we  need  only  consider  what  comparison  is,  to  see  that  where 
the  objects  are  more  than  two,  and  still  more  when  they  are  an  indefi- 
nite number,  a  type  of  some  sort  is  an  indispensable  condition  of  the 
comparison.  When  we  have  to  an-ange  and  classify  a  great  number  of 
objects  according  to  their  agreements  and  differences,  we  do  not  make 
a  confused  attempt  to  compare  all  with  all.  We  know  that  two  things 
are  as  much  as  the  human  mind  can  attend  to  at  a  time,  and  we  there- 
fore fix  upon  one  of  tho  objects,  either  at  hazard  or  because  it  offers  in 
a  peculiarly  striking  manner  some  important  character,  and,  taking  this 
as  our  standard,  we  compare  with  it  one  object  after  another.  If  we 
find  a  second  object  which  presents  a  remarkable  agieement  with  the 
first,  inducing  us  to  class  them  together,  the  question  instantly  arises, 
in  what  circumstances  do  they  agree  1  and  to  take  notice  of  these  cir- 


ABSTRACTION.  393 

cumstances  is  already  a  first  stage  of  abstraction,  giving  rise  to  a 
general  conception.  HaNnng  advanced  thus  far,  when  we  now  take  in 
hand  a  third  object,  we  naturally  ask  ourselves  the  question,  not  merely 
whether  this  third  object  agrees  with  the  first,  but  whether  it  agrees 
with  it  in  the  same  circumstances  in  which  the  second  did  1  in  other 
words,  whether  it  agi'ees  with  the  general  conception  which  has  been 
obtained  by  abstraction  from  the  first  and  second  I  Thus  we  see  the 
tendency  of  general  conceptions,  as  soon  as  formed,  to  substitute  them- 
selves as  types,  for  whatever  individual  objects  previously  answered 
that  purpose  in  our  comparisons.  We  may,  perhaps,  find  that  no 
considerable  number  of  other  objects  agree  with  this  first  general  con^ 
ception;  and  that  we  must  drop  the  conception,  and  beginning  again 
with  a  different  individual  case,  proceed  by  different  com[)arisons  to  a 
diffei-ent  general  conception.  Sometimes,  again,  we  find  that  the  same 
conception  will  serve,  by  merely  leaving  out  some  of  its  circumstances  ; 
and.  by  this  higher  effort  of  abstraction,  we  obtain  a  still  more  general 
conception;  as,  in  the  case  formerly  refeired  to,  we  rose  from  the 
conception  of  poles  to  the  general  conception  of  opposite  properties  in 
opposite  directions  ;  or  as  those  South  Sea  islanders,  whose  conception 
of  a  quadruped  had  been  abstracted  from  hogs  (the  only  animals  of  that 
description  which  they  had  seen),  when  they  afterwards  compared  that 
conception  with  other  quadrupeds,  dropped  some  of  the  circumstances, 
and  arrived  at  the  more  general  conception  which  Europeans  associate 
with  the  term. 

These  brief  remarks  contain,  I  believe,  all  that  is  well-grounded  in 
Mr.-Whewell's  doctrine  that  the  conception  by  which  the  mind  ar- 
ranges and  gives  unity  to  phenomena  must  be  furnished  by  the  mind 
itself,  and  that  we  find  the  right  conception  by  a  tentative  process, 
trying  first  one  and  then  another  until  we  hit  the  mark.  It  has  been 
seen  that  the  conception  is  not  furnished  hi/  the  mind  until  it  litis  been 
furnished  to  the  mind  ;  and  that  the  facts  which  supply  it  are  some- 
times extraneous  facts,  but  more  often  the  very  facts  which  we  are 
attempting  to  arrange  by  it.  It  is  quite  true,  however,  that  in  e'ndeav- 
oring  to  arrange  the  facts,  at  whatever  point  we  begin,  we  never  ad- 
vance three  steps  without  forming  a  general  conception,  more  or  less 
distinct  and  precise  ;  and'  that  this  general  conception  becomes  the 
clue  which  we  instantly  endeavor  to  trace  through  the  rest  of  the  facts, 
or  rather,  becomes  the  standard  with  which  we  thenceforth  compare 
them.  If  we  are  not  satisfied  with  the  agreements  which  we  discover 
among  the  phenomena  by  comparing  them  with  this  type,  or  with  some 
still  more  general  conception  which  by  an  additional  stage  of  abstrac- 
tion we  can  form  from  the  type :  we  change  our  course,  and  look  out 
for  other  agreements  :  we  recommence  the  comparison  from  a  differei;vt 
starting  point,  and  so  generate  a  different  set  of  general  conceptions. 
This  is  the  tentative  process  wlilch  Mr.  Whewell  speaks  of;  and  this 
it  is  which  suggested  the  theory  tliat  the  conception  is  supplied  by  the 
mind  itself.  The  different  conceptions  which  the  mind  successively 
tries,  it  either  already  possessexl  from  its  previous  experience,  or  they 
were  supplied  to  it  in  the  very  first  stage  of  the  corresponding  act  of 
comparison ;  and  since,  in  the  subsequent  part  of  the  process,  the  con- 
ception manifested  itself  as  something  compared  with  the  phenomena, 
not  evoh  ed  from  them,  Mr.  Whewell's  opinion,  though  I  cannot  help 
thinking  it  erroneous,  is  not  unnatural. 
3  D 


394  OPERATIONS    SUBSIDIARY   TO    INDUCTION. 

§  4.  If  this  be  a  coirect  account  of  the  instrumentality  of  general 
conceptions  in  the  comparison  which  necessarily  precedes  Induction, 
we  shall  easily  be  able  to  translate  into  our  own  language  what  Mr. 
Whewell  means  by  saying  that  conceptions,  to  be  subservient  to  Induc- 
tion, must  be  "  clear"  and  "  appropriate." 

If  the  conception  corresponds  to  a  real  agreement  among  the  phe- 
nomena ;  if  the  comparison  which  we  have  made  of  a  set  of  objects  has 
led  us  to  class  them  according  to  real  resemblances  and  differences ; 
the  conception  which  does  this  inay  not  indeed  be  clear,  but  it  cannot 
fail  to  be  appi"opriate,  for  some  purpose  or  other.  The  question  of  ap- 
propriateness is  relative  to  the  particular  object  we  have  in  view.  As 
soon  as,  by  our  comparison,  we  have  ascertained  some  agreement,  some- 
thing which  can  be  predicated  in  common  of  a  number  of  objects;  we 
have  obtained  a  basis  on  which  an  inductive  process  is  capable  of  being 
founded.  But  the  agreements,  or  the  ulterior  consequences  to  which 
those  agreements  lead,  may  be  of  very  different  degrees  of  importance. 

If,  for  instance,  we  only  compare  animals  according  to  their  color, 
and  class  those  together  which  are  colored  alike,  we  form  the  general 
conceptions  of  a  white  animal,  a  black  animal,  &c.,  which  are  concep- 
tions legitimately  formed ;  and  if  an  induction  were  to  be  attempted 
concerning  the  causes  of  the  colors  of  animals,  this  comparison  would 
be  the  proper  and  necessary  preparation  for  such  an  induction,  but 
would  not  help  us  towards  a  knowledge  of  the  laws  of  any  other  of  the 
properties  of  animals :  while  if,  with  Cuvier,  we  compare  and  class 
them  according  to  the  structure  of  the  skeleton,  or,  with  Blainville, 
according  to  the  nature  of  their  outward  integuments,  the  agreements 
and  differences  which  are  observable  in  these  respects  are  not  only  of 
much  greater  importance  in  themselves,  but  are  marks  of  agreements 
and  differences  in  many  other  most  important  particulars  of  the  struc- 
ture and  mode  of  life  of  the  animals.  If,  therefore,  the  study  of  their 
structure  and  habits  be  our  object,  the  conceptions  generated  by  these 
last  comparisons  are  far  more  "  appropriate"  than  those  generated  by 
the  former.  Nothing,  other  than  this,  can  be  meant  by  the  appropri- 
ateness of  a  conception. 

When  Mr.  Whewell  says  that  the  ancients,  or  the  schoolmen,  or  any 
modern  philosophers,  missed  discovering  the  real  law  of  a  phenomenon 
because  they  applied  to  it  an  inappropriate  instead  of  an  appropriate 
conception  ;  he  can  only  mean  that  in  comparing  various  instances  of 
the  phenomenon,  to  ascertain  in  what  those  instances  agreed,  they 
missed  the  important  points  of  agi-eement ;  and  fastened  upon  such  as 
were  either  imaginary,  and  no  agreements  at  all,  or  if  real  agreements, 
were  comparatively  trifling,  and  had  no  connexion  with  the  phenom- 
enon, the  law  of  which  was  sought. 

Aristotle,  philosophizing  on  the  subject  of  motion,  remarked  that 
certain  motions  apparently  take  place  spontaneously  ;  bodies  fall  to  the 
ground,  flame  ascends,  bubbles  of  air  rise  in  water,  &c :  and  these  he 
called  natural  motions  ;  while  others  not  only  never  take  place  vrithout 
external  incitement,  but  even  when  such  incitement  is  applied,  tend 
spontaneously  to  cease  ;  which,  to  distinguish  them  from  the  former, 
he  called  violent  motions.  Now,  in  comparing  the  so-called  natural 
motions  with  one  another,  it  appeared  to  Aristotle  that  they  agreed  in 
one  circumstance,  namely,  that  the  body  which  moved  (or  seemed  to 
move)  spontaneously,  was  moving  towards  its  own  place;  meaning 


ABSTRACTION.  395 

thereby  the  place  from  whence  it  originally  came,  or  the  place  whore 
a  great  quantity  of  matter  similar  to  itself  was  assembled.  In  the  other 
class  of  motions,  as  when  bodies  are  thrown  up  in  the  air,  they  are,  on 
the  contrary,  mo\mgf/om  their  own  place.  Now,  this  conception  of 
a  body  moving  towards  its  own  place  may  justly  be  considered  inap- 
propriate ;  because,  though  it  expresses  a  circumstance  really  found  in 
some  of  the  most  famiHar  instances  of  motion  apparently  spontaneous, 
yet,  Jirsf,  there  are  many  other  cases  of  such  motion,  in  which  that  cir- 
cumstance is  absent:  the  motion,  for  instance,  of  the  earth  and  planets. 
Secondly,  even  when  it  is  present,  the  motion,  on  closer  examination, 
would  often  be  seen  not  to  be  spontaneous :  as,  when  air  rises  in  water, 
it  docs  not  rise  by  its  own  nature,  but  is  pushed  up  by  the  superior 
weight  of  the  water  which  presses  upon  it.  Fhially,  there  are  many 
cases  in  which  the  spontaneous  motion  takes  place  in  the  contrary 
direction  to  what  the  theory  considers  as  the  body's  own  place  ;  for 
instance,  when  a  fog  rises  from  a  lake,  or  when  water  dries  up.  There 
is,  therefore,  no  agi-eement,  but  only  a  superficial  semblance  of  agree- 
ment, which  vanishes  on  closer  inspection :  and  hence  the  conception 
is  "  inappropriate."  We  may  add  that,  in  the  case  in  question,  no  con- 
ception would  be  appropriate;  there  is  no  agreement  which  runs 
through  all  the  cases  of  spontaneous,  or  apparently  spontaneous,  mo- 
tion :  they  cannot  be  brought  under  one  law — it  is  a  case  of  Plurality 
of  Causes.* 

§  5.  So  much  for  the  first  of  Mr.  Wlievvell's  conditions,  that  concep- 
tions must  be  appropriate.  The  second  is,  that  they  shall  be  "clear;" 
and  let  us  consider  what  thi-s  implies.  Unless  the  conception  corre- 
sponds to  a  real  agreement,  it  has  a  worse  defect  than  that  of  not  being 
clear ;  it  is  not  applicable  to  the  case  at  all.  Among  the  phenomena, 
therefore,  which  we  ai'e  attempting  to  connect  by  mefuis  of  the  con- 
ception, we  must  suppose  that  there  really  is  an  agreement,  and  that 
the  conception  is  a  conception  of  that  agreement.  In  order,  then,  that 
it  should  be  clear,  the  only  requisite  is,  that  we  shall  know  exactly  in 
what  tho  agreement  consists;  that  it  shall  have  been  carefully  observed, 
and  accurately  remembered.  We  are  said  not  to  have  a  clear  concep- 
tion of  the  resemblance  among  a  set  of  objects,  when  we  have  only  a 
general  feeling  that  they  resemble,  without  having  analyzed  their 
resemblance,  or  perceived  in  what  points  it  consists,  and  fixed  in  our 
memoiy  an  exact  recollection  of  those  points.  This  want  of  clearness, 
or,  as  it  may  be  otherwise  called,  this  vagueness,  in  the  general  con- 

*  Other  examples  of  inappropriate  conceptions  are  given  by  Mr.  Whevvell  (Phil.  Iml.  Sc. 
ii.,  185),  as  follows: — "Aristotle  and  his  followers  endeavored  in  vain  to  accoont  for  the 
mechanical  relation  of  forces  in  the  lever,  by  applying  the  inapjiropriate  geometrical  con- 
ceptions of  the  properties  of  the  circle  :  they  failed  in  explaining  the  form  of  the  luminous 
spot  made  by  the  sun  shining  through  a  hole,  tecause  they  applied  the  inappropriate  con- 
ception of  a  circular  quality  in  the  sun's  light :  they  speculated  to  no  purpose  about  the 
elementary  composition  of  bodies,  because  they  assumed  the  inappropriate  conception  of 
likeness  between  the  elements  and  the  compound,  instead  of  the  genuine  notion  of  elements 
merely  determining  the  qtialilies  of  the  compound."  Rut  in  these  cases  there  is  more  than 
an  inappropriate  conception  ;  there  is  a  false  conception  ;  one  which  has  no  prototype  in 
nature,  nothing  corresponding  to  it  in  facts.  This  is  evident  in  the  last  two  examples,  and 
is  equally  true  in  the  first;  the  "  properties  of  the  circle"  which  were  referred  to,  being 
purely  fantastical.  There  is,  therefore,  an  error  beyond  the  wrong  choice  of  a  principle  oi 
generalization  ;  there  is  a  false  assumption  of  matters  of  fact.  The  attempt  is  made  to  re- 
solve certain  laws  of  nature  into  a  more  general  law,  that  law  being  not  one  which,  though 
real,  is  inappropriate,  but  one  wholly  imaginary. 


396  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

ception,  may  be  owing  either  to  our  having  no  accurate  knowledge  of 
the  objects  themselves,  or  merely  to  our  not  having  carefully  compared 
them.  Thus  a  person  may  have  no  clear  idea  of  a  ship  because  he  has 
never  seen  one,  or  because  he  remembers  but  little,  and  that  faintly, 
of  what  he  has  seen.  Or  he  may  have  a  perfect  knowledge  and 
remembrance  of  many  ships  of  various  kinds,  frigates  among  the  rest, 
but  he  may  have  no  clear  but  only  a  confused  idea  of  a  frigate,  because 
he  has  not  compared  them  sufficiently  to  have  remarked  and  remem- 
bered in  what  particular  points  a  frigate  differs  from  some  other  kind 
of  ship. 

It  is  not,  however,  necessary,  in  order  to  have  clear  ideas,  that  we 
should  know  all  the  common  properties  of  the  things  which  we  class 
together.  That  would  be  to  have  our  conceptions  of  the  class  com- 
plete as  well  as  clear.  It  is  sufficient  if  we  never  class  things  together 
without  knowing  exactly  why  we  do  so  —  without  having  ascertained 
exactly  what  agi'eements  we  are  about  to  include  in  our  conception ; 
and  if,  after  having  thus  fixed  our  conception,  we  never  vary  from  it, 
never  include  in  the  class  anything  which  has  not  those  common 
properties,  nor  exclude  from  it  anything  which  has.  A  clear  concep- 
tion means  a  determinate  conception;  one  which  does  not  fluctuate, 
which  is  not  one  thing  to-day  and  another  to-morrow,  but  remains  fixed 
and  invariable,  except  when,  from  the  progress  of  our  knowledge,  or 
the  correction  of  some  error,  we  consciously  add  to  it  or  alter  it. 
A  person  of  clear  ideas,  is  a  person  who  always  knows  in  virtue  of 
what  properties  his  classes  are  constituted ;  what  attributes  are  con- 
noted by  his  general  names. 

The  principal  requisites,  therefore,  of  clear  conceptions,  are  habits 
of  attentive  observation,  an  extensive  experience,  and  a  memory  which 
receives  and  retains  an  exact  image  of  what  is  obsei-ved.  And  in 
proportion  as  any  one  has  the  habit  of  obsei'ving  minutely  and  com- 
paring carefiilly  a  particular  class  of  phenomena,  and  an  accurate 
memory  for  the  results  of  the  observation  and  comparison,  so  will  his 
conceptions  of  that  class  of  phenomena  be  clear ;  provided  he  has  the 
indispensable  habit,  (naturally,  however,  resulting  from  those  other 
endowments,)  of  never  using  general  names  without  a  precise  con- 
notation. 

As  the  clearness  of  our  conceptions  chiefly  depends  upon  the  care- 
fulness and  accuracy  of  our  observing  and  comparing  faculties,  so  their 
appropriateness,  or  rather  the  chance  we  have  of  hitting  upon  the 
appropriate  conception  in  any  case,  mainly  depends  upon  the  activity 
of  the  same  faculties.  He  who  by  habit,  grounded  on  sufficient  naturaJ 
aptitude,  has  acquired  a  readiness  in  accurately  obsei"ving  and  com- 
paring phenomena,  will  perceive  so  many  more  agreements  and  will 
perceive  them  so  much  more  rapidly  than  other  people,  that  the  chances 
are  much  greater  of  his  perceiving,  in  any  instance,  the  agreement  on 
which  the  important  consequences  depend. 

§  6.  We  are  not,  at  the  same  time,  to  forget,  that  the  agreement 
cannot  always  be  discovered  by  mere  comparison  of  the  very  phenom- 
ena in  question,  without  the  aid  of  a  conception  acquired  elsewhere  ; 
as  in  the  case,  so  often  referred  to,  of  the  planetary  orbits. 

The  search  for  the  agreement  of  a  set  of  phenomena  is  in  truth 
very  similar  to  the  search  for  a  lost  or  hidden  object.     At  first  we  placQ 


NAMING.  397 

ourselves  in  a  sufficiently  commantline;  position,  and  cast  our  eyes 
round  us,  and  if  we  can  see  the  object,  it  is  well ;  if  not,  we  ask  our- 
selves mentally  what  are  the  places  in  which  it  may  be  hid,  in  order 
that  we  may  there  search  for  it :  and  so  on,  until  we  imagine  the  place 
where  it  really  is.  And  here  too  we  nujuire  to  have  had  a  previous 
conception,  or  knowledge,  of  those  different  places.  As  in  this  fa- 
miliar process,  so  in  the  philosophical  operation  which  it  illustrates, 
we  first  endeavor  to  find  the  lost  object  or  recognize  the  common 
atti'ibute,  without  conjecturally  invoking  the  aid  of  any  pr-eviously 
acquired  conception,  or  in  other  words,  of  any  hypothesis.  Having 
failed  in  this,  we  call  upon  our  nnagination  for  some  hypothesis  of  a 
possible  place,  or  a  possible  point  of  resemblance,  and  then  look,  to 
see  whether  the  facts  agree  with  the  conjecture. 

For  such  cases  something  more  is  required  than  a  mind  accustomed 
to  accurate  bbservation  and  comparison.  It  must  be  a  mind  stored 
with  general  conceptions,  previously  acquired,  of  the  sorts  ^vhich  bear 
affinity  to  the  subject  of  the  particular  inquiry.  And  much  will  also 
depend  upon  the  natural  strength  and  acquired  culture  of  what  has 
been  tenned  the  scientific  imagination ;  upon  the  faculty  possessed  of 
mentally  arranging  known  elements  into  new  combinations  such  as 
have  not  yet  been  observed  in  nature,  though  not  contradictory  to  any 
known  laws. 

But  the  variety  of  intellectual  habits,  the  purposes  which  they  sei-ve, 
and  the  modes  in  which  they  may  be  fostered  and  cultivated,  are  con- 
siderations belonging  to  the  Art  of  Education :  a  subject  far  wider 
than  Logic,  and  which  the  present  treatise  does  not  profess  to  discuss. 
Here,  therefore,  the  present  chapter  may  properly  close.  It  constitutes 
a  real  digi'ession  from  the  main  purpose  of  this  work ;  to  which  no- 
thing would  have  tempted  me  but  the  apparent  necessity,  in  promul- 
gating a  view  of  induction  opposed  to  that  which  is  taught  by  an 
eminent  living  wi'iter,  of  not  shrinking  from  an  encounter  with  him  on 
his  own  ground,  but  entering  sufficiently  into  the  spirit  of  his  views 
to  show  how  much  of  the  difference  is  apparent  and  how  much  real; 
what  is  the  equivalent  expression  for  his  doctrines  in  my  own  language ; 
and  what  are  the  reasons  which  lead  me,  even  where  the  opinions  are 
similar,  to  adopt  a  different  mode  of  statement. 


CHAPTER  III. 

OF   NAMING,   AS  SUBSIDIARY  TO   INDUCTION. 

§  1.  It  does  not  belong  to  the  present  undertaking  to  dwell  on  the 
importance  of  language  as  a  medium  of  human  intercourse,  whether 
for  puqioses  of  sympathy  or  information.  Nor  does  our  design  admit 
of  more  than  a  passing  allusion  to  that  groat  property  of  names,  upon 
which  their  functions  as  an  intellectual  instrument  are,  in  reality,  ulti- 
mately dependent ;  their  potency  as  a  means  of  forming,  and  of  rivet- 
ing, associations  among  our  other  ideas :  a  subject  on  which  an  able 
thinker  has  thus  written  : — 

"  Names  are  impressions  of  sense,  and  as  such  take  the  strongest 


398  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

hold  on  the  mind,  and  of  all  other  impressions  can  be  most  easily  re- 
called and  retained  in  view.  They  therefore  serve  to  give  a  point  of 
attachment  to  all  the  moi'e  volatile  objects  of  thought  and  feeling. 
Impressions,  that  when  past  might  be  dissipated  for  ever,  are,  by  their 
connexion  with  language,  always  within  reach.  Thoughts,  of  them- 
selves, are  perpetually  slipping  out  of  the  field  of  immediate  mental 
vision ;  but  the  name  abides  with  us,  and  the  utterance  of  it  restores 
them  in  a  moment.  Words  are  the  custodiers  of  every  product  of 
mind  less  impressive  than  themselves.  All  extensions  of  human  knowl- 
edo-e,  all  new  generalizations,  are  fixed  and  spread,  even  uninten- 
tionally, by  the  use  of  words.  The  child  growing  up  leanis,  along 
with  the  vocables  of  his  mother-tongue,  that  things  which  he  would 
have  believed  to  be  different,  are,  in  important  points,  the  same. 
Without  any  formal  instruction,  the  language  in  which  we  gi'ow  up 
teaches  us  all  the  common  philosophy  of  the  age.  It  directs  us  to  ob- 
serve and  know  things  which  we  should  have  overlooked ;  it  supplies 
us  with  classifications  ready  made,  by  which  things  are  arranged  (as 
far  as  the  light  of  by-gone  generations  admits)  with  the  objects  to 
which  they  bear  the  greatest  total  resemblance.  The  number  of 
general  names  in  a  language,  and  the  degree  of  generality  of  those 
names,  afford  a  test  of  the  knowledge  of  the  era,  and  of  the  intellectual 
insight  which  is  the  birth-right  of  any  one  born  into  it." 

It  is  not,  however,  of  the  functions  of  Names,  considered  generally, 
that  we  have  here  to  treat,  but  only  of  the  manner  and  degree  in  which 
they  are  directly  instrumental  to  the  investigation  of  truth ;  in  other 
words,  to  the  process  of  induction. 

§  2.  Observation  and  Abstraction,  the  operations  which  formed  the 
subject  of  the  two  foregoing  chapters,  are  conditions  indispensable  to 
induction  :  there  can  be  no  induction  where  they  are  not.  It  has  been 
imagined  that  Naming  is  also  a  condition  equally  indispensable.  There 
are  philosophers  who  have  held  that  language  is  not  solely,  according 
to  a  phrase  generally  cuiTent,  an  instrument  of  thought,  but  the  instru- 
ment :  that  names,  or  something  equivalent  to  them,  some  species  of 
artificial  signs,  are  necessary  to  reasoning ;  that  there  could  be  no  in- 
ference, and  consequently  no  induction,  without  them.  But  if  the 
nature  of  reasoning  was  correctly  explained  in  the  earlier  part  of  the 
present  work,  this  opinion  must  be  held  to  be  an  exaggeration,  though 
of  an  important  tmth.  If  reasoning  be  from  particulars  to  particulars, 
and  if  it  consist  in  recognizing  one  fact  as  a  mark  of  another,  or  a 
mark  of  a  mark  of  another,  nothing  is  required  to  render  reasoning 
possible  except  senses,  and  association :  senses,  to  perceive  that  two 
facts  are  conjoined;  association,  as  the  law  by  which  one  of  those  two 
facts  raises  up  the  idea  of  the  other.  For  these  mental  phenomena,  as 
well  as  for  the  belief  or  expectation  which  follows,  and  by  which  we 
recognize  as  having  taken  place,  or  as  about  to  take  place,  that  of 
which  we  have  perceived  a  mark,  there  is  evidently  no  need  oi  lan- 
guage. And  this  inference  of  one  particular  fact  fi-om  another  is  a 
case  of  induction.  It  is  of  this  sort  of  induction  that  brutes  are  capable ; 
it  is  in  this  shape  that  uncultivated  minds  make  almost  all  their  induc- 
tions, and  that  we  all  do  so  in  the  cases  in  which  familiar  experience 
forces  our  conclusions  upon  us  without  any  active  process  of  inquiry 
on   our   part,   and   in  which   the  belief  or   expectation  follows   the 


NAMING.  399 

suggestion  of  the  evidence,  with  tlie  promptitude  and  certainty  of  an 
instinct. 

§  3.  But  although  inf(;roiicc  of  an  inductive  character  is  possible 
without  the  use  of  signs,  it  could  never,  without  them,  be  canned  much 
beyond  the  very  simple  cases  which  wc  have  just  described,  and  which 
form,  in  all  probability,  the  limit  of  the  reasonings  of  those  animals  to 
whom  conventional  language  is  unknown.  Without  language,  or  some- 
thing equivalent  to  it,  there  could  only  be  as  much  of  reasoning  from 
experience,  as  can  take  place  \\-ithout  the  aid  of  general  propositions. 
Now,  although  in  strictness  wc  may  reason  from  past  experience  to  a 
fiesh  individual  case  without  the  intermediate  stage  of  a  general  pro- 
position, yet  without  general  propositions  we  should  seldom  remember 
what  experience  we  have  had,  and  scarcely  ever  what  conclusions  that 
experience  will  warrant.  The  division  of  the  inductive  process  into 
two  paits,  the  first  ascertaining  what  is  a  mark  of  the  given  fact,  the 
second  whether  in  the  new  case  that  mark  exists,  is  natural,  and 
scientifically  indispensable.  It  is,  indeed,  in  a  majority  of  cases, 
rendered  necessary  by  mere  distance  of  time.  The  experience  by 
which  we  are  to  guide  our  judgments  may  be  other  people's  expe- 
rience, little  of  which  can  be  communicated  to  us  otherwise  than  by 
language ;  when  it  is  our  own,  it  is  generally  experience  long  past ; 
unless,  therefore,  it  were  recorded  by  means  of  artificial  signs,  little  of 
it  (except  in  cases  involving  our  intenser  sensations  or  emotions,  or  the 
subjects  of  our  daily  and  hourly  contemplations)  would  be  retained  in 
the  memory.  It  is  hardly  necessary  to  add,  that  when  the  inductive 
inference  is  of  any  but  the  most  direct  and  obvious  nature — when  it 
requires  several  observations  or  experiments  in  varying  circumstances, 
and  the  comparison  of  one  of  these  with  another — it  is  impossible  to 
proceed  a  step,  without  the  artificial  memory  which  words  bestow, 
without  words,  we  should,  if  we  had  often  seen  A  and  B  in  imme- 
diate and  obvious  conjunction,  expect  B  whenever  we  saw  A;  but  to 
discover  their  conjunction  when  not  obvious,  or  to  determine  whether 
it  is  really  constant  or  only  casual,  and  whether  there  is  reason  to  ex- 
pect it  under  any  given  change  of  circumstances,  is  a  process  far  too 
complex  to  be  performed  without  some  contrivance  to  make  our 
remembrance  of  our  own  mental  oj^erations  accurate.  Now,  language 
is  such  a  contrivance.  Wlien  that  instrument  is  called  to  our  aid,  the 
difficulty  is  reduced  to  that  of  making  our  remembrance  of  the  mean- 
ing of  words  accurate.  This  being  secured,  whatever  passes  through 
our  minds  may  be  remembered  accurately,  by  putting  it  carefully  into 
words,  and  committing  the  words  either  to  writing  or  to  memory. 

The  function  of  Naming,  and  particularly  of  General  Names,  in  In- 
duction, may  be  recapitulated  as  follows.  Every  inductive  inference 
which  is  good  at  all,  is  good  for  a  whole  class  of  cases  ;  and,  that  the 
inference  may  have  any  better  warrant  of  its  coiTectness  than  the  mere 
clinging  together  of  two  ideas,  a  process  of  experimentation  and  com- 
paris(m  is  necessary ;  in  which  the  whole  class  of  cases  must  be 
brought  to  view,  and  some  uniformity  in  the  course  of  nature  evolved 
and  ascertained,  since  the  existence  of  such  an  uniformity  is  required 
as  a  justification  for  drawing  the  inference  in  even  a  single  case.  This 
uniformity,  therefore,  may  be  ascertained  once  for  all ;  and  if,  being 
ascertained,  it  can  be  remembered,  it  will  serve   as   a  formula  for 


400  OPERATIONS    SUBSIDIAUY   TO  INDUCTION. 

making  in  particular  cages  all  sucli  inferences  as  the  previous  experi- 
ence will  warrant.  But  we  can  only  secure  its  being  remembered, 
oj  give  ourselves  even  a  chance  of  carrying  in  our  memory  any  con- 
siderable number  of  such  uniformities,  by  registering  them  through,  the 
medium  of  permanent  signs;  which  (being  from  the  nature  of  the  case, 
signs  not  of  an  individual  fact  but  of  an  uniformity,  that  is,  of  an  indefi- 
nite number  of  facts  similar  to  one  another)  are  general  signs ;  uni- 
versals;  general  names,  and  general  propositions. 

§  4.  And  here  I  cannot  omit  to  notice  an  oversight  committed  by 
some  eminent  metapbysicians ;  who  have  said  that  the  cause  of  our 
using generalnames  is  the  infinite  multitude  of  individual  objects,  which, 
making  it  impossible  to  have  a  name  for  each,  compels  us  to  make 
one  name  serve  for  many.  This  is  a  very  limited  view  of  the  func- 
tion of  general  names.  Even  if  there  were  a  name  for  every  individual 
object,  we  should  require  general  names  as  much  as  we  now  do. 
Without  them  we  could  not  express  the  result  of  a  single  comparison, 
nor  record  any  one  of  the  uniformities  existing  in  nature  ;  and  should 
be  hardly  better  off  in  respect  to  Induction  than  if  we  had  no  names 
at  all.  With  none  but  names  of  individuals  (or,  in  other  words,  proper 
names),  we  might  by  pronouncing  the  name,  suggest  the  idea  of  the  ob- 
ject, but  we  could  not  assert  a  single  proposition  ;  except  the  unmean- 
ing ones  formed  by  predicating  two  proper  names  one  of  another.  It  is 
only  by  means  of  general  names  that  we  can  convey  any  information, 
predicate  any  attribute,  even  of  an  individual,  much  more  of  a  class. 
Rigorously  speaking  we  could  get  on  without  any  other  general  names 
than  the  abstract  names  of  attributes ;  all  our  propositions  might  be  of 
the  form  "  such  an  individual  object  possesses  such  an  attribute,"  or 
"  such  an  attribute  is  always  (or  never)  conjoined  with  such  another 
attribute."  In  fact,  however,  mankind  have  always  given  general 
names  to  objects  as  well  as  attributes,  and  indeed  before  attributes: 
but  the  general  names  given  to  objects  imply  attributes,  derive  their 
whole  meaning  from  attributes ;  and  are  chiefly  usefiil  as  the  language 
by  means  of  which  we  predicate  the  attributes  which  they  connote. 

It  remains  to  be  considered  what  principles  are  to  be  adhered  to  in 
giving  general  names,  so  that  these  names,  and  the  general  propositions 
in  which  they  fill  a  place,  may  conduce  most  to  the  purposes  of  Induc- 
tion. 


CHAPTER  IV. 

OF  THE  REQUISITES  OF  A  PHILOSOPHICAL   LANGUAGE  ;  AND  THE  PRINCIPLES  OF 
DEFINITION. 

§  1.  In  order  that  we  may  possess  a  language  perfectly  suitable  for 
the  investigation  and  expression  of  general  truths,  there  are  two  prin- 
cipal, and  several  minor,  requisites.  The  first  is,  that  every  general 
name  should  have  a  meaning,  steadily  fixed,  and  precisely  determined. 
When,  by  the  fulfilment  of  this  condition,  such  names  as  we  possess 
are  fitted  for  the  due  performance  of  their  functions,  the  next  requisite, 
and  the  second  in  order  of  importance,  is  that  we  should  possess  a 


REaUISITES    OP    LANGUA&E.    •  401 

name  wherever  one  is  needed;  wherever  there  is  anything  to  he  desig- 
nated by  it,  which  it  is  of  iniportartce  to  express.  . 

The  I'ornier  of  these  requisites  is  that  to  which  our  attention  will  be 
exclusively  directed  in  the  present  diapter. 

§  2.  Every  general  name,  tlicn,  must  have  a  certain  and  knowablo 
meaning.  Now  the  meaning  (as  has  -so  often  been"  explained)  of  a 
general  connotative  name,  resides  in  the  connotation ;  in  the  attribute 
on  accouiit  of  which,  and  to  express  which,  the  name  is  given.  Thus, 
tlie  name  animal  being  given  to  all  things  which  possess  the  attributes 
of  sensation  and  voluntary  moti(in,  the  word  connotes  tliose  attributes 
exclusively,  and  they  constitute  the  whole  of  its  meaning.  If  the 
name  be  abstract,  its  denotation  is  the  same  with  the  connotation 
of  the  corresponding  concrete:  it  designates  di^rectly  the  attribute, 
which  tire  concrete  term  implies.  •  To  give  a  precise  meaning  to 
general  names  is,  then,  to  fix  with  steadii>ess  the  attribute  or  attributes 
connoted  by  each  concrete  general  name,  and  denoted  by  the  coire- 
sponding  abstract.  Since  -abstract  names,  in  the  order  of  their  creation, 
do  not  precede  but  follow  concrete  ones,  as  is  proved  by  the,  etymolo- 
gical fact  that  they  are  almost  always  derived  from  them ;  we  may 
consider  their  meaning  as.  determined  by,  and  dependent  npon,  the 
meaning  of  their  concrete  :  and  thus  the  problem  of  giving  a  distinct 
meaning  to  general  language,  is  all  included  in  that  of  giving  a  precise 
connotation  to  all  concrete  general  names. 

This  is  not  difficult  in  the  case  of  new  names  ;''  of  the  technical  terms 
created  by  philosophic  inquirers  for  the  purposes  of  science  or  art. 
But  when  a  name  is  in  common  use,  the  difficulty  is  greater  ;  the  pro- 
blem in  this  case  not  being  that  df  choosing  a  convenient  connotation 
for  the  name,  but  of  ascertaining  and  fixing  the  connotation  with  which 
it  is  already  used.  That  thie  can  ever  be  a  matter  of  doubt,  is  a  sort 
of  paradox.  But  the  vulgar  (including  in  that  term  all  who  have  not 
accurate  habits  of  thought)  seldom  know  exactly  what  assertion  they 
intend  to  make,  what  common  property  th^y  mean  to  express,  when 
they  apply  the  same  name  to  a  immber  of  different  things.  All  which 
the  name  expresses  with  them,  when  they  predicate  it  of  an  object,  is 
a  confused  feeling  of  resemblance  between  that  object  and  some  of  the 
other  things  which  they  have  been  accustomed  to  denote  by  the  name. 
They  have  applied  the  name  Stone  to  various  objects  previously  seen  ; 
they  see  a  new  object,  which  appears  to  ihem  something  like  the 
former,  and  they  call  it  a  stone,  without  asking  thcrnselves  in  what 
respect  it  is  like,  or  what  mode  or  degree  of  teserhblance  the  best 
authorities,  or  even  they  themselves,  requixc  as  a  waiTant  for  using 
the  name.  This  rough,  general  impression  of  resemblance  is,  how- 
ever, made  up'  of  particular  circumstaiices  of  resemblance ;  and  into 
these  it  is  the  business  of  the  logician  to  analyze  it ;  to  ascertain  what 
points  of  resemblance  among  the  different  things  commonly  called  by 
the  name,  have  pivjduced  upon  the  common  mind  this  vague  feeling  of 
likeness  ;  have  given  to  the  things  the  similarity  of  aspect,  which  has 
made  them  a  class,  and  has  caused  the  same  name  to  be  bestowed 
upon  them.  '    •  , 

But  although  general  hames,  aie  imposed  by  the  vulgar  without  any 
more  definite  connotation  than  that  <»f  a  vague  resemblance  ;  general 
propositions  come  in  time  to  be,  made,  in  wliich  predicates  are  applied 
3E 


402  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

to  those  names,  that  is,,  general  assertions  are  made  concerning  the 
whole  of  the  things  which  are  denoted  by  the  name.  And  since  by  each 
of  these  propositions  some  attribute,  .more  or  less  precisely  conceived, 
is  of  com-se  predicated,  the  idea  of  these  varittus  attributes  thus  be- 
comes associated  with  the  name,  and  in  a.  scrrt  of  uncertain  way  it 
comes  to  connote  them;  there  is  a  hesitation  to  apply  the  name  in  any 
new  case  in  which  any  of  the  attributes  familiarly  predicated  of  the 
class  does  not  exist.  And  thus  to  common  minds,  the  propositions 
which  they  are  in  the  habit  of  hearing  or  uttering  concerning  a  class, 
make  up  in  a  loose  way  a  sort  of  connotation  for  the  class-name.  Let 
us  take,  for  instance,  the  word  Civilized.  How  few  could  be  found, 
even  among  the  most  educated  persons,  who  would  undertake  to  say 
exactly  what  the  term  Civilized  connotes.  Yet  there  is  a  feeling  in 
the  minds  of  all  who  use  it,  that  they  are  using  it  with  a  meaning; 
and  this  meaning  is  made  up,  in  a  confused  manner,  of  everything 
which  they  have  heard  or  read  that  civilized  men  or  civilized  commu- 
nities, are,  or  should  be. 

It  is  at  this  stage,  probably,  in  the  progress  of  a  concrete  name,  that 
the  corresponding  abstract  name  generally  comes  into  use..  Under 
the  notion  that  the  concrete, name- must  of  course  convey  a  meaning, 
or  in  other  words,  that  there  is  some  property  common  to  all  things 
which  it  denotes,  men  give  a  name  to  this  common  property ;  from 
the  concrete  Civilized,  they  form  the  abstract  Civilization.  But  since 
most  people  have  never  compared  the  different  things  which  are  called 
by  the  concrete  name,  in  such  a  manner  as  to  ascertain  what  proper- 
ties these  things  have  in  common,  or  whether  they  have  any;  each  is 
thrown  back  upon  the  marks  by  wliich  he  himself  has  been  accustomed 
to  be  guided  in  his  application  of  the  term  :  and  these  being  merely 
vague  hearsays  and  cun-ent  phrases,  are  not  the  same  in  any  two  per- 
sons, nof  in  the  same  person  at  different  times.  Hence  the  word  (as 
Civilization,  for  example,)  which  professes  to  be  the  designation  of  the 
unknown  common  property^  conveys  scarcely  to  any  two  minds  the 
same  idea.  No  two  persons  agree  in  the  things  they  predicate  of  it ; 
and  when  it  is  itself  predicated  of  anything,  no  other  person  knows, 
nor  does  the  speaker  himself  know  with  precision,  what  he  means 
to  assert.  Many  other  words  which  could  be  named,  as  the  word 
honor,  or  the  word  gentleman,  exemplify  this  uncertainty  still  more 
strikingly. 

It  needs  scarcely  be  observed,  that  general  propositions  of  which 
no  one  can  tell  exactly  what  they  assert,  cannot  possibly  have  been 
brought  to  the  test  of  a  connect  induction.  Whether  a  name  is  to  be 
used  as  an  instrument  of  thinking,  or  as  a  means  of  communicating  the 
result  of  tliought,  it  is  imperative  to  determine  exactly  the  attribute  or 
attributes  which  it  is  to  express  :  to  give  it,  in  short,  a. fixed  and  ascer- 
tained connotation. 

§  3.  It  would,  however,  be  a  complete  misunderstanding  of  the 
proper  office  of  a  logician,  in  dealing  with  terms  already  in  use,  if  he 
were  to  think  that  because  a  name  has  not  at  present  an  ascertained 
connotation,  it  is  competent  to  any  one  to  give  it  such  a  connotation  at 
his  own  choice.  The  meaning  of  a  term  actually  in  use  is  not  an  ar- 
bitrary quantity  to  be  fixed,  but  an  unknown  quantity  to  Tae  sought. 

In  the  first  place,  it  is  obviously  desirable  to  avail  oui'selves,  as  far 


REaUISITES    OF    LANGUAGE.  403 

as  possible,  of  the  associations  alrefady  connected  with  the  name ;  not 
enjoining  the  employment  of  it  in  a  manner  which  confli'cts  with  all 
previous  hahits,  and  especially  not  so  as  to  require  the  rupture  of  those 
strongest  of  all  associations  between  names,  which  are  created  by 
famiharity  with  in-()j)ositions  in  whicli  they  are  predicated  of  otio  another. 
A  philosopher  would  have  little  chance  of  having  his  example  followed, 
if  he  were  to  gire  such  a  metuiing  to  his  terms  as  should  recjuire  us  to 
call  the  North  American  Indians  a  civilized  people,  or  the  higher  classes 
in  France  or  England  savages ;  or  to  say  that  civilized  people  live  by 
lumting,  and  savages  by  agriculture.  Were  there  no  other  reason,  the 
extreme  difficulty  of  eftecting  so  complete  a  revolution  in  speech,  would 
be  more  than  a  sufficient  one.  The  endeavor  should  be,  that  all  gen- 
erally received  propositions  into  which  the  term  enters,  should  be  at 
least  as  tiue  after  its  meaning  is  fixed,  as  they  were  before ;  and  that 
the  concrete  name  (therefore)  should  not  receive  such  a  connotation  as 
shall  prevent  it  from  denoting  things  which,  in  common  language,  it  is' 
currently  affimied  of.  The  fixed  and  precise  connotation  which  it 
receives,  should  not  be  in  doNaation  from,  but  in  agreement  (as  far  as 
it  goes)  with,  the  vague  and  fluctuating  cotihotation  which  the  term 
already  had. 

To  fix  the  connotation  of  a  concrete  name,  or  the  denotation  of  the 
coiTesponding  abstract,  is  to  define  the  name.  When  this  can  be  done 
without  rendering  any  received  assertions  inadmissible,  the  name  can 
be  defined  in  accoi'dance  with  its  received  use,  which  is  vulgarly  called 
defining  not  the  name  but  the  thing.  What  is  meant  by  the  improper 
expression  of  defining  a  thing  (or  rather  a  class  of  things  —  for  nobody 
talks  of  defining  an  individual),  is  to  define  the  name,  subject  to  the 
condition  that  it  shall  denote  those  things.  This,  of  course,  supposes 
a  comparison  of  the  things,  feature  by  feature  and  property  by  prop- 
erty, to  ascertain  what  attributes  they  agi'ee  in ;  and  not  unfrequently 
an  operation  still  more  strictly  inductive,  for  the  purpose  of  ascertain- 
ing some  unobvious  agreement  which  is  the  cause  of  the  obvious 
agreements. 

For,  in  order  to  give  a  connotation  to  a  name  consistently  with  its 
denoting  certain  objects,  we  have  to  make  our  selection  from  among 
the  various  attributes  in  which  those  objects  agree.  To  ascertain  in 
what  they  do  agree  is,  therefore,  the  first  logical  operation  requisite. 
When  this  has  been  done  as  far  as  is  necessary  or  practicable,  the 
question  arises,  which  of  these  common  attributes  shall  be  selected  to 
be  associated  with  the  name.  For  if  the  class  which  the  name  denotes 
be  a  Kind,  the  common  properties  are  innumerable ;  and  even  if  not, 
they  are  often  extuemely  numerous.  Our  choice  is  first  limited  by  the 
preference  to  be  given  to  properties  which  are  well  known,  and 
familiarly  predicated  of  tlie  class  ;  "but  even  those  are  often  too  numer- 
ous to  be  all  included  in  the  definition,  and,  besides,  the  properties 
most  generally  known  may  not  be  those  which  serve  best  to  mark  out 
the  class  from  all  others.  We  should  therefore  select  fi-om  among  the 
common  properties  (if  among  them  any  such  are  to  be  found),  those 
on  which  it  has  beeu  ascertained  by  experience,  or  proved  by  deduc- 
tion, that  many  otliers  depend ;  or  at  least  which  arc  sure  marks  of 
them,  and  from  whence,  therefore,  many  others  will  follow  by  inference. 
We  thus  see  that  to  frame  a  good  definition  of  a  name  already  in  use, 
is  not  a  matter  of  choice  but  of  discussion,  aud  discussion  not  merely 


404  OPERATIONS    SUBSIDIARY    TO    INDUCTION, 

respecting  the  usage  of  language,  but  respecting  the  properties  of  things, 
and  even  the  origin  of  those  properties.  And  lience  every  enlarge- 
ment of  our  knowledge  of  the  objects  to  which  the  name  is  applied, 
is  liable  to  suggest  an  improvement  in  the  definition.  It  is  impossible 
to  frame  a  perfect  set  of  definitions  on  any  subject,  until  the  theory  of 
the  subject  is  perfect ;  and  as  science  makes  progi-ess,  its  definitions 
■are  also  progressive. 

§  4.  The  discussion  of  Definitions,  in  so  far  as  it  does  not  turn  upon 
the  use  of  words,  but  upon  the  properties  of  things,  Mr.  Whewell  calls 
the  Explication  of  Conceptions.  The  act  of  ascertaining,  better  than 
before,  in  what  particulars  any  phenomena  which  are  classed  together 
agree,  Mr.  Whewell  in  his  technical  phraseology  calls,  unfolding  the 
general  conception  in  virtue  of  which  they  are  so  classed.  Making 
allowance  for  what  appears  to  me  the  darkening  and  misleading  ten- 
dency of  this  mode  of  expression,  several  of  his  remarks  are  so  much 
to  the  purpose,  that  I  shall  take  the  liberty  of  transcribing  them. 

He  observes,*  that  many  of  the  controversies  which  have  had  an 
important  share  in  the  formation  of  the  existing  body  of  science,  have 
"  assumed  the  form  of  a  battle  of  Definitions.  For  example,  the 
inquiry  concerning  the  laws  of  falling  bodies,  led  to  the  question 
Vi^hether  the  proper  definition  of  a  tmiform  force  is  that  it  generates  a 
velocity  proportional  to  the  space  from  rest,  or  to  the  time.  The  con- 
troversy of  the  vis  viva  was,  what  was  the  proper  definition  of  the 
meastire  of  force.  A  principal  question  in  the  classification  of  minerals 
is,  what  is  the  definition  of  a  mineral  species.  Physiologists  have 
endeavored  to  throw  light  on  their  subject  by  defining  organization, 
or  some  similar  teiTU."  Questions  of  the  same  nature  are  still  open 
respecting  the  definitions  of  Specific  ,  Heat,  Latent  Heat,  Chemical 
Combination,  and  Solution. 

._  "  It  is  very  important  for  us  to  observe,  that  these  controversies 
have  never  been  questions  of  insulated  and  arhitrary  definitions,  as 
men  seem  ofi;en  tempted  to  imagine  them  to  have  been.  In  all  cases 
there  is.  a  tacit,  assumption  of  some  proposition  which  is  to  be  expressed 
by  means  of  the  definition  and  which  gives  it  its  impor-tance.  The 
dispute  concerning  the  definition  thus  acquires  a  real  value,  and  be- 
comes a  question  concerning  true  and  false.  Thus  in  the  discussion. 
of  the  question.  What  is  a  uniform  force  ?  it  was  taken  for  granted 
that  gravity  is  a  uniform  force.  In  the  debate  of  the  vis  viva,  it  was 
assumed  that  in  the  mutual  action  of  bodies  the  whole  effect  of  the 
force  is  unchanged.  In  the  zoological  definition  of  species  (that  it 
coixsists  of  individuals  which  have,  or  may  have,  sprung  from  the  same 
parents,)  it  is  presumed  that  individuals  so  related  resemble  each  othei 
more  than  those  which  are  excluded  by  such  a  definition ;  or,  perhaps, 
that  species  so  defined  have  permanent  and  definite  differences.  A 
definition  of  organization,  or  of  some  other  term,  which  was  not  em- 
ployed to  express  some  principle,  would  be  of  no  value. 
!■•  "  The  establishment,  therefore,  of  a  right  definition  of  a  term,  may 
be  a  useful  step  in  the  explication  of  our  conceptions ;  but  this  will  be 
the  case  then  only  when  we  have  under  our  consideration  some  prop- 
osition in  which  the  term  is  employed.     For  then  the  question  really 

♦  Phil,  of  the  Ind.  Sc.  ii.,  177-9. 


REQUISITES    OF    LANGUAGE.  405 

is,  how  the  conception  shall  be  unJorstood  and  defined  in  order  that 
the  proposition  may  be  true." 

"  To  unfold  our  conceptions  by  means  of  definitions  has  never  been 
serviceable  to  science,  except  when  it  has  been  associated  with  an 
immediate  Tise  of  the  definitions.  The  endeavor  to  define  a  Uniform 
Force  was  combined  with  the  assertion  that  gravity  is  a  uniform  force  : 
the  attempt  to  define  Accelerating  Force  was  immediately  followed  by 
the  doctruie  that  accelerating  forces  maybe  compounded:  the  process 
of  defining  Momentum  was  connected  with  the  principle  that  momenta 
gained  and  lost  are  ecpial :  naturalists  would  Imve  given  in  vain  the 
definition  of  Species  which  we  have  quoted,  if  they  had  not  also  given 

the  characters  of  species  so  sejiarated Dcifinitiou  may  be  the  best 

mode  of  explaining  our  conception,  but  that  which  alone  makes  it 
worth  while  to  explain  it  in  any  mode,  is  the  opportunity  of  using  it  in 
the  expression  of  truth.  When  a  definition  is  jiropounded  to  us  as  a 
useful  ^tep  in  knowledge,  we  are  always  entitled  to  ask  what  principle 
it  serves  to  enunciate." 

In  giving  an  exact  connotation  to  tlie  phrase,  "  an  uniform  force," 
philosophers  (as  JNIr.  Wliewell  observes)  restricted  themselves  by  the 
condition,  that  the  phrase  should  continue  to  denote  gravity.  The 
discussion,  therefore,  respecting  the  definition,  resolved  itself  into  this 
question.  What  is  there  of  an  uniform  nature  in  the  motions  produced 
by  gravity]  By  observations  and  comparisons  it  was  found,  that  what 
was  uniform  in  those  motions  was  the  ratio  of  the  velocity  required  to 
the  time  elapsed;  equal  velocities  being  added  in  equal  terms.  An 
uniform  force,  therefore,  was  defined,  a  force  which  adds  e<jual  veloci- 
ties in  equal  times.  So,  again,  in  defining  momentum.  It  was  already 
a  received  doctrine,  that  when  two  objects  impinge  upon  one  another, 
the  momentum  lost  by  the  one  is  equal  to  that  gained  by  the  other. 
This  proposition  it  was  deemed  necessary  to  preserve,  not  however 
from  the  motive  (which  operates  in  many  other  cases)  that  it  was  firmly 
fixed  in  popular  belief;  for  the  proposition  in  question  had  never  been 
heard  of  by  any  but  scientific  men.  But  it  was  felt  to  contain  a  truth : 
even  a  superficial  obserA'ation  of  the  phenomena  left  no  doubt  that  in 
the  propagation  of  motion  from  one  body  to  another,  there  was  some- 
thing of  which  the  one  body  gained  precisely  what  the  other  lost;  and 
the  word  momentum  had  been  invented  to  express  this  unknown  some- 
thing. In  the  settlement,  therefore,  of  the  definition  of  momentum,  was 
contained  th(;  determination  of  the  question,  What  is  that  of  which  a 
body,  when  it  sets  another  body  in  motion,  loses  exactly  as  much  as  it 
communicates'?  And  when  experiment  had  showni  that  this  something 
was  the  ))roduct  of  the  velocity  of  the  body  by  its  mass,  or  quantity  of 
matter,  this  became  the  defijiition  of  momentum. 

Mr.  Wliewell  very  justly  adds,*  ''The  business  of  definition'is  part 

of  the  business  of  discovery To  define,  so  that  our  definition 

shall  have  any  scientific  value,  requires  no  small  portion  of  that  saga- 
city by  which  truth  is  detected. '. When  it  has  been  clearly  seen 

what  ought  to  be  our  definition,  it  must  bo  pretty  well  known  what 
truth  we  bav(>  to  state.  The  definition,  as  well  as  the  discovery,  sup- 
poses a  decided  step  in  our  knowledge  to  have  been  made.  The 
writers  on  Logic,  in  the  middle  ages,  made  Definition  the  last  stage  in 

♦  Phil,  of  the  Ind.  Sc,  ii..  181-2. 


406  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

the  progress  of  knowledge ;  and  in  this  arrangement  at  least,  the  hi.H- 
tory  of  science,  and  the  philosophy  derived  from  the  histor}^  confirm 
their  speculative  views."  For  in  order  to  judge  how  the  name  which 
denotes  a  class  may  best  be  defined,  we  must  know  all  the  properties 
common  to  the  class,  and  all  the  relations  of  causation  or  dependence 
among  those  properties. 

If  the  properties  which  are  fittest  to  be  selected  as  marks  of  other 
common  properties  are  also  obvious  and  familiar,  and  especially  if  they 
bear  a  gj-eat  part  in  producing  that  general  and  superficial  air  ofi re- 
semblance which  was  the  original  inducement  to  the  formation  of  the 
class,  the  definition  will  then  be  most  felicitous.  But  it  is  often  neces- 
sary to  define  the  class  by  some  property  not  familiarly  known,  provi- 
ded that  property  be  the  best  mark  of  those  which  are  known.  M.  de 
Blainville,  for  instance,  has  founded  his  definition  of  life,  upon  the 
process  of  decomposition  and  recomposition  which  incessantly  goes  on 
in  every  living  body,  so  that  the  particles  composing  it  are  never  for 
two  instants  the  same.  This  is  by  no  means  one  of  the  most  obvious 
properties  of  living  bodies;  it  might  escape  altogether  the  notice  of  an 
unscientific  observer.  Yet  gi-eat  authorities  (independently  of  M.  de 
Blainville,  who  is  himself  a  first-rate  authority,)  have  thought,  seem- 
ingly with  much  reason,  that  no  other  property  so  well  answers  the 
conditions  required  for  the  definition. 

§  5.  Having  laid  down  the  principles  which  ought  for  the  most  part 
to  be  observed  in  attempting  to  give  a  precise  connotation  to  a  term  in 
use,  I  must  now  add,  that  it  is  not  always  practicable  to  adhere  to 
those  jjrinciples,  and  that  even  when  practicable,  it  is  occasionally  not 
desirable.  Cases  in  which  it  is  impossible  to  comply  mth  all  the  con- 
ditions of  a  precise  definition  of  a  name  in  agreement  with  usage,  occur 
very  frequently.  There  is  often  no  one  connotation  capable  of  being 
given  to  a  word,  so  that  it  shall  still  denote  everything  it  is  accustomed 
to  denote ;  or  that  all  the  propositions  into  which  it  is  accustomed  to 
enter,  and  which  have  any  foundation  in  truth,  shall  remain  true.  In- 
dependently of  accidental  ambiguities,  in  which  the  different  meanings 
have  no  connexion  with  one  another;  it  continually  happens  that  a 
word  is  used  in  two  or  more  senses  derived  fi-om  each  other,  but  yet 
radically  distinct.  So  long  as  a  term  is  vague,  that  is,  so  long  as  its 
connotation  is  not  ascertained  and  permanently  fixed,  it  is  constantly 
liable  to  be  applied  by  extension  from  one  thing  to  another,  until  it 
reaches  things  which  have  little,  or  even  no,  resemblance  to  those  which 
were  first  designated  by  it.  ■  , 

Suppose,  says  Dugald  Stewart,  in  his  PhilmopJiical  Essays ,*"  that 
the  letters  A,  B,  C,  D,  E,  denote  a  series  of  objects ;  that  A  possesses 
some  one  quahty  m  common  wdth  B;  B  a  quality  in  common  with  C; 
C  a  quality  in  common  witli  D  ;  D  a  quality  in  common  with  E  ;  while 
at  the  same  time,  no  quality  can  be  found  which  belongs  in  common 
to  any  three  objects  in  the  series.  Is  it  not  conceivable,  that  the  affin- 
ity between  A  and  B  may  produce  a  transference  of  the  name  of  the 
first  to  the  second ;  and  that,  in  consequence  of  the  other  aflinities 
which  connect  the  remaining  objects  together,  the  same  name  m^'  pas3 
in  succession  from  B  to  C  ;  from  C  to  D  ;  and  from  D  to  E  ?     In  this 

*  P.  217,  4to  edition. 


EEaUISITES   OF   LANGUAGE.  407 

manner  a  common  appellation  will  arise  between  A  and  E,  altliou<rh  the 
two  objocts  may,  m  their  nature  and  properties,  be  so  widely  distant 
from  each  other,  that  no  stretch  of  imagination  can  conceive  how  the 
thoughts  were  led  from  the  former  to  the  latter.    The  transitions,  never- 
theless, may  have  been  all  so  easy  and  gradual,  that,  were  they  suc- 
cessfully detected  by  the  fortunate  ingenuity  of  a  theorist,  we  should 
instantly  recognize,  not  only  tlie  verisimilitude,  but  the  truth   of  ,the 
conjectui'e  :  in  the  same  way  as  Vve  admit,  with  the  confidence  of  intu- 
itive conviction,  the  certainty  of  the  well-known  etymological  process 
which  connects  the  Latin  prej)osition  e  or  ej;  with  the  English  substan- 
tive ftf ranger,  the  moment  that  the  intermediate  links  of  the  chain  are 
submitted  to  our  examination."* 

The  applications  which  a  word  acquires  by  this  gradual  extension 
of  it  ft-om  one  set  of  objects  to  another,  Stewart,  adopting  an  expres- 
sion from  Mr.  Payne  Knight,  cajls  it  transitive  applications ;  and  after  ■ 
briefly  illustrating  such  of  them  as  are  the  result  of  local  or  casual 
associations,  he  proceeds  as  follows  : — f 

"  J^ut  although  by  far  the  greater  part  of  the  transitive  or  derivative 
applications  of  words  depend  on  casual  and  unaccountable  caprices  of 
the  feelings  or  the  fancy,^  there  are  certain  cases  in  which  they  open  a 
vcT-y  interesting  field  of  philosophical  speculation.     Such  are  those,  in 
which  an  analogous  transference  of  the  corresponding  term  may  be 
remarked  universally,  or  very  generally,  in  other  languages ;  and  in 
which,  of  course,  the  uniformity  of  the  result  must  be  asci-ibed  to  the 
essential  principles  of  the  human  frame.     Even  in  such  cases,  however, 
it  will  by  no  means  be  always  found,  on  examination,  that  the  various 
applications  of  the  same  term  have  arisen  from  any  common  quality 
or  qualities  in  the  objects  to  which  they  relate.    In  the  greater  number 
of  instances,  they  may  be  traced  to  some  natural  and  universal  asso- 
ciations of  ideas,  founded  in  the  common  faculties,  common  organs, 
and  common  condition  of  the    human    race. ......  According  to  the 

different  degrees  of  intimacy  and  strength  in  the  associations  on  which 
the  transitions  of  language  are  founded,  very  different  effectsfmay 
be  expected  to  arise.  Where  thia  association  is  slight  and  casual, 
the  several  meanings  will  remain  distinct  from  each  other,  and  will 
often,  in  process  of  time,  assume  the  appearance  of  capricious  varieties 
in  the  use  of  the  same  arbitrary  sign.  Where  the  association  is  so 
natural  and  habitual,  as  to  become  virtually  indissoluble,  the  transitive 
meanings  will  coalesce  into  one  coTnpleai  conception ;  and  every  neip 
transition  will  become  a  more  comprehensive  generalization  of  the  terrrC 
in  question." 

I  solicit  particular  attention  to  the  law  of  mind  expressed  in  the  last 
sentence,  and  which  is  the  source  of  the  peqjlexity  so  often  experienced 
in  detecting  these  transitions  of  meaning.  Ignorance  of  that  law  is 
the  shoal  upon  which  some  of  the  greatest  intellects  which  have  adorrjed 
the  human  race  have  been  wi-ecked.  The  inquiries  of  Plato  into  the 
definitions  of  some  of  the  most  general  terms  of  moral  speculation, 
are  characterized  by  Bacon  as  a  far  nearer  approach  to  a  true  indac- 

*  "  E,  ex,  extra,  extraneus,  Stranger,  stranger." 

Another  etymological  exam[)le  soiiietiines  cited  is  the  derivation  of  the  English  uncU 
from  the  Latin  amis.  It  is  scarcely  possible  for  two  words  to  bear  fewer  outward  marks 
of  relationship,  yet  there  is  but  one  step  between  them  ;  avua,  avunculus,  uncle. 

So  pilgrim  from  ager :  per  agrum,  peragrinus,  peregrinw,  pellegrino,  pilgrim. 

i  Pp.  226-7. 


408  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

live  method  thaii  is  elsewhere  to  be  found  among  the  ancients',  and  are, 
indeed,  ahnost  jjerfect  examples  of  the  preparatory  process  of  com- 
parison and  abstraction ;  but,  from  being  unaware  of  the  law  just 
mentioned,  he  wasted  the  powers  of  this  great  logical  instrument  upon 
inquiries  in  which  it  cbuld  realize  no  result,  since  the  phenomena 
whose  common  properties  he  so  elaborately  endeavored  to  detect,  had 
not  really  any  common  properties.  Bacon  himself  fell  into  the  same 
eiTor  in  his  speculations  on  the  nature  of  Heat,  in  which  it  is  impossi- 
ble not  to  think,  with  Mr.  Whewell,  that  he  confounded  under  the 
name  hot,  classes  of  phenomena  which  had  no  property  in  common.* 
Dugald  Stewart  certainly  overstates  the  matter  when  he  speaks  of  "a 
prejudice  which  has  descended  to  modern  times  from  the  scholastic 
ages,  that  when  a  word  admits  of  a  vai'iety  of  significations,  these 
different  significations  must  all  be  species  of  the  same  genus,  and 
must  consequently  include  some  essential  idea  common  to  every  indi- 
vidual to  which  the  generic  term  can  be  apphed:"t  for  both  Aristotle 
and  his  followers  were  well  aware  that  there  are  such  things  as  am- 
biguities of  language,  and  delighted  in  distinguishing  them.  But  they 
never  suspected  ambiguity  in  the  cases  where  (as  Stewart  remarks) 
the  association  on  which  the  transition  of  meaning  was  founded  is  so 
natural  and  habitual,  that  the  two  meanings  blend  together  in  the  mind, 
and  a  real  transition  becomes  an  apparent  generalization.  Accordingly 
they  wasted  an  infinity  of  pains  in  endeavoring  to  find  a  definition 
which  would  serve  for  sevei-al  distinct  meanings  at  once  :  as  in  an  in- 
stance noticed  by  Stewart  himself,  that  of  "  causation  ;  the  ambiguity 
of  the  word  which,  in  the  Greek  language,  coiTesponds  to  the  English 
word  cause,  having  suggested  to  them  the  vain  attempt  of  tracing  the 
common  idea  which,  in  the  case  of  any  effect,  belongs  to  the  efficient, 
to  the  matter,  to  the  form,  and  to  the  end.  The  idle  generalities"  (he 
adds)  "  we  meet  with  in  other  philosophers,  about  the  ideas  of  the  good, 
the  jit,  and  the  becoming,  have  taken  their  rise  from  the  same  undue 
influence  of  popular  epithets  on  the  speculations  of  the  learned. "| 

Among  words  which  have  undergone  so  many  successive  transitions 
of  meaning  that  every  trace  of  a  property  common  to  all  the  things 
they  are  applied  to,  or  at  least  common  and  also  peculiar  to  those 
things,  has  been  lost,  Stewart  considei's  the  word  Beautiful  to  be  one. 
And  (without  attempting  to  decide  a  question  which  in  no  respect 
belongs  to  logic)  I  cannot  but  feel,  with  him,  considerable  doubt, 
whether  the  word  beautiful  coimotes  the  same  property  when  we 
speak  of  a  beautiful  color,  a  beautiful  face,  a  beautiful  action,  a  beauti- 
ful character,  and  a  beautiful  solution  of  a  mathematical  problem.  The 
word  was  doubtless  extended  from  one  of  these  objects  to  another  on 
account  of  some  resemblance  be4;ween  them,  or,  more  probably, 
between  the  emotions  they  excited  ;  but,  by  this  progi-essive  extension, 
it  has  at  last  reached  things  very  remote  from  those  objects  of  sight  to 
which  there  is  no  doubt  that  it  was  first  appropriated ;  and  it  is  at 
least  questionable  whether  there  is  now  any  property  common  to  all 
the  things  we  call  beautiful,  except  the  property  of  agreeableness, 
which  the  term  certainly  does  connote,  but  which  cannot  be  all  that  we 
in  any  instance  intend  to  express  by  it,  since  there  are  many  agreeable 
things  which  we  never  call  beautiful.      If  such  be'  the   case,  it  is 

*  History  of  the  Inductive  Sciences,  i.,  48. 

t  Philosophical  Essays,  p.  214.  t  Ibid,  p.  215. 


REaUISITEB    OF    LANGUAGE.  409 

impossible  to  give  to  the  word  beautiful  any  fixed  connotation,  such 
that  it  shall  denote  all  the  objects  mIhcIi  in  common  use  it  .now  denotes, 
but  no  others.  A  fixed  connotation,  however,  it  ought  to  have ;  for,  flf^ 
so  long  as  it  has  not,  it  is  unfit  to  be  lised  as  a  scientific  term,  and, 
even  as  a  word  in  popular  use,  must  be  a  perpetual  source  of  false 
analogies  and  erroneous  generalizations. 

This  then,  constitutes  a  ca.so  in  exemplification  of  our  remark,  that 
dven  when  there  is  a  property  common  to  all  the  things  denoted  by  a 
name,  to  erect  that  pi-operty  into  the  definition  and  exclusive  connota- 
tion of  the  name  is  not  always  desirable.  The  various  things  called 
beautiful  unquestionably  resemble  one  another  in  being  agreeable; 
but  to  make  this  the  definition  of  beauty,  and  so  extend  the  word, 
Beautiful  to  all  agreeable  things,  would  be  to  drop  altogether  a  jx>rtion 
of  meaning  which  the  word  really,  although  indistinctly,  conveys,  and 
to  do  what  depends  upon  us  towards  causing  those  qualities  of  th^ 
'objects  which  the  word  previously,  though  vaguely,  pointed  at,  to  be 
overlooked  and  forgotten.  It  is  better,  in  such  a  case,  to  give  a  fixed 
connotation  to  the  term  by  restricting,  than  by  extending  its  use  ;  rather 
excluding  from  the  epithet  beautiful  some  things  to  which  it  is  com- 
monly considered  applicable,  than  leaving  out  of  its  connotation  any 
of  the  qualities  by  which,  though  occasionally  lost  sight  of,  the  general 
mind  may  have  been  habitually  guided  in  the  commonest  and  most 
interesting  applications  of  the  term.  For  there  is  no  question  that 
when  people  call  anything  beautiflil,  they  think  they  are  asserting  more 
thqn  that  it  is  merely  agreeable.  They  think  they  are  ascribing  a 
peculiar  sort  of  agreeableness,  analogous  to  that  which  they  find  in 
some  other  of  the  things  to  which  they  are  accustomed  to  apj)ly  the 
same  name.  If,  therefore,  there  be  any  peculiar  sort  of  agreeableness 
which  is  common,  though  not  to  all,  yet  to  the  principal  things  which 
are  called  beautiful,  it  is  better  to  limit  the  denotation  of  the  term  to 
those  things,  than  to  leave  that  kind  of  quality  without  a  term'  to  con- 
note it,  and  thereby  divert  attention  from  its  peculiarities. 

§  6.  The  last  remark  exemplifies  a  rule  of  temiinology,  which  is  of 
great  importance,  and  which  has  hardly  yet  been  recognized  as  a  rule, 
but  by  a  few  thinkers  of  the  present  generation.  In  attempting  to 
rectify  the  use  of  a  vague  terra  by  giving  it  a  fixed  connotation,  we 
must  take  care  not  to  discard  (unless  advisedly,  and  on  the  ground  of 
a  deeper  knowledge  of  the  subject,)  any  portion  of  the  connotatioTX 
which  the  word,  in  however  indistinct  a  manner,  previously  carried 
with  it.  For  otherwise  language  loses  one  of  its  inherent  and  most 
valuable  properties,  thaf  of  being  the  consers'ator'  of  ancient  experi- 
ence ;  the  keeper-alive  of  those  thoughts  and  obsei-vations  of  by-gone 
ages,  which  may  be  alien  to  the  tendencies  of  the  passing  time.  This 
fiinction  of  language  is  so  often  overlooked  or  undervalued,  that  a  few 
observations  upon  it  appear  to  be  extremely  required. 

Even  when  the  connotation  of  a  term  has  been  accurately  fixed,  and 
still  more  if  it  has  been  left  in  the  state  of  a  vague  unanalyzed  feeling 
of  resemblance  ;  there  is  a  constant  tendency  in  the  word,  through 
familiar  use,  to  part  with  a  poition  of  its  connotation.  It  is  a  well- 
known  law  of  the  mind,  that  a  word  originally  associated  with  a  very 
complex  cluster  of  ideas,  is  far  fi'om  calling  up  all  those  ideas  in  the 
mind,  every  time  the  word  is  used :  it  calls  up  only  one  or  two,  from 
3F 


410  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

which  the  mind  ruiis  on  by  fresh  associations  to  another  set  of  ideas, 
without  waiting  for  the  suggestion  of  the  remainder  of  the  complex 
cluster.  If  this  were  not  the  case,  our  processes  of  thought  could  not 
take  place  with  anything  like  the  rapidity  which  we  know  they  possess. 
Very  often,  indeed,  \yhen  we  are  employing  a  word  in  our  mental 
operations,  we  are  so  far  from  waiting  until  the  complex  idea  which 
corresponds  to  the  meaning  of  the  word  is  consciously  brought  before 
us  in  all  its  parts,  that  we  run  on  to  new  trains  of  ideas  by  the  other 
associations  which  the  mere  word  excites,  without  having  realized  in 
our  imagination  any  pait.  whatever  of  the  meaning :  thus  using  the 
word,  and  even'  using  it  well  and  accurately,  and  carrying  on  impor- 
tant processes  of  reasoning  by  means  of  it,  in  an  almost  mechanical 
manner:  so  much  so,  that  some  philosophers,  generalizing  fi'om  an 
extreme  case,  have  fancied  that  «ZZ  reasoning  is  but  the  mechanical 
use  of  a  set  of  terms  according  to  a  certain  form.  We  may  discuss 
and  settle  the  most  important  interests  of  towns  or  nations,  by  the 
application  of  general  theorems  or  practical  maxims  previously  laid 
down,  without  having  had  consciously  suggested  to  us,  once  in  the 
whole  process,  the  houses  and  green  fields,  the  thronged  market- 
places and  domestic  hearths,  of  which  not  only  those  towns  and  nations 
consist,  but  which  the  words  town  and  nation  confessedly  mean. 

Since,  then,  general  names  come  in  this  manner  to  be  used  (and 
even  to  do  a  portion  of  their  work  well)  without  suggesting  to  the 
mind  the  whole  of  their  meaning,  and  often  with  the  suggestion  of  a 
very  small,  or  no  part  at  all  of  that  meaning ;  we  cannot  wonder  that 
words  so  used  come  in  time  to  be  no  longer  capable  of  suggesting  any 
other  of  the  ideas  appropriated  to  them,  than  those  with  which  the 
association  is  most  immediate  and  strongest,  or  most  kept  up  by  the 
incidents  of  life  :  the  remainder  being  lost  altogether ;  unless  the 
mind,  by  often  consciously  dwelling  upon  them,  keeps  up  the  associa- 
tion. Words  naturally  retain  much  more  of  their  meaning  to  persons 
of  active  imagination,  who  habitually  represent  to  themselves  things  in 
the  concrete,  with  the  detail  which  belongs  to  them  in  the  actual  world. 
To  minds  of  a  different  description,  the  only  antidote  to  this  corruption 
of  language  is  predicg-tion.  The  habit  of  predicating  of  the  name,  all 
the  various  properties  which  it  originally  connoted,  keeps  up  the  asso- 
ciation between  the  name  and  those  properties. 

But  in  order,  that  it  may  do  so,  it  is  necessary  that  the  predicates 
should  themselves  retain  their  association  with  the  properties  which 
they  severally  connote.  For  the  propositions  cannot  keep  the  mean- 
ing of  the  words  alive,  if  the  meaning  of  the  propositions  themselves 
should  die.  And  nothing  is  more  common  than  for  propositions  to  be 
mechanically  repeated,  mechanically  retained  in  the  memory,  and 
their  truth  entirely  assented  to  and  relied  upon,  while  yet  they  carry 
no  meaning  distinctly  home  to  the  mind;  and  while  the  matter  of  fact 
or  law  of  nature  which  they  originally  expressed,  is  as  much  lost  sight 
of,  and  practically  disregarded,  as  if  it  never  had  been  heard  of  at  all. 
In  those  subjects  which  are  at  the  same  time  familiar  and  complicated, 
and  especially  in  those  which  are  so  much  of  both  these  things  as  moral 
and  social  subjects  are,  it  is  matter  of  common  remark  how  many  im- 
portant propositions  are  believed  and  repeated  from  habit,  while  no 
account  could  be  given,  and  no  sense  is  practically  manifested,  of  the 
truths  which  they  convey.     Hence  it  is,  that  the  traditional  maxims  of 


REQUISITES    OF   LANGUAGE.  411 

old  experience,  though  seklom  questioned,  have  so  little  efTcct  on  tho 
conduct  of  life ;  because  their  meaning  is  never,  by  most  persons, 
really  felt,  until  personal  experience  has  brought  it  home.  And  thus 
also  it  is  that  so  many  principles  of  religion,  ethics,  and  even  politics, 
so  full  of  meaning  and  reality  to  first  converts,  have  manifested  (after 
the  association  of  that  meaning  with  the  verbal  foi'mulas  has  ceased  to 
be  kept  up  by  the  controversies  which  accortipanied  their  first  intro- 
duction) a  tendency  to  degenerate  rapidly  into  lifeless  dogmas;  which 
tendency,  all  the  efforts  of  an  education  expressly  and  skillfully 
;directed  to  keeping  the  meaning  alive,  are  barely  found  sufficient  to 
counteract. 

Considering,  then,  that  the  human  mind,  in  differenjt  generations, 
occupies  itself  with  diflerent  things,  and  in  one  age  is  led  by  the  cir- 
cumstances which  surround  it  to  fix  more  of  its  attention  upon  one  of 
the  properties  of  a  thing,  in  another  age  upon,  another ;  it  is  natural 
and  inevitable  that  in  every  age  a  certain  portion  of  our  recorded  and 
traditional  knowledge,  not  being  contiimally  suggested  by  the  pursuits 
and  inquiries  with  which  mankind  are  at  that  time  engrossed,  should 
"fall  asleep,  as  it  were,  and  fade  irom  the  memory.  It  would  be  utterly 
lost,  if  the  propositions  or  formulas,  the  results  of  the  previous  expe- 
rience, did  not  remain,  and  continue  to  be  repeated  and  believed  in, 
as  forms  of  words  it  may  be,  but  of  words  that  once  really  conveyed, 
and  ai-e  still  supposed  to  conv,ey,  a  meaning :  which  meaning,  though 
suspended,  may  be  historically  traced,  and  when  suggested,  is  recog- 
nized by  minds  of  the  necessary  endowments  as  being  still  matter  ol 
fact,  or  truth.  While  the  formulfe  remain,  the'  meaning  may  at  any 
time  revive  ;  and  as  on  the  one  hand  the  formulas  progressively  lose 
the  meaning  they  were  intended  to  convey,  so  on  the  other,  when  tins 
forgetfulness  has  reached  its  height  and  begun  to  produce  consequences 
of  obvious  evil,  minds  arise  which  from  the  contemplation  of  the  for- 
mulae rediscover  the  whole  truth,  and  announce  it  again  to  mankind, 
not  as  a  discovery,  but  as  the  meaning  of  that  which  they  have  long 
been  taught,  and  still  profess  to  believe. 

Thus  there  is  a  perpetual  oscillation  in  spiritual  truths,  and  in 
spiritual  doctrines  of  any  significance,  even  when  not  truths.  Thqir 
meaning  is  almost  always  in  a  process  either  of  being  lost  or  of  being 
recovered  ;  a  remark  upon  which  all,  history  is  a  comment.  Whoever 
has  attended  to  the  history  of  the  more  serious  convictions  of  mankind 
— of  the  opinions  by  which  the  general  conduct  of  their  lives  is,  or  as 
they  conceive  ought  to  be,  more  especially  regulated — is  aware  that 
while  recognizing  verbally  the  very  same  doctrines,  they  attach  to' 
them  at  different  periods  a  greater  or  a  loss  quantity,  and  even  a  differ- 
ent kind,  of  meaning.  The  words  in  thqir  original  acceptation  con- 
noted, and  the  propositions  expressed,  a  complication  of  outward  facta- 
and  inward  feelino-s,  to  different  portions  of  which  the  general  mind  is 
more  particularly  alive  in  different  gc'uerations  of  mankind.  To  com- 
mon minds,  only  that  portion  of  the  meaning  is  in  each  generation 
suggested,  of  which  that  generation  possesses  the  counteqiait  in  its  , 
own  habitual  experience.  But  the  words  and  propositi! ms  lie  ready, 
to  suggest  to  any  mind  duly  prepared,  tho  remainder  of  the  meaning. 
Such  individual  minds  are  almost  always  to  be  found  :  and  the  lost 
meaning,  revived  by  them,  again  by  degrees  works  its  way  into  tho 
general  mind. 


413  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

There  s  scarcely  anything  which  can  materially  retard  the  arrival 
of  this  salutax-y  reaction,  except  the  shallow  conceptions  and  incautious 
proceedings  of  mere  logicians.  It  sometimes  happens  that  towards 
the  close  of  the  downward  period,  when  the  words  have  lost  part  of 
'their  significance  and  have  not  yet  begun  to  recover  it,  persons  arise 
whose  leading  and  favorite  idea  is  the  importance  of  clear  conceptions 
and  precise  thought,  and  the  necessity,  therefore,  of  definite  language. 
These  persons,  in  examining  the  old  formulas,  easily  perceive  that 
words  are  used  in  them  without  a  meaning ;  and  if  they  are  not  the 
sort  of  persons  who  are  capable  of  rediscovering  the  lost  signification, 
they  natui^ally  enough  dismiss  the  foraiula,  and  define  the  name 
without  any  reference  to  it.  In  so  doing  they  fasten  down  the  name 
to  what  it  connotes  in  common  use  at  the  time  when  it  conveys  the 
smallest  quantity  of  meaning ;  and  introduce  the  practice  of  employing 
it,  consistently  and  uniformly^  according  to  that  connotation.  The 
word  in  this  way  acquires  an  extent  of  denotation  far  beyond  what  it 
had  before;  it  becomes  extended  to  many  things  to  which  it  was 
previously,  in  appearance  capriciously,  refused.  Of  the  propositions 
in  which  it  was  fonnerly  used,  those  which  were  true  in  virtue  of  the 
forgotten  part  of  its  meaning  are  now,  by  the  clearer  light  which  the 
definition  diffuses,  seen  not  to  be  true  according  to  the  definition; 
which,  however,  is  the  recognized  and  sufficiently  correct  expression 
of  all  that  is  perceived  to  be  in  the  mind  of  any  one  by  whom  the  term 
is  used  at  the  present  day.  The  ancient  formulas  are  consequently 
treated  as  prejudices ;  and  people  are  no  longer  taught,  as  before, 
though  not  to  understand  them,  yet  to  believe  that  there  is  truth  in 
them.  They  no  longer  remain  in  men's  minds  suiTOunded  by  respect, 
and  ready  at  any  time  to  suggest  their  original  meaning.  The  truths 
which  they  convey  are  not  only,  under  these  circumstances,  redis- 
covered far  more  slowly,  but,  when  rediscovered,  the  prejudice  with 
which  novelties  are  regarded  is  now,  in  some  degree  at  least,  against 
them,  instead  of  being  on  their  side. 

An  example  may  make  these  remarks  more  intelligible.  In  all  ages, 
except  where  moral  speculation  has  been  silenced  by  outward  compul- 
sion, or  where  the  feelings  which  prompt  to  it  have  received  full  satis- 
faction from  an  established  faith  unhesitatingly  acquiesced  in,  one  of 
the  subjects  which  have  most  occupied  the  minds  of  thinking  men  is 
the  inquiry.  What  is  virtue  1  or.  What  is  a  virtuous  character  ]  Among 
the  diffej-ent  theories  on  the  subject  which  have,  at  different  times, 
grown  up  and  obtained  currency,  every  one  of  which  reflected  as  in 
the  clearest  miiTor  the  express  image  of  the  age  which  gave  it  birth; 
there  was  one,  brought  forth  by  the  latter  half  of  the  eighteenth  cen- 
tury, according  to  which  virtue  consisted  in  a  correct  calculation  of  our 
own  personal  interests,  either  in  this  world  only,  or  also  in  the  next. 
There  probably  had  been  no  era  in  history,  except  the  declining  period 
of  the  Roman  empire,  in  whicli  this  theory  could  have  grov\ai  up  and 
made  many  converts.  It  could  only  have  originated  in  an  age  essen- 
tially unheroic.  It  was  a  condition  of  the  existence  of  such  a  theory, 
that  the  only  beneficial  actions  which  people  in  general  were  much 
accustomed  to  see,  or  were  therefore  much  accustomed  to  praise,  should 
be  such  as  were,  or  at  least  might  without  contradicting  obvious  facts 
be  supposed  to  be,  the  result  of  the  motive  above  characterized. 
Hence  the  words  really  connoted  no  more  in  common  acceptation, 


REaUISITES     OF    LANGUAGE.  413 

than  was  set  down  in  the  definition :  to  which  consequently  no  objec- 
tion lay  on  the  score  of  deviation  from  usage,  if  the  usage  of  that  ago 
alone  was  to  be  considered. 

Su]ipose,  now,  that  the  partisans  of  this  theory  had  contrived  to 
introduce  (as,  to  do  them  justice,  tlicy  sliowed  themselves  sufiicioptly 
incliued)  a  consistent  and  undeviating  use  of  the  term  according  to 
this  definition.  Suppose  that  they  had  succeeded  in  banishing  the 
word  disinterestedness  from  the  language,  in  obtaining  the  disuse  of 
all  expressions  attaching  odium  to  selfishness  or  commendation  to  self- 
sacrifice,  or  which  implied  generosity  or  kindness  to  be  anything  but 
doing  a  benefit  in  order  to  receive  a  gi'eater  advantage  in  return. 
Need  we  say,  that  this  abrogation  of  the  old  formulas  for  the  sake  of 
preserving  clear  ideas  and  consistency  of  thought,  would  have  been  an 
incalculable  evil  ?  while  the  very  inconsistency  incurred  by  the  coexist- 
ence of  the  formulas  with  philosophical  opinions  which  virtually  con- 
demned them  as  absurdities,  operated  as  a  stimulus  to  the  reexamina- 
tion of  the  subject ;  and  thus  the  very  doctrines  originating  in  the  oblivion 
into  which  great  moral  truths  had  fallen,  were  rendered  indirectly,  but 
powerfully,  instrumental  to  the  revival  of  those  truths. 

The  doctrine,  therefore,  of  the  Coleridge  school,  that  the  language  of 
any  people  among  whom  culture  is  of  old  date,  is  a  sacred  deposit,  the 
property  of  all  ages,  and  which  no  one  age  should  consider  itself  empow- 
ered to  alter — is  far  from  being  so  devoid  of  im])ortant  truth  as  it 
ajipears  to  that  class  of  logicians  who  think  more  of  having  a  clear  than 
of  having  a  complete  meaning;  and  who  perceive  that  every  age  is- 
adding  to  the  truths  which  it  has  received  from  its  predecessors,  but 
fail  to  see  that  a  counter-process  of  losing  truths  already  possessed,  is 
also  constantly  going  on,  and  requiring  the  most  sedulous  attention  to 
counteract  it.  Language  is  the  depositary  of  the  accumulated  body  of 
experience  to  which  all  former  ages  have  contributed  their  part,  and 
which  is  the  inheritance  of  all  yet  to  come.  We  have  no  right  to  pre- 
vent oui'selves  from  transmitting  to  posterity  a  larger  portion  of  this  in- 
heritance than  we  may  ourselves  have  profited  by.  We  continually  havo 
cause  to  give  up  the  opinions  of  our  forefathers ;  but  to  tamper  v/ith; 
their  language,  even  to  the  extent  of  a  word,  is  an  operation  of  much 
greater  responsibility,  and  implies  as  an  indispensable  requisito,-  an 
accurate  acquaintance  with  the  history  of  the  particular  word,  and  of  tho 
opinions  which  in  different  stages  of  its  progress  it  served  to  express.  To 
be  qualified  to  define  the  name,  we  must  know  all  that  has  ever  been 
known  of  the  projierties  of  the  cla.ss  of  objects  which  are,  or  originally 
were,  denoted  by  it.  For  if  we  give  it  a  meaning  according  to  which 
any  propositi(3n  will  be  false  which  ^philosophers  or  mankind  have  ever 
held  to  be  true,  it  is  at  lea^^t  incumbent  upon  us  to  be  sure  that  we 
know  all  which  those  who  believed  the  proposition  understood  by  it. 


414  OPERATIONS    SUBSIDIARY  TO    INDUCTION. 

CHAPTER  V. 

ON  .THE  NATURAL  HISTORY  OF  THE  VARIATIONS  IN  THE  MEANING    OF  TERMS. 

§  1.  It  is  not  only  in  the  mode  which  has  now  been  pointed  out, 
namely,  by  gradual  inattention  to  a  portion  of  the  ideas  conveyed,  that 
words  in  common  use  are  liable  to  shift  their  connotation.  The  truth 
is,  that  the  connotation  of  such  words  is  perpetually  varying  ;  as  might 
be  expected  from  the  manner  in  which  words  in  common  use  acquire 
their  connotation.  A  technical  term,  invented  for  purposes  of  art  or 
science,  has,  from  the  first,  the  connotation  given  to  it  by  its  inventor; 
but  a  name  which  is  in  every  one's  mouth  before  any  one  thinks  of  de- 
fining it,  derives  its  connotation  only  fi'om  the  circumstances  which  are 
habitually  brought  to  mind  when  it  is  pronounced.  Among  these  cir- 
cumstances, the  properties  common  to  the  things  denoted  by  the  name, 
have  naturally  a  principal  place ;  and  would  have  the  sole  place,  if 
language  were  regulated  by  convention  rather  than  by  custom  and  ac- 
cident. But  besides  these  common  properties,  which  if  they  exist  are 
necessarily  present  whenever  the  name  is  applied,  any  other  circum- 
stance may  casually  be  found  along  with  it,  so  frequently  as  to  become 
associated  with  it  in  the  same  manner,  and  as  strongly  as  the  common 
properties  themselves.  In  proportion  as  this  association  forms  itself, 
people  give  up  using  the  name  in  cases  in  which  those  casual  circum- 
stances do  not  exist.  They  prefer  using  some  other  name,  or  the  same 
name  with  some  adjunct,  rather  than  employ  an  expression  which  will 
necessarily  call  up  an  idea  they  do  not  want  to  excite.  The  circum- 
stance originally  casual,  thus  becomes  regularly  ji  part  of  the  connota- 
tion of  the  word.    . 

It  is  this  continual  incorporation  of  circumstances  originally  acci- 
dental, into  the  permanent  signification  of  words,  which  is  the  cause 
that  tliere  are  so  few  exact  synonyms.  It  is  this  also  which  renders 
the  dictionary  meaning  of  a  word,  by  universal  remark  so  imperfect  an 
exponent  of  its  real  meaning.  The  dictionary  meaning  is  marked  out 
in  a  broad,  blunt  way,  and  probably  includes  all  that  was  originally 
necessary  for  the  coiTect  employment  of  the  term  ;  but  in  process  of 
time  so  many  collateral  associations  adhere  to  words,  that  whoever 
should  attempt  to  use  them  with  no  other  guide  than  the  dictionary 
would  confound  a  thousand  nice  distinctions  and  subtle  shades  of  mean- 
ing which  dictionaries  take  no  account  of;  as  we  notice  in  the  use  of 
a  language  -in  conversation  or  wr'iting  by  a  foreigner  not  thoroughly 
master  of  it.  The  history  of  a  word,  by  showing  the  causes  which  de- 
tennined  its  use,  is  in  these  cases  a  better  guide  to  its  employment 
than  any  definition ;  for  definitions  can  only  show  its  meaning  at  the 
particular  time,  or  at  most  the  series  of  its  successive  meanings,  but  its 
history  may  show  the  law  by  which  the  succession  was  produced. 
The  word  gentleman,  for  instance,  to  the  correct  employment  of  which 
a  dictionary  would  be  no  guide,  originally  meant  simply  a  man  of 
family.  From  this  it  came  by  degrees  to  connote  all  such  qualities  or  ad- 
ventitious circumstances  as  were  usually  found  to  belong  to  persons  of 
family.  This  consideration  at  once  explains  why  in  one  of  its  vulgar 
acceptations  it  means  any  one  who  lives  without  labor,  in  another  with- 


VARIATIONS  IN   MEANING  OF  TERMS.  415 

out  manual  labor,  and  in  its  moro  elevated  signification  it  has  in  every 
age  signified  the  conduct,  character,  habits,  and  outward  appearance,  in 
whomsoever  found,  which,  according  to  the  ideas  of  that  age,  belonged 
or  were  expected  to  belong  to  persons  boru>and  educated  m  a  hijgh  so- 
cial position.  ' 

It  continually  happens  that  of  two  wprds,  whose  dictionary  mean- 
ings are  either  the ,  same  or  very  slightly  diflcrent,  one  will  be  the 
proper  word  to  use  in  one  set  of  circumstances,  another  in  another, 
without  its  being  pqssible  to  show  how  the  custom  of  so  employing 
them  originally  gi'cw  up.  The  accident  that  one  of  the  words  was 
used  and  not  the  other  on  a  particular  occasion  or  in  a  particular  social 
circle,  will  be  sufficient  to  produce  so  strong  an  association  between  the 
word  and  some  speciality  of  circumstances,, that  mankind  abandon  the 
use  of  it  in  any  other  case,  and  the  speciality  becomes  part  of  its  sig- 
nifica,tion.  The  tide  of  custom  first  drifts  the  word  on  the  shore  of  a. 
particular  meaning,  then  retires  and  leaves  it  there. 

An  instance  in  point  is  the  remarkable  change  which,  in  the  English 
language  at  least  has  taken  place  in  tlie  signification  of  the  word  loyal- 
ty. That  word  originally  meant  in  English,  as  it  still  means  in  the 
language  from  whence  it  came,  fair,  open  dealing,  and  fidelity  to  en- 
gagements :  in  that  sense  the  quality  it  expressed  was  part  of  the  ideal 
chivalrous  or  knightly  character.  By  what  process,  in  England,  the 
term  became  restricted  to  the  single  case  of  fidelity  to  the  throne,  I  am 
not  sufficiently  versed  in  the  history  of  courtly  language  to  be  able  to 
pronounce.  ■  The  interval  between  a  loyal  chevalier  and  a  loyal  subr 
ject  is  certainly  great.  I  can  only  suppose  that  the  word  was,  at  some 
period,  the  favorite  term  at  court  to  express  fidelity  to  tho  oath  of  al- 
legiance, until  at  length  those  who  wished  to  speak  of  any  other,  and 
as  it  was  probably  considered,  inferior  sort  of  fidelity,  either  did  not 
venture  to  use  so  dignified  a  term,  or  found  it  convenient  to  employ 
some  other  in  order  to  avoid  being  misunderstood. 

§  2.  Cases  are  not  unfrequent  in  which  a  circumstance,  at  first  cas- 
ually incorporated  into  the  connotation  of  a  word  which  originally  had 
no  reference  to  it,  in  time  wholly  supersedes  the  original  nieaning,  and 
becomes  not  merely  a  part  of  the  connotation,  but  the  whole  of  it. 
This  is  exemplified  in  the  word  pagan,  jmganus  ;  which  originally,  as 
its  etymology  imports,  was  equivalent  to  villager  ;  the  inhabitant  of  a 
pagus,  or  village.  At  a  particular  era  in  the  extension  of  Christianity 
over  the  Roman  empire,  the  adherents  of  tlic  old  religion,  and  the  vil- 
lagers or  country  people,  were  nearly  the  same  body  of  individuals, 
the  inhabitants  of  the  towns  having  been  earliest  convei'ted  ;  as  in  cmi 
own  day  and  at  all  times  the  greater  activity  of  social  intercoui-se  ren- 
ders them  the  earliest  recipients  of  new  opinions  and  modes,  while  pld 
habits  and  prejudices  linger  longest  amon^  the  country  people  :  not  to 
mention  that  the  towns  were  more  immediately  und('r  the  direct  influ- 
ence of  the  government,  which  at  that  time  had  embraced  Cln-istianity. 
From  this  casual  ccnncidcncc,  the  w(jrd  jiaganus  canied  with  it,  and 
began  more  and  more  steadily  to  suggest,  the  idea  of  a  worshiper' of 
the  ancient  divinities  ;  until  at  length  it  suggested  that  idea  so  fwrcibly, 
that  people  who  did  not  desire  to  suggest  the  idea  avoided  using  the 
word.  But  when  paganus  had  come  to  connote  heathenism,  the  very 
unimportant  circumstance,  with  reference  to  that  fact,  of  the  place  of 


416  OPERATIONS    SUBSIDIARY    TO  INDUCTION. 

residence,  was  soon  disregarded  in  the  employment  of  the  word.  As 
there  was  seldom  any  occasion  for  making  separate  assertion  respect- 
ing heathens  who  lived  in  the  country,  there  was  no  need  for  a  separate 
W£>rd  to  denote  them ;  and  pagan  came  not  only  to  mean  heathen,  but 
to  mean  that  exclusively.  .  ^  "  ■ '. 

"A  case  still  more  familiar  to  most  readers  is  that  of  the  -wovA  villain, 
or  villein.  This  term,  as  everybody  knows,  had  in  the  middle  ages  a 
connotation  as  strictly  defined  as  a  word  could  have,  being  the  proper 
legal  designation  for  those  persons  who  were  the  subjects  of  the  least 
onerous  form  of  feudal  bondage,  those  serfs  who  were  adscripti  glehce. 
The  scorn  of  the  semibarbarous  military  aristocracy  for  these  their  ab- 
ject dependents,  rendered  the  act  of  likening  any  person  to  this  class 
of  men  a  mark  of  the  greatest  contumely:  the  same  scorn  led  them  to 
ascribe  to  the' same  people  all  manner  of  hateful  qualities,  which  doubt- 
less also,  in  the  degrading  situation  in  which  they  were  held,  were  often 
not  unjustly  imputed  to  them.  These  circumstances  combined  to 
attach  to  the  term  villain,  ideas  of  crime  and  guilt,  in  so  forcible  a 
manner,  that  the  application  of  the  epithet,  even  to  those  to  whom  it 
legally  belonged,  became  an  affront,  and  was  abstained  from  whenever 
no  affront  was  intended;  From  that  time  guilt  was  part  of  the  conno- 
tation ;  and^soon  became  the  whole  of  it,  since  mankind  were  not 
prompted  by  any  urgent  motive  to  continue  making  a  distinction  in 
their  language  between  bad  men  of  sei^vile  station  and  bad  men  of  any 
other  rank  in  life. 

These  and  similar  instances  in  which  the  original  signification  of  a 
term  is  totally  lost — another  arid  an  entirely  distinct  meaning  being 
first  engrafted  upon  the  former,  and  finally  substituted  for  it — afford 
examples  of  the  double  movement  which  is  always  taking  place  in  lan- 
guage ;  the  counter-movements,  one  of  Generalization,  by  which  words 
are  perpetually  losing  portions  of  their  connotation  and  becoming  of 
less  meaning  and  more  general  acceptation ;  the  other  of  Specialization, 
by  which  other,  or  even  these  same  words,  are  continually  taking  on 
fresh  connotation ;  acquiring  additional  meaning,  by  being  restricted  in 
their  employmentto  a  part  only  of  the  occasions  on  which  they  might 
projjerly  be  used  before.  This  double  movement  is  of  sufficient  im- 
portance m  the  natural  history  of  language  (to  which  natural  history, 
the  artificial  modifications  ought  always  to  have  some  degree  of  refer- 
ence), to  justify  our  dwelling  for  a  little  longer  on  the  nature  of  the 
two-fold  phenomenon,  and  the  causes  to  which  it  owes  its -existence; 

^  3.  To  begin  with  the  movement  of  generalization.  It  is  unneces- 
sary to  dwell  upon  the  changes  in  the  meaning  of  names  which  take 
place  merely  from  their  being  used  ignorantly,  by  persons  who,  not 
having  properly  mastered  the  received  connotation  of  a  word,  apply  it 
in  a  looser  and  wider  sense  than  belongs  to  it.  This,  however,  is  a 
real  source  of  alterations  in  the  language ;  for  when  a  word>  from  being 
often  employed  in  cases  where  one  of  the  qualities  which  it  connotes 
does  not  exist,  ceases  to  suggest  that  quality  with  certainty,  then  even 
those  who  are  under  no  mistake  as  to  the  proper  meaning  of  the  word, 
prefer  expressing  that  meaning  in  some  other  way,  and  leave  the  orig- 
inal word  to  its  fate.  The  word  'Squire,  as  standing, for  an  owner  of 
a  landed  estate;  Parson,  as  denoting  not  the  rector  of  the  parish  but 
clergymen  in  general;  Artist,  to  denote  only  a  painter  or  sculptor;  are 


VARIATIONS    IV    MEANING    OF    TERMS.  417 

cases  in  point.  Independently,  however,  of  the  generalization  of 
names  through  their  ignorant  misuse,  there  is  a  tendency  in  the  same 
direction,  consistently  with  the  most  thorough  knowledge  of  their 
meaning;  arising  from  the  fact,  that  the  number  of  things  known  to 
us,  and  of  which  we  feel  a  desire  to  speak,  nudtiply  faster  than  the 
names  for  them.  Except  on  subjects  for  wliicli  there  has  been  con- 
structed a  scientific  terminology,  with  which  unscientific  persons  do 
not  meddle,  great  dithculty  is  generally  f<)und  in  bringing  a  new  name 
into  use;  and  independently  of  that  difficulty,  it  is  natural  to  prefer 
giving  to  a  new  object  a  name  which  at  least  expresses  its  resemblance 
to  something  already  known,  since  by  predicating  of  it  a  name  entirely 
new  we  at  first  convey  no  information.  In  this  manner  the  name  of  a 
species  often  becomes  the  name  of  a  genus;  as  salt,  for  example,  or 
oil;  the  former  of  which  words  originally  denoted  only  the  muriate  of 
soda,  the  latter,  as  its  etymology  indicates,  only  olive  oil ;  but  which 
now  denote  large  and  diversified  classes  of  substances  resembling 
these  in  some  of  their  qualities,  and  connote  only  those  common  quali- 
ties, instead  of  the  whole  of  the  distinctive  properties  of  olive  oil  and 
sea  salt.  Tlie  words  glass  and  soap  are  used  by  modern  chemists  in  a 
similar  manner,  to  denote  genera  of  which  the  substances  vulgai'ly  so 
called  are  single  species.*  And  it  often  happens,  as  in  those  instances, 
that  the  term  keeps  its  special  signification  in  addition  to  its  more  gen- 
eral one,  and  becomes  ambiguous,  that  is,  two  names  instead  of  one. 

These  changes,  by  which  words  in  ordinary  use  become  more  and 
more  generalized,  and  less  and  less  expressive,  take  place  in  a  still 
greater  degree  with  the  words  which  express  the  complicated  phe- 
nomena of  mind  and  society.  Historians,  travellers,  and  in  general 
those  who  speak  or  write  concerning  moral  and  social  phenomena  with 
which  they  are  not  familiarly  acquainted,  are  the  great  agents  in  this 
modification  of  language.  The  vocabulary  of  all  except  unusually 
instructed  persons,  is,  on  such  subjects,  eminently  scanty.  They  have 
a  certain  small  set  of  words  to  which  they  are  accustomed,  and  which 
they  employ  to  express  phenomena  the  most  heterogeneous,  because 
they  have  never  sufficiently  analyzed  the  facts  to  which  those  words 
correspond  in  their  own  country,  to  have  attached  perfectly  definite 
ideas  to  the  words.  The  first  English  conquerors  of  Bengal,  for  ex- 
ample, carried  with  them  the  phrase  landed  proprietor  into  a  country 
where  the  rights  of  individuals  over  the  soil  were  extremely  different 
in  degree,  and  even  in  nature,  from  those  recognized  in  England. 
Applying  the  term  with  all  its  English  associaticms  in  such  a  state  of 
things ;  to  one  who  had  only  a  limited  right  they  gave  an  absolute  right, 
from  another  because  he  had  not  an  alisolute  right  they  took  away  all 
right,  drove  whole  classes  of  men  to  ruin  and  despair,  filled  the  country 
with  banditti,  created  a  feeling  that  nothing  was  secure,  and  produced, 
with  the  best  intentions,  a  disorganization  of  society  which  had  not 
been  produced  in  that  country  by  the  most  ruthless  of  its  barbarian 
invaders.  Paul  Louis  Courier  might  well  say,  "  Gardez-nous  de  I'equi- 
voque !"  Yet  the  usage  of  persons  capable  of  so  gross  a  misappre- 
hension, determines  the  meaning  of  language  :  and  the  words  they  thus 

*"  The  term  a?/t«/i,  in  its  original  sense,  signified  that  particular  rcsidmim  which  was 
alone  obtained  by  lixiviating  the  ashes  of  the  plant  named  kali,  but  the  word  is  now  so  gen- 
eralized, that  it  drnotcs  any  body  possessed  of  a  certain  number  of  properties." — Paris's 
Pharmacologia,  vol.  j.,  p.  68. 

3G 


418  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

misuse  grow  in  generality,  until  the  instructed  are  obliged  to  acquiesce; 
and  to  employ  those  words  (first  freeing  them  from  vagueness  by  giv- 
ing them  a  definite  connotation)  as  generic  terms,  subdividing  the  gen- 
era into  species. 

§  4.  While  the  more  rapid  growth  of  ideas  than  of  names  thus  creates 
a  perpetual  necessity  for  making  the  same  names  serve,  even  if  imper- 
fectly, on  a  greater  number  of  occasions  ;  a  counter-operation  is  going 
on,  by  which  names  become  on  the  contrary  restricted  to  fewer  occa- 
sions, by  taking  on,  as  it  were,  additional  connotation,  from  circum- 
stances not  originally  included  in  the  meaning,  but  which  have  become 
connected  with  it  in  the  mind  by  some  accidental  cause.  We  have 
seen  above,  in  the  words  pagan  and  villain,  remarkable  examples  of  the 
specialization  of  the  meaning  of  words  from  casual  associations,  as  well 
as  of  the  generalization  of  it  in  a  new  direction,  which  often  follows. 

Similar  specializations  are  of  frequent  occurrence  in  the  history  even 
of  scientific  nomenclature.  "  It  is  by  no  means  uncommon,"  says  Dr. 
Paris,  in  his  Pharmacologia,*  "  to  find  a  word  which  is  used  to  express 
general  characters  subsequently  become  the  name  of  a  specific  sub- 
stance in  which  such  characters  are  predominant ;  and  we  shall  find 
that  some  important  anomalies  in  nomenclature  may  be  thus  explained. 
The  term  Apaevmov,  from  which  the  word  Arsenic  is  derived,  was  an 
ancient  epithet  applied  to  those  natural  substances  which  possessed 
strong  and  acrimonious  properties,  and  as  the  poisonous  quality  of 
arsenic  was  found  to  be  remarkably  powerful,  the  term  was  especially 
applied  to  Orpiment,  the  form  in  which  this  metal  most  usually  occur- 
I'ed.  So  the  term  Verhena  (quasi  IIerbc7ia)  originally  denoted  all 
those  herbs  that  were  held  sacred  on  account  of  their  being  employed 
in  the  rites  of  sacrifice,  as  we  learn  from  the  poets ;  but  as  one  herb 
was  usually  adopted  upon  these  occasions,  the  word  Verbena  came  to 
denote  that  particular  herb  onli/,  and  it  is  transmitted  to  us  to  this  day 
under  the  same  title,  viz.  Verbena  or  Vervain,  and  indeed  luitil  lately 
it  enjoyed  the  medical  reputation  vvhich  its  sacred  origin  conferred 
upon  it,  for  it  was  worn  suspended  around  the  neck  as  an  amulet. 
Vitriol,  in  the  original  application  of  the  word,  denoted  any  crystaline 
body  with  a  certain  degree  of  transparency  {vitrum) ;  it  is  hardly 
necessary  to  observe  that  the  term  is  now  appropriated  to  a  particular 
species  :  in  the  same  manner,  Bark,  which  is  a  general  teiTn,  is  applied 
to  express  one  genus,  and  by  way  of  eminence,  it  has  the  article  The 
prefixed,  as  The  bark  :  the  same  observation  will  apply  to  the  word 
Opium,  which,  in  its  primitive  sense,  signifies  any  juice  (otto^,  Succus), 
while  it  now  only  denotes  one  species,  viz.  that  of  the  poppy.  So, 
again,  Elaterium  was  used  by  Hippocrates  to  signify  various  internal 
applications,  especially  purgatives,  of  a  violent  and  drastic  nature 
(from  the  word  EAaux'w,  agito,  moveo,  stimulo),  but  by  succeeding 
authors  it  was  exclusively  applied  to  denote  the  active  matter  which 
subsides  from  the  juice  of  the  wild  cutumber.  The  word  Fecula, 
again,  originally  meant  to  imply  any  substance  which  was  derived  by 
spontaneous  subsidence  from  a  Hquid  (from  fa;x,  the  grounds  or 
settlement  of  a7iy  liquor) ;  afterwards  it  was  applied  to  Starch,  which 
is  deposited  in  this  manner  by  agitating  the  flour  of  wheat  in  water ; 

*  Historical  Introduction,  vol.  i.,  pp.  66-8. 


VARIATIONS    IN    MEANING    OP    TERMS.  419 

and  histly,  it  has  been  applied  to  a  peculiar  vegetable  principle,  which, 
like  starch,  is  insoluble  in  cold,  but  completely  soluble  in  boiling  water, 
with  which  it  forms  a  gelatinous  solution.  This  indciinite  meaning  of 
the  word,  fecula  has  created  numerous  mistakes  in  pharmaceutic  chem- 
istry ;  Elaterium,  for  instance,  is  said  to  hcfecula,  and,  in  the  original 
sense  of  the  word,  it  is  properly  so  called,  inasmuch  as  it  is  procured 
from  a  vegetable  juice  by  spontaneous  subsidence,  but  in  the  limited' 
and  modem  acceptation  of  the  term,  it  conveys  an  erroneous  idea ;  for 
instead  of  the  active  principle  of  the  juice  residing  in  fccula,  it  is  a 
peculiar  proximate  principle,  sui  generis,  to  which  I  have  ventured  to 
bestow  the  name  of  Elathi.  For  the  same  reason,  much  doubt  and 
obscurity  involve  the  meaning  of  the  word  Extract,  because  it  is  ap- 
plied gencrallij  to  any  substance  obtained  by  the  evaporation  of  a  vege- 
table solution,  and  specijicall y  to  a  peculiar  })roximato  principle,  pos- 
sessed of  certain  characters,  by  which  it  is  distinguished  from  every 
other  elementary  body." 

A  generic  term  is  always  liable  to  become  thus  limited  to  a  single 
speciet;,  or  even  individual,  if  people  have  occasion  to  think  and  speak 
of  that  individual  or  species  much  oftener  than  of  anything  else  which 
is  contained  in  the  genus.  Thus,  by  cattle,  a  stage  coachman  will 
understand  horses  ;  beasts,  in  the  language  of  agriculturists,  stands  for 
oxen  ;  and  birds,  with  some  sportsmen,  for  partridges  only.  The  law 
of  language  which  operates  in  these  trivial  instances,  is  the  very  same 
in  conformity  to  which  the  terms  Qeog,  Deus,  and  God,  were  adopted 
fi'om  Polytheism  by  Christianity,  to  express  the  single  object  of  its 
own  adoration,  in  lieu  of  the  ancient  and  specially  appropriated  name 
Jehovah.  Almost  all  the  terminology  of  the  Christian  Church  is  made 
up  of  words  originally  used  in  a  much  more  general  acceptation : 
JGccZes/a,  Assembly  ;  Bishojy,  Episcopus,  Overseer ;  Pr/e*^,  Presbyter, 
Elder;  Deacon,  Diaconus,  Administrator;  Sacrament,  a  vow  of  alle- 
giance ;  Evangelium,  good  tidings ;  and  some  words,  as  Minister,  are 
still  used  both  in  the  gdneral  and  in  the  limited  sense.  It  would  be 
interesting  to  trace  the  progress  by  which  author,  in  its  most  familiar 
sense,  came  to  signify  a  writer,  and  7TOiT]T7]g,  or  Maker,  a  poet. 

Of  the  incorporation  into  the  meaning  of  a  term,  of  circumstances 
accidentally  connected  with  it  at  some  j)articular  period,  as  in  the  case 
of  Pagan,  instances  might  easily  be  multiplied.  Physician  {(pvatKog,  or 
naturalist)  became,  in  England  at  least,  synonymous  with  a  healer  of 
diseases,  because  until  a  comparatively  late  period  medical  practitioners 
were  the  only  naturalists.  Clerc  or  Clericus,  a  scholar,  came  to  signify 
an  ecclesiastic,  because  the  clergy  were  for  many  centuries  the  only 
scholars. 

Of  all  ideas,  however,  the  most  lialdc  to  cling  by  association  to  any- 
thing with  which  they  have  ever  been  connected  by  proximity,  are 
those  of  our  pleasures  and  pains,  or  of  the  things  wliich  we  habitually 
contemplate  as  sources  of  our  pleasures  or  pains.  The  additional  con- 
notation, therefore,  wluch  a  woi'd  soonest  and  most  readily  takes  on, 
is  that  of  agreeableness  or  painfulness,  in  their  various  kinds  and  de- 
grees:  of  being  a  good  or  a  bad  thing;  desirable  or  to  be  avoided; 
an  object  of  hati'ed,  of  dread,  of  contemjjt,  admiration,  hope,  or  love. 
Accordingly  there  is  hardly  a  single  name,  expressive  of  any  moral  or 
social  fact  calculated  to  call  forth  strong  aflections  cither  of  a  favorable 
or  of  a  hostile  nature,  which  does  not  caiTy  with  it  decidedly  and  irre- 


420  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

sistibly  a  connotation  of  those  strong  affections,  or,  at  the  least,  of 
approbation  or  censure ;  insomuch  that  to  employ  those  names  in 
conjunction  with  others  by  which  the  contrary  sentiments  were  ex- 
pressed, would  produce  the  effect  of  a  paradox,  or  even  a  contradic- 
tion in  terms.  The  baneful  influence  of  the  connotation  thus  acquired, 
on  our  reasonings  and  habits  of  thought,  has  been  well  pointed  out  on 
many  occasions  byBentham.  It  give^  rise  to  the  fallacy  of  "question- 
begging  names."  The  very  property  which  we  are  inquiring  whether 
a  tiling  possesses  or  not,  has  become  so  associated  with  the  name  of  the 
thing  as  to  be  part  of  its  meaning,  insomuch  that  by  merely  uttering 
the  name  we  assume  the  point  which  was  to  be  made  out :  one  of  the 
most  frequent  sources  of  apparently  self-evident  propositions. 

There  is  still  another  mode  in  which  the  meaning  of  a  name  is  apt  to 
be  specialized,  sufficiently  frequent  to  be  worthy,  of  being  pointed  out. 
We  have  often  the  choice  between  a  more  and  a  less  general  name  for 
designating  an  object,  either  of  them  sufficiently  answering  the  pur- 
pose of  distinction.  Thus  we  may  say  either  that  dog,  or  that  animal ; 
m  many  cases,  that  creature,  or  that  object,  would  be  sufficient.  Now 
there  is,  in  many  cases  of  frequent  occurrence,  a  tendency,  which 
grows  as  civilization  advances,  to  adopt  the  practice  of  designating 
things  by  the  most  general  words  which  with  all  the  aids  of  context 
and  gesture  will  suffice  to  point  them  out.  Natural  good  taste,  and 
still  more  the  conventional  quality  which  usurps  its  name,  consist  to  a 
great  degi'ee  in  keeping  some  aspects  of  things  as  much  as  possible  out 
of  sight ;  speaking  of  disagreeable  things  with  the  least  possible  sug- 
gestion of  their  disagi'eeablc  details,  and  of  agreeable  things  with  as 
little  obtrusion  as  possible  of  the  mere  mechanism  of  their  production, 
which,  except  in  our  scientific  observations,  is  not  what  interests  us  in 
them,  and  the  close  contemplation  of  wliich  generally  diminishes  their 
charm  to  the  imagination.  The  practice  thus  grows  up  among  culti- 
vated people,  of  speaking  of  common  things  in  a  way  much  less  literal 
and  definite  than  is  the  custom  of  the  vulgar.;  in'a  way  which  indicates 
the  thing  meant,  with  the  faintest  possible  suggestion  of  its  character- 
istic qualities ;  and  the  mere  words  used  would  Often  not  suffice  to 
convey  the  meaning,  unless  there  were  something  in  the  accompanying 
circumstances  to  assist  in  exciting  the  idea.  The  vulgar,  meanwhile, 
continue  to  use  the  appropriate,  peculiar,  and,  if  scientific  fitness  were 
the  only  thing  to  be  considered,  the  best  phraseology,  because  unam- 
biguous; while,  for  purposes  of  refinement,  ambiguity  is  often  the 
very  quality  desired. 

Now  this  practice  of  using  more  general  terms  where  specific  ones 
might  have  been  employed,  is  constantly  spoiling  the  general  terms  by 
rendering  them  specific.  They  become  the  terms  particularly  associ- 
ated with  the  very  specialities  of  meaning  which  it  was  desired  not  to 
suggest.  A  ridiculous  instance  is  the  anecdote  of  a  lady  of  the  court 
of  Louis  XIV.,  who  having  stated  to  her  confessor  that  she  felt  esteem 
for  a  certain  cavalier,  (this  being,  it  seems,  the  phrase  of  the  day  to 
express  a  meaning  which  persons  usually  prefer  to  convey  by  a  circum- 
locution,) was  asked  by  the  priest,  "  Combien  de  fois  vous  a-t-il 
estimee  1"  which  story,  whether  true  or  invented,  got  into  circulation, 
and  led  to  the  abandonment  of  the  phrase  in  that  peculiar  sense.  If 
it  had  not  been  abandoned  in  that  sense,  it  would  soon  have  been 
discai'ded  in   any   other  sense;  and  finally,  perhaps,  lost  altogether, 


TERMINOLOGY    AND   NOMENCLATURE.  421 

because  when  confined  to  that  particular  meaning,  it  would  no  longer 
have  had  the  indistinctness  which  formed  its  recommendation.  Many 
terms,  in  many  diHcrent  languages,  which  originally  had  a  more  general 
meaning,  have  been  unfitted  for  other  uses  by  acquiring  this  very  con- 
notation. And  a  vast  variety  of  other  words,  without  any  relation  to 
that  peculiar  subject,  have  one  after  another  fallen  into  disuse  except 
among  the  coarse  and  uncultivated,  because  tlicy  had  come  to  connote 
too  directly  and  unequivocally  something  which  people  did  not  like  to 
have  brought  very  distinctly  before  their  imagination. 

"Without  any  further  multiplication  of  examples  to  illustrate  the 
changes  which  usage  is  continually  making  in  the  signification  of  terms, 
I  shall  add,  as  a  practical  rule,  that  the  logician,  not  being  able  to  pre- 
vent such  transformations,  should  submit  to  them  with  a  good  grace 
when  they  are  iiTevocably  effected,  and  if  a  definition  is  necessary, 
define  the  word  according  to  its  new  meaning  ;  retaining  the  former  as 
a  second  signification,  if  it  is  needed,  and  if  there  be  any  chance  of 
behig  able  to  preserve  it  either  in  the  language  of  philosophy  or  in 
common  use.  Logicians  cannot  ma1<c  the  meaning  of  any  but  scien- 
tific terms  :  that  of  all  other  words  is  made  by  the  collective  human 
race.  But  logicians  can  ascertain  clearly  what  it  is  which,  working 
obscurely,  has  guided  the  general  mind  to  a  particular  employment  of 
a  name ;  and  when  they  have  found  this,  they  can  clothe  it  in  such 
distinct  and  j^ermanent  terms,  that  mankind  shall  see  the  meaning 
which  before  they  only  felt,  and  shall  not  suffer  it  to  be  afterwards 
forgotten  or  misapprehended.  And  this  is  a  power  not  lower  in  dignity, 
and  far  less  liable  to  abuse,  than  the  chimerical  one  of  domineering 
over  language. 


CHAPTER  VI. 

THE  PRINCrPLES  OF  A  PHILOSOPHICAL  LANGUAGE  FURTHER  CONSIDERED. 

§  1.  We  have,  thus  far,  considered  only  one  of  the  requisites  of  a 
language  adapted  for  the  investigation  of  truth ;  that  its  terms  shall 
each  of  them  convey  a  determinate  and  unmistakable  meaning.  There 
are,  however,  as  we  have  already  remarked,  other  requisites  ;  some  of 
them  important  only  in  the  second  degree,  but  one  which  is  funda- 
mental, and  barely  yields  in  point  of  importance,  if  it  yields  at  all,  to 
the  ([uality  which  we  have  already  discussed  at  so  much  length.  That 
the  language  may  be  fitted  for  its  purposes,  not  only  should  every 
word  perfectly  express  its  meaning,  but  there  should  be  no  important 
meaning  without  its  word.  Whatever  we  have  occasion  to  think  of 
often,  and  for  scientific  purposes,  ought  to  have  a  name  appropriated 
to  it. 

This  requisite  of  philosophical  language  may  be  considered  under 
three  different  heads;  that  number  of  separate  conditions  being  in- 
volved in  it. 

§  2.  First;  there  ought  to  be  all  such  names,  as  are  needful  for 
making  such  a  record  of  individual  observations  that  the  words  of  the 


422  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

record  shall  exactly  show  what  fact  it  is  which  has  been  observed.  In 
other  words,  there  must  be  an  accurate  Descriptive  Terminology. 

The  only  things  which  we  can  obsei-\e  directly  being  our  own  sen- 
sations, or  other  feelings,  a  complete  descriptive  language  would  be 
one  in  which  there  should  be  a  name  for  eveiy  variety  of  elementary 
sensation  or  feeling.  Combinations  of  sensations  or  feelings  may  al- 
ways be  described,  if  we  have  a  name  for  each  of  the  elementary 
feelino- s  which  compose  them ;  but  brevity  of  description,  as  well  as 
clearness  (which  often  depends  very  much  upon  brevity,)  is  greatly 
promoted  by  giving  distinctive  names  not  to  the  elements  alone,  but  also 
to  all  combinations  which  are  of  frequent  recuiTence.  On  this  occasion 
I  cannot  do  better  than  quote  from  Mr.  Whewell  some  of  the  excellent 
remarks  which  he  has  made  on  this  important  branch  of  our  subject. 

"  The  meaning"  (says  he*)  "of  [descriptive]  technical  terms,  can 
be  fixed  in  the  first  instance  only  by  convention,  and  can  be  made 
intelligible  only  by  presenting  to  the  senses  that  which  the  terms  are 
to  signify.  The  knowledge  of  a  color  by  its  name  can  only  be 
taught  through  the  eye.  No  description  can  convey  to  a  hearer  A\hat 
we  mean  by  apple-green  or  French-gray.  It  might,  perhaps,  be  sup- 
posed that,  in  the  first  example,  the  term  apple,  refemng  to  so 
familiar  an  object,  sufficiently  suggests  the  color  intended.  But  it  may 
easily  be  seen  that  this  is  not  true ;  for  apples  are  of  many  different 
hues  of  green,  and  it  is  only  by  a  conventional  selection  that  we  can 
appropriate  the  term  to  one  special  shade.  When  this  appropriation 
is  once  made,  the  term  refers  to  the  sensation,  and  not  to  the  paxts  of 
the  terra ;  for  these  enter  into  the  compound  merely  as  a  help  to  the 
-memory,  wliether  the  suggestion  be  a  natural  connexion  as  in  '  apple- 
green,'  or  a  casual  one  as  in  '  French-gray.'  In  oi'der  to  derive  due 
advantage  from  technical  terms  of  this  kind,  they  must  be  associated 
imjnediatehj  with  the  perception  to  which  they  belong,  and  not  con- 
nected with  it  through  the  vague  usages  of  common  language.  The 
memory  must  retain  the  sensation ;  and  the  technical  word  must  be 
understood  as  directly  as  the  most  familiar  word,  and  more  distinctly. 
When  we  find  such  terms  as  tin-white  or  pinchbeck-broun,  the  metallic 
color  so  denoted  ought  to  start  up  in  our  memory  without  delay  or 
search. 

"  This,  which  it  is  most  important  to  recollect  with  respect  to  the 
simpler  properties  of  bodies,  as  color  and  form,  is  no  less  ti'ue  with 
respect  to  more  compound  notions.  In  all  cases  the  terai  is  fixed  to  a 
peculiar  meaning  by  convention ;  and  the  student,  in  order  to  use  the 
word,  must  be  completely  familiar  with  the  convention,  so  that  he  has 
no  need  to  frame  conjectures  from  the  word  itself  Such  conjectures 
would  always  be  insecure,  and  often  eiToneous.  Thus  the  ierm  papi- 
lionaceous  applied  to  a  flower  is  employed  to  indicate,  not  only  a  re- 
semblance to  a  butterfly,  but  a  resemblance  arising  from  five  petals  of 
a  certain  peculiar  shape  and  arrangement ;  and  even  if  the  resem- 
blance were  much  stronger  than  it  is  in  such  cases,  yet  if  it  were  pro- 
duced in  a  different  way,  as,  for  example,  by  one  petal,  or  two  only, 
instead  of  a  'standard,'  two  'wings,'  and  a  '  keel' consisting  of  two 
parts  more  or  less  united  into  one,  we  should  no  longer  be  justified  in 
speaking  of  it  as  a  'papilionaceous'  flov/er." 

•  Philosophy  of  the  Inductive  Sciences,  i.,  464-5. 


TERMINOLOGY   AND    NOMKNCLATURE.  423 

When,  however,  the  tliin<r  nainecl  is,  as  in  this  last  case,  a  combina- 
tion of  simple  sensations,  it  is  not  necessary  ih  order  to  learn  the 
meaning  of  the  word,  tliat  the  student  should  refer  back  to  the  sensa- 
tions themselves  ;  it  may  be  communicated  to  him  through  the  medium 
of  other  words ;  the  terms,  in  short,  may  be  delined.  But  the  names 
of  elementary  sensations,  or  elementary  feelings  of  luiy  sort,  cannot  be 
dehned  ;  nor  is  there  any  means  of  making  theiy  signification  known 
but  by  making  the  learner  experience  the  sensation,  or  referring  him, 
through  some  known  mark,  to  his  remembrance  of  having  experienced 
it  before.  Hence  it  is  only  the  impressions  on  the  outward  senses,  or 
those  inward  feelings  which  are  connected  in  a  very  obvious  and 
uniform  manner  with  outward  objects,  that  are  really  susceptible  of 
an  exact  descriptive  language.  The  countless  variety  of  sensations 
which  arise,  for  instance,  from  disease,  or  fiom  peculiar  physiological 
states,  it  would  be  in  vain  to  attempt  to  name  ;  for  as  no  one  can  judge 
whether  the  sensation  1  have  is  the  same  with  his,  the  name  may  not 
have,  to  us  two,  any  community  of  meaning.  Tlie  same;  may  be  said, 
to  a  considerable  extent,  of  purely  mental  feelings.  But  in  some  of 
the  sciences  which  are  conversant  with  external  objects,  it  is  scarcely 
possible  to  surpass  the  perfection  to  which  this  quality  of  a  philosophi- 
cal language  lias  been  carried. 

"  The  formation"  (continues  Mr.  Whewell*)  "  of  an  exact  and  ex- 
tensive descriptive  language  for  botany  has  been  executed  with  a 
degree  of  skill  and  felicity,  which,  before  it  was  attained,  could  hardly 
have  been  dreamed  of  as  attainable.  Every  part  of  a  plant  has  been 
named ;  and  the  form  of  every  part,  even  the  most  minute,  has  had  a 
large  assemblage  of  descriptive  terms  appropriated  to  it,  by  means  of 
which  the  botanist  can  convey  and  receive  knowledge  of  form  and 
structure,  as  exactly  as  if  each  minute  })art  were  presented  to  him 
vastly  magnified.  This  acquisition  was  part  of  the  Linnaean  reform  .... 
*  Tournefort,'  says  Decandolle,  '  appears  to  have  been  the  first  who 
really  perceived  the  utility  of  fixing  the  sense  of  terms  in  such  a  way 
as  always  to  employ  the  same  word  in  the  same  sense,  and  always  to 
express  the  same  idea  by  the  same  word ;  but  it  was  Linnteus  who 
really  created  and  fixed  this  .botanical  language,  and  this  is  his  fairest 
claim  to  glory,  for  by  this  fixation  of  language  lie  lias  shed  clearness 
and  precision  over  all  parts  of  the  science.' 

"  It  is  not  necessary  here  to  give  any  detailed  account  of  the  terms 
of  botany.  The  fundamental  ones  have  been  gradually  introduced,  as 
the  parts  of  plants  were  more  carefully  and  minutely  examined. 
Thus  the  flower  was  necessarily  distinguished  into  the  calyx,  the 
corolla,  the  stamcnx,  and  the  piatils;  the  sections  of  the  corolla  were 
termed  petals  by  Columna ;  those  of  the  calyx  were  called  sepals  by 
Necker.  Sometimes  terms  of  greater  generality  were  devised;  as 
perianth  to  include  the  calyx  and  corolla,  whether  one  or  both  of  these 
were  present;  pericarp,  for  the  part  inclosing  the  grain,  of  whatever 
kind  it  be,  fruit,  nut,  pod,  &c.  And  it  may  easily  be  imagined  that 
descriptive  terms  may,  by  definition  and  combination,  become  very 
numerous  and  distinct.  Thus  leaves  may  be  called  pinnatiful,  pinna- 
tiparlite,  pinnatiscct,  pinnatil abate,  palmatijid,  palmatipartite,  &c., 
and  each  of  these  words  designates  difl'erent  combinations  of  the  modes 

♦  Philosophy  of  the  Inductive  Sciences,  i.,  465-7. 


424  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

and  extent  of  the  divisions  of  the  leaf  with  the  divisions  of  its  outHne, 
In  some  cases,  arbiti-ary  numerical  relations  are  introduced  into  the 
definition :  thus,  a  leaf  is  called  bilobate,  when  it  is  divided  into  two 
parts  by  a  notch ;  but  if  the  notch  go  to  the  middle  of  its  length,  it  is 
bijid;  if  it  go  near  the  base  of  the  leaf,  it  is  bipartite;  if  to  the  base, 
it  is  bisect.  Thus,  too,  a  pod  of  a  cruciferous  plant  is  a  silica,  if  it  is 
four  times  as  long  as  it  is  broad,  but  if  it  be  shorter  than  this  it  is  a 
silicula.  Such  terms  being  established,  the  form  of  the  very  complex 
leaf  or  frond  of  a  fern*  is  exactly  conveyed  by  the  following  phrase :  — 
'fronds  rigid  pinnate,  pinnae  recurved  subunilateral  pinnatifid,  the  seg- 
ments linear  undivided  or  bifid  spinuloso-serrate.' 

"Other  characters,  as  well  as  form,  are  conveyed  with  the  like  pre- 
cision: Color  by  means  of  a  classified  scale  of  colors. ...  This  was 
done  with  most  precisionby  Werner,  and  his  scale  of  colors  is  still  the 
most  usual  standard  of  naturalists.  Werner  also  introduced  a  more 
exact  terminology  with  regard  to  other  characters  which  are  impor- 
tant in  mineralogy,  as  lustre,  hardness.  But  Mohs  improved  upon 
this  step  by  giving  a  numerical  scale  of  hardness,  in  which  talc  is  1, 

gypsum  2,   calc   spar    3,  and   so    on Some   properties,  as   specific 

gi'avity,  by  their  definition  give  at  once  a  numerical  measure ;  and 
others,  as  crystaline  form,  require  a  very  considerable  array  of  math- 
ematical calculation  and  reasoning,  to  point  out  their  relations  and 
gradations." 

§  3.  Thus  far  of  Descriptive  Terminology,  or  of  the  language 
requisite  for  placing  upon  record  our  observation  of  individual  in- 
stances. But  when  we  proceed  from  this  to  Induction,  or  rather  to 
that  comparison  of  observed  instances  which  is  the  preparatory  step 
towards  it,  we  stand  in  need  of  an  additional  and  a  difierent  sort  of 
general  names. 

Whenever,  for  purposes  of  Induction,  we  find  it  necessary  to  intro- 
duce (in  Mr.  Whewell's  phraseology)  some  new  general  conception; 
that  is,  whenever  the  comparison  of  a  set  of  phenomena  leads  to  the 
recognition  in  them  of  some  common  circumstance,  which,  our  atten- 
tion not  having  been  directed  to  it  on  any  former  occasion,  is  to  us  a 
new  phenomenon  ;  it  is  of  importance  that  this  new  conception,  or  this 
new  result  of  abstraction,  should  have  a  name  appropriated  to  it; 
especially  if  the  circumstance  it  involves  be  one  which  leads  to  many 
consequences,  or  which  is  likely  to  be  found  also  in  other  classes  of 
phenomena.  No  doubt,  in  most  cases  of  the  kind,  the  meaning  might 
be  conveyed  by  joining  together  several  words  already  in  use.  But 
when  a  thing  has  to  be  often  spoken  of,  there  are  more  reasons  than 
the  saving  of  time  and  space,  for  speaking  of  it  in  the  most  concise 
manner  possible.  What  darkness  would  be  spread  over  geometrical 
demonstration,  if  wherever  the  word  circle  is  used,  the  definition  of  a 
circle  were  inserted  histead  of  it.  In  mathematics  and  its  applications, 
where  the  nature  of  the  processes  demands  that  the  attention  should 
be  strongly  concentrated,  but  does  not  require  that  it  should  be  widely 
diffused,  the  importancd  of  concentration  also  in  the  expressions  has 
always  been  duly  felt ;  and  a  mathematician  no  sooner  finds  that  he 
ahall  often  have  occasion  to  speak  of  the  same  two  things  together, 

*  "  Hymeiiovhyllum  WihonV 


TERMINOLOGY    AND    NOMENCLATURE.  425 

than  he  at  once  creates  a  term  to  express  them  whenever  conihined.: 
just  as,  in  his  algebraical  operations,  he  substitutes  for  [a"'  +  }/')  J^,  or 

for  -  -| h  -r  +  &c.,  the  sinprle  letter  P,  Q,,  or  S;  not  solely  to  shorten 

bed 

his  symbolical  expressions,  but  to  simplify  the  purely  intellectual  part 
of  his  operations,  by  enabling  the  mind  to  give  its  exclusive  attention 
to  the  relation  between  the  (puintity  S  and  the  other  quantities  which 
enter  into  the  equatibn,  without  being  distracted  by  thinking  unneces- 
sarily of  the  parts  of  which  S  is  itself  composed. 

But  there  is  another  reason,  in  addition  to  that  of  promoting  perspi- 
cuity, for  giving  a  brief  and  compact  name  to  each  of  the  more  con- 
siderable results  of  abstraction  which  are  obtained  in  the  course  of  our 
intellectual  phenomena.  By  naming  them,  we  fix  our  attention  upon 
them  ;  we  keep  them  more  constantly  before  the  mind.  The  names  are 
remembered,  and  being  remembered,  suggest  their  definition  ;  while  if 
instead  of  specific  and  characteristic  names, the  meaning  had  been  ex- 
pressed by  putting  together  a  number  of  other  names,  that  particular 
combination  of  words  already  in  common  use  for  other  purposes  would 
liave  had  nothing  to  make  itself  remembered  by.  If  we  want  toren- 
der  a  particular  combination  of  ideas  permanent  in  the  mind,  there  is 
nothing  which  clenches  it  like  a  name  specially  devoted  to  express  it. 
If  mathematicians  had  been  obliged  to  speak  of  "  that  to  which  a 
quantity,  in  increasing  or  diminisliing,  is  always  approaching  nearer^ 
so  that  the  difference  becomes  less  than  any  assignable  quantity,  but 
to  which  it  never  becomes  exactly  equal,"  instead  of  expressing  all 
this  by  the  simple  phrase,  "  the  limit  of  a  quantity,"  we  should  probably 
have  long  remained  without  most  of  the  important  truths  which  have 
been  discovered  by  means  of  the  relation  between  quantities  of  various 
kinds  and  their  limits.  If  instead  of  speaking  of  momentum,  it  had 
been  necessary  to  say  "  the  product  of  the  number  of  units  of  velocity 
in  the  velocity  by  the  number  of  units  of  mass  in  the  mass,"  many  of 
the  dynamical  truths  now  apprehended  by  means  of  this  complex  idea, 
would  probably  have  escaped  notice  for  want  of  recalling  the  idea 
itself  with  sufficient  readiness  and  familiarity.  And  on  subjects  less 
remote  from  the  toj)ics  of  popular  discussion,  whoever  wishes  to  draw 
attention  to  some  new  or  unfamiliar  distincti(m  among  things,  will  find 
no  way  so  sure  as  to  invent  or  select  suitable  names  for  the  express 
purpose  of  marking  it. 

A  volume  devoted  to  explaining  what  civilization  is  and  is  not,  does 
not  raise  so  vivid  a  conception  of  it  as  the  single  expression,  that  Civi- 
lization is  a  different  thing  from  Cultivation ;  the  compactness  of  that 
brief  designation  for  the  contrasted  quality  being  an  equivalent  for  a 
long  discussion.  So,  if  we  would  imjiress  forcibly  upon  the  under- 
standing and  memory  the  distinction  between  what  a  representative 
government  should  be  and  what  it  (jftcn  is,  we  cannot  more  effectually 
do  so  than  by  saying  that  Rej)resentation  is  not  Delegation.  Dr. 
Chalmers,  in  order  to  distinguish  his  scheme  of  clerical  sujierintcnd- 
ence  of  a  parish  from  the  mere  keeping  a  church  open  which  people 
might  come  to  or  not  as  they  s[)ontaneously  chose,  called  very  expres- 
sively the  fi)rmcr  the  "  aggressive"  system,  the  latter  the  "  attractive." 
When  the  earlier  electricians  fi)und  that  there  were  two  different  kuids 
of  electrical  excitement,  they  soon  made  tlic  world  familiar  with  them 
by  giving  them  the  names  of  positive  and  negative,  vitreous  and  resinous. 
3H 


426  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

Hardly  any  original  thoughts  on  raeiital  or  social  subjects  ever  make 
their  way  among  mankind  or  assume  their  proper  importance  in  the 
minds  even  of  their  inventors,  until  aptly  selected  words  or  phrases 
have  as  it  were  nailed  them  down  and  held  them  fast. 

§  4.  Of  the  three  essential  parts  of  a  philosophical  language,  we 
have  now  mentioned  two  :  a  terminology  suited  for  describing  with 
precision  the  individual  facts  observed  ;  and  a  name  for  every  common 
property  of  any  importance  or  interest,  which  we  detect  by  comparing 
those  facts  :  including  (as  the  concretes  coi'responding  to  those  abstract 
terms)  names  for  the  classes  which  we  artificially  construct  in  virtue  of 
those  properties,  or  as  many  of  them,  at  least,  as  we  have  frequent 
occasion  to  predicate  anything  of. 

But  there  is  a  sort  of  classes,  for  the  recognition  of  which  no  such 
elaborate  process  is  necessary ;  because  each  of  them  is  marked  out 
fi'om  all  others  not  by  some  one  property,  the  detection  of  which  may 
depend  upon  a  difficult  act  of  abstraction,  but  by  its  properties  generally. 
I  mean,  the  Kinds  of  things,  in  the  sense  which,  in  this  treatise,  has 
been  systematically  attached  to  that  term.  By  a  Kind,  it  will  be  re- 
membered, we  mean  one  of  those  classes  which  are  distinguished  from 
all  others  not  by  one  or  a  few  definite  properties,  but  by  an  unknown 
multitude  of  them  ;  the  combination  of  properties  on  which  the  class 
is  grounded,  being  a  mere  index  to  an  indefinite  number  of  other  dis- 
tinctive attributes.  The  class  horse  is  a  Kind,  because  the  things  which 
agree  in  possessing  the  characters  by  which  we  recognize  a  horse, 
agree  in  a  gi-eat  number  of  other  properties  as  we  know,  and  it  cannot 
be  doubted,  in  many  more  than  we  know.  Animal,  again,  is  a  Kind, 
because  no  definition  that  could  be  given  of  the  name  animal  could 
either  exhaust  the  properties  common  to  all  animals,  nor  supply  prem- 
isses fi'om  which  the  remainder  of  those  properties  could  be  inlbrred. 
But  a  combination  of  properties  which  does  not  give  evidence  of  the 
existence  of  any  other  independent  peculiarities,  does  not  constitute  a 
Kind,  White  horse,  therefore,  is  not  a  Kind  :  because  horses  which 
agree  in  whiteness,  do  not  agree  in  anything  else,  except  in  the  quali- 
ties common  to  all  horses,  and  in  whatever  may  be  the  causes  or  efiects 
of  that  particular  color.  • 

On  the  principle  that  there  should  be  a  name  for  everything  which 
we  have  frequent  occasion  to  make  assertions  about,  there  ought  evi- 
dently to  be  a  name  for  every  Kind  ;  for  as  it  is  the  very  nature  of  a 
Kind  that  the  individuals  composing  it  have  an  indefinite  multitude  of 
properties  in  common,  it  follows  that,  if  not  with  our  present  knowl- 
edge, yet  with  that  which  we  may  hereafter  acquire,  the  Kind  is  a 
subject  to  which  there  will  have  to  be  applied  many  predicates.  The 
third  component  element  of  a  philosophical  language,  therefore,  is  that 
there  shall  be  a  name  for  every  Kind.  In  other  words,  there  must 
not  only  be  a  terminology  but  also  a  nomenclature.  ' 

The  words  Nomenclature  and  Terminology  are  employed  by  most 
authors  almost  indiscriminately  ;  Mr.  Whewell  being,  as  far  as  I  am 
aware,  the  first  wi'iter  who  has  regularly  assigned  to  the  two  words 
different  meanings.  The  distinction  however  which  he  has  drawn 
between  them  being  a  real  and  an  important  one,  his  example  is  likely 
to  be  followed  ;  and  (as  is  apt  to  be  the  case  when  such  innovations  in 
language  are  felicitously  made)  a  vague  sense  of  the  distinction  is  found 


TERMINOLOGY    AND    NOMENCLATURE.  427 

to  have  influenced  the  employment  of  the  terms  in  common  practice, 
before  the  expediency  had  been  pointed  out  of  discriminatiu'j^  lh(!ni 
philosophically.  Every  one  would  say  that  the  refoi'm  eff'ectcul  by 
Lavoisier  and  Guyton-Morveau  in  the  language  of  chemistry  consisted 
in  the  introduction  of  a  new  nomenclature,  not  of  a  new  terminology. 
Linear,  lanceolate,  oval,  or  oblong,  serrated,  dentate,  or  crenate  leaves, 
are  expressions  forming  part  of  the  terminology  of  botany,  while  the 
names  "  Viola  odorata,"  and  "  Ulex  europa^us,"  belong  to  its  nomen- 
clature. 

A  nomenclature  may  be  defined,  the  collection  of  the  names  of  all 
the  Kinds  with  which  any  branch  of  knowledge  is  conversant,  or  more 
properly,  of  all  the  lowest  Kinds,  or  ivfimcc  species,  those  which  may 
be  subdivided  indeed,  but  not  into  Kinds,  and  which  generally  accord 
with  what  in  natural  history  are  termed  simply  species.  Science 
possesses  two.spiendid  examples  of  a  systematic  nomenclature  ;  that 
of  plants  and  animals,  constructed  by  Linnjeus  and  his  successors,  and 
that  of  chemistry,  wiiich  we  owe  to  the  illustrious  group  of  chemists 
who  tlourislied  in  France  towards  the  close  of  the  eighteenth  century. 
In  these  two  departments,  not  only  has  every  known  species,  or  lowest 
Kind,  a  name  assigned  to  it,  but  when  new  lowest  Kinds  are  discovered, 
names  are  at  once  given  to  them  upon  an  uniform  principle.  In  other 
sciences  the  nomenclature  is  not  at  present  constructed  upon  any  sys- 
tem, either  because  the  species  to  be  named  are  not  mnnerous  enough 
to  require  one  (as  in  geometry  for  example),  or  because  no  one  has 
yet  suggested  a  suitable  principle  for  such  a  system,  as  in  mineralogy; 
in  which  the  want  of  a  scientifically  constructed  nomenclature  is  now 
the  principal  cause  which  retards  the  progress  of  the  science. 

§  5.  A  word  which  carries  on  its  face  that  it  belongs  to  a  nomen- 
clature, seems  at  first  sight  to  differ  from  other  concrete  general  names 
in  this — that  its  meaning  does  not  reside  in  its  connotation,  in  the 
attributes  implied  in  it,  but  in  its  denotation,  that  is,  in  the  particular 
group  of  things  which  it  is  appointed  to  designate ;  and  cannot,  there- 
fore, be  unfolded  by  means  of  a  definition,  but  must  be  made  known  in 
another  way.  Mr.  Whewell  seems  to  incline  to  this  opinion,  which, 
however,  appears  to  me  erroneous.  Woids  belonging  to  a  nomencla- 
ture differ,  I  conceive,  from  other  words  mainly  in  this,  that  besides 
the  ordinary  connotation,  they  have  a  peculiar  one  of  their  own : 
besides  connoting  certain  attributes,  they  also  connote  that  those  attri- 
butes are  distinctive  of  a  Kind.  The  tenn  "  peroxide  of  iron,"  for 
example,  belonging  by  its  form  to  the  systematic  nomenclature  of 
chemistry,  bears  upon  its  face  that  it  is  the  name  of  a  peculiar  Kind 
of  substance.  It  moreover  connotes,  like  the  name  of  any  other  class, 
some  portion  of  the  properties  common  to  the  class;  in  this  instance 
the  property  of  being  a  compound  of  iron  and  the  largest  dose  of  oxygen 
with  which  iron  will  combine.  These  two  things,  the  fact  of  being 
such  a  compound,  and  the  fact  of  being  a  Kind,  constitute  the  conno- 
tation of  the  name  peroxide  of  iron.  When  we  say  of  the  sid)stance 
before  us,  that  it  is  the  peroxide  of  iron,  we  thereby  assert,  first,  that 
it  is  a  compound  of  iron  and  a  maximum  of  oxygen,  and  next,  that  the 
substance  so  composed  is  a  peculiar  Kind  of  substance. 

Now,  this  second  part  of  the  connotation  of  any  word  belonging  to 
a  nomenclature  is  as  essential  a  portion  of  its  meaning  as  the  first  part, 


428  OPERATIONS    SUDSIDIARY    TO    INDUCTION. 

while  the  definition  can  only  declare  the  first :  and  hence  the  appear- 
ance that  the  signification  of  such  terms  cannot  be  conveyed  by  a 
defijiition :  which  appearance,  however,  is  fallacious.  The  name  Viola 
odorata  denotes  a  Kind,  of  which  a  certain  number  of  characters, 
sufficient  to  distinguish  it,  are  enunciated  in  botanical  works.  This 
enumeration  of  characters  is  stu'ely,  as  in  other  cases,  a  definition  of  the 
name.  No,  say  some,  it  is  not  a  definition,  for  the  name  Viola  odorata 
does  not  mean  those  characters ;  it  means  that  particular  gi-oup  of 
plants,  and  the  characters  are  selected  from  among  a  much  gTcater 
number,  merely  as  marks  by  which  to  recognize  the  group.  By  no 
means,  I  reply ;  the  name  does  not  mean  that  group,  for  it  Avould  be 
applied  to  that  group  no  longer  than  while  the  gi'oup  is  believed  to  be 
an  infima  species;  if  it  were  to  be  discovered  that  several  distinct 
Kinds  have  been  confounded  under  this  one  name,  no  one  would  any 
longer  apply  the  name  Viola  odorata  to  the  whole  of  the  group,  but 
would  apply  it,  if  retained  at  all,  to  one  only  of  the  Kinds  contained 
therein.  What  is  imperative,  therefore,  is  not  that  the  name  shall  de- 
note one  particular  collection  of  objects,  but  that  it  shall  denote  a  Kind, 
and  a  lowest  Kind.  The  form  of  the  name  declares  that,  happen  what 
will,  it  is  to  denote  an  infima  species ;  and  that,  therefore,  the  proper- 
ties which  it  connotes,  and  which  are  expressed  in  the  definition,  are 
to  be  connoted  by  it  no  longer  than  while  we  continue  to  believe  that 
those  properties,  when  found  together,  indicate  a  Kind,  and  that  the 
whole  of  them  are  found  in  no  more  than  one  Kind. 

With  the  addition  of  this  peculiar  connotation,  imj^lied  in  the  form 
of  every  word  which  belongs  to  a  systematic  nomenclature;  the  set  of 
characters  which  is  employed  to  discriminate  each  Kind  from  all  other 
Kinds  (and  which  is  a  real  definition)  constitutes  as  completely  as  in 
any  other  case  the  whole  meaning  of  the  term.  It  is  no  objection  to 
say  that  (as  is  often  the  case  in  natural  history),  the  set  of  characters 
may  be  changed,  and  another  substituted  as  being  better  suited  for  the 
pui'poSe  of  distinction,  while'  the  word,  still  continuing  to  denote  the 
same  group  of  things,  is  not  considered  to  have  changed  its  meaning. 
For  this  is  no  more  than  may  happen  in  the  case  of  any  other  general 
name  :  we  may,  in  reforming  its  connotation,  leave  its  denotation  un- 
touched ;  and  it  is  generally  desirable  to  do  so.  The  connotation, 
however,  is  not  the  less  for  this  the  real  meaning,  for  we  at  once  apply 
the  name  wherever  the  characters  set  down  in  the  definition  are  found; 
and  that  which  exclusively  guides  us  in  applying  the  term,  must  con- 
stitute its  signification.  If  we  find,  contrary  to  our  previous  belief, 
that  the  characters  are  not  peculiar  to  one  species,  we  cease  to  use  the 
term  coextensively  with  the  characters ;  but  then  it  is  because  the 
other  portion  of  the  connotation  fails ;  the  condition  that  the  class  must 
be  a  Kind.  The  connotation,  therefore,  is  still  the  meaning ;  the  set 
of  descriptive  characters  is  a  true  definition :  and  the  meaning  is  un- 
folded, not  indeed  (as  in  other  cases)  by  the  definition  alone,  but  by 
the  definition  and  the  form  of  the  word  taken  together. 

§  6.  We  have  now  analyzed  what  is  implied  in  the  two  principal 
requisites  of  a  philosophical  language ;  first,  precision  or  definiteness, 
and  secondly,  completeness.  Any  further  remarks  on  the  mode  of 
constructing  a  nomenclature  must  be  deferred  until  we  treat  of  Classi- 
fication ;  the  mode  of  naming  the  Kinds  of  things  being  necessarily 


TERMINOLOGY    AND    NOMENCLATCTRE.  429 

subordinate  to  the  mode  of  aiTaiif^insr  those  Kinds  into  larger  classes. 
With  respect  to  the  minor  n'<iuisitos  of  Tenninology,  some  of  them 
are  well  stated  and  copiously  iUustrated  in  the  "Aphorisms  on  the 
Language  of  Science,"  included  in  Mr,  Wlievveirs  Philos02>hu  nf  the 
Inductive  Sciences.  These,  as  being  of  secondary,  importance  in  the 
peculiar  pouit  of  view  of  Logic,  we  shall  leave  the  reader  to  seek  in 
Mr.  Whewell's  pages,  and  shall  confine  our  own  observations  to  one 
more  quality,  which,  next  to  the  two  already  treated  of,  appears  to  be 
the  most  valuable  which  the  language  of  science  can  possess.  Of  this 
quality  a  general  notion  may  be  conveyed  by  the  following  aphorism: 

Whenever  the  nature  of  the  subject  permits  our  reasoning  process 
to  be,  without  danger,  carried  on  mechanically,  the  language  should 
be  constructed  on  as  mechanical  principles  as  possible ;  while  in  the 
contrary  case,  it  should  be  so  constructed  that  there  shall  be  the  greatest 
possible  obstacles  to  a  merely  mechanical  use  of  it. 

I  am  conscious  that  this  maxim  requires  much  explanation,  which  I 
shall  at  once  proceed  to  give.  And  first,  as  to  what  is  meant  by  using 
a  language  mechanically.  The  complete  or  extreme  case  of  the  mo 
chanical  use  of  language,  is  when  it  is  used  without  any  consciousness 
of  eP  meaning,  and  with  only  the  consciousness  of  using  certain  visible 
or  audible  marks  in  conformity  to  technical  rules  previously  laid  down. 
This  extreme  case  is,  so  far  as  I  am  aware,  nowhere  realized  except 
in  the  figures  of  arithmetic  and  the  symbols  of  algebra,  a  language 
unique  in  its  kind,  and  approaching  as  nearly  to  perfection,  for  the  pur- 
poses to  which  it  is  destined,  as  can,  perhaps,  be  said  of  any  creation 
of  the  human  mind.  Its  perfection  consists  in  the  completeness  of  its 
adaptation  to  a  purely  mechanical  use.  The  symbols  are  mere  coun- 
ters, without  even  the  semblance  of  a  meaning  apart  from  the  conven- 
tion which  is  renewed  each  time  they  are  employed,  and  which  is  al- 
tered at  each  renewal,  the  same  symbol  a  or  x  being  used  on  diflbrertt 
occasions  to  represent  things  which  (except  that,  like  all  things,  they 
are  susceptible  of  being  numbered)  have  no  property  in  common. 
There  is  nothing,  therefore,  to  distract  the  mind  from  the  set  of  mechani- 
cal operations  which  are  to  be  perft)rmed  upon  the  symbols,  such  as 
squaring  both  sides  of  the  equation,  multiplying  or  dividing  by  the 
same  or  by  equivalent  symbols,  and  so  forth.  Each  of  these  opera- 
tions, it  is  true,  coiTesponds  to  a  syllogism  ;  represents  one  step  of  a 
ratiocination  relating  not  to  the  symbols,  but  to  the  things  signified  by 
them.  But  as  it  has  been  found  -jiracticable  to  frame  a  techirical  form, 
by  conforming  to  which  we  can  make  sure  of  finding  the  conclusion  of 
the  ratiocination,  our  end  can  be  completely  attained  without  our  ever 
thinking  of  anything  but  the  symbols.  Being  thus  intended  to  work 
merely  as  mechanism,  they  have  the  qualities  which  mechanism  ought 
to  have.  They  are  of  the  least  possible  bulk,  so  that  they  take  up 
scarcely  any. room,  and  waste  no  time  in  their  manipulation ;  they  are 
compact,  and  fit  so  closely  together  that  the  eye  can  take  in  the  whole 
at  once  of  almost  every  operation  wliich  they  are  employed  to  perfoiTn. 

These  admirable  properties  of  the  symbolical  language  of  mathe- 
matics have  made  so  strong  an  impression  on  the  minds  of  many  phi- 
losophers, as  to  have  led  them  to  consider  the  symbolical  language  in 
question  as  the  ideal  type  of  philosophical  language  generally ;  to 
think  that  names  in  general,  or  (as  they  are  fond  of  calling  them)  signs, 
are  fitted  for  the  purposes  of  thought  in  proportion  as  they  can  be 


430  OPERATIONS    SUBSIDIARY  TO   INDUCTION. 

made  to  approximate  to  the  compactness,  the  entix-e  unmeaningness, 
and  the  capability  of  being  used  as  counters  without  a  thought  of  what 
they  represent,  which  are  characteristic  of  the  a  and  h,  the  x  and  y,  of 
algebra.  This  notion  has  led  to  sanguine  views  of  the  acceleration  of 
the  progress  of  science  by  means  which,  as  I  conceive,  cannot  possi- 
bly conduce  to  that  end,  and  forms  part  of  that  exaggerated  estimate 
of  the  influence  of  signs,  which  has  contributed  in  no  small  degree  to 
prevent  the  real  laws  of  our  intellectual  ojaerations  fi-om  being  kept  in 
view,  or  even  rightly  understood. 

In  th-3  first  place,  a  set  of  signs  by  which  we  reason  without  con- 
sciousness of  their  meaning,  can  be  seniceable,  at  most,  only  in  our 
deductive  operations.  In  our  direct  inductions  we  cannot  for  a  mo- 
ment dispense  with  a  distinct  mental  image  of  the  phenomena,  since 
the  whole  operation  turns  upon  a  perception  of  the  particulars  in  which 
those  phenomena  agree  and  difler.  But,  further,  this  reasoning  by 
counters  is  only  suitable  to  a  very  limited  portion  even  of  our  deduc- 
tive processes.  In  our  reasonings  respecting  numbers,  the  only  gen- 
eral principles  which  we  ever  have  occasion  to  introduce,  are  these, 
Things  which  are  equal  to  the  same  thing  are  equal  to  one  another, 
and  The  sums  or  differences  of  equal  things  are  equal ;  with  tlfeir 
various  corollaries.  Not  only  can  no  hesitation  ever  arise  respecting 
the  applicability  of  these  principles,  since  they  are  true  of  all  mag- 
nitudes whatever  ;  but  every  possible  application,  of  which  they  are 
susceptible,  may  be  reduced  to  a  technical  rule  ;  suc"h  as,  in  fact,  the 
rules  of  the  calculus ,  are.  But  if  the  symbols  represent  any  other 
things  than  mere  numbers,  let  us  say  even  straight  or  curve  lines,  we 
hare  then  to  apj^ly  theorems  of  geometry  not  tnie  of  all  lines  withovit 
exception,  and  to  select  those  which  are  true  of  the  lines  we  are  rea- 
soning about.  And  how  can  we  do  this  unless  we  keep  completely  in 
mind  what  particular  lines  these  are  %  Since  additional  geometrical 
truths  may  be  introduced  into  the  ratiocination  in  any  stage  of  its  pro- 
gress, we  cannot  suffer  ourselves,  during  even  the  smallest  part  of  it, 
to  use  the  names  mechanically  (as  we  use  algebraical  symbols)  without 
an  image  annexed  to  them.  It  is  only  after  ascertaining  that  the  so- 
lution of  a  question  concerning  lines  can  be  made  to  depend  upon  a 
previous  question  concerning  numbers,  or  in  other  words  after  the 
question  has  been  (to  speak  technically)  reduced  to  an  equation,  that 
the  unmeaning  signs  become  available,  and  that  the  nature  of  the  facts 
themselves  to  which  the  investigation  relates  can  be  dismissed  from 
the  mind.  Up  to  the  establishment  of  the  equation,  the  language  in 
which  mathematicians  cairy  on  their  reasoning  does  not  differ  in  char- 
acter fi-om  that  employed  by  close  reasoners  on  any  other  kind  of 
subject. 

I  do  not  deny  that  every  correct  ratiocination,  when  thrown  into  the 
syllo.gistic  shape,  is  conclusive  from  the  mere  form  of  the  expression, 
provided  none  of  the  terms  used  be  ambiguous;  and  this  is  one  of  the 
circvmistances  which  have  led  some  philosophers  to  think  that  if  all 
names  were  so  judiciously  constiiicted  and  so  carefully  defined  as  not 
to  admit  of  any  ambiguity,  the  improvement  thus  made  in  language 
would  not  only  give  to  the  conclusions  of  every  deductive  science  the 
same  certainty  with  those  of  mathematics,  but  would  reduce  all  reason- 
ings to  the  application  of  a  technical  form,  and  enable  their  conclu- 
siveness to  be  rationally  assented  to  after  a  merely  mechanical  pro- 


TERMINOLOGY  AND    NOMENCLATURE.  431 

cess,  as  is  umloubtedly  the  case  in  algebra.  But,  if  we  except  c;eom- 
etry,  the  cDiichisioiis  ofvvliich  are  ah-eaily  as  certain  anil' exact  as  tliey 
can  be  made,  tliere  is  no  si'Ience  but  that  of  number,  in  wliicli  tht;  prac- 
ticiU  vaUcUty  of  a  reasoning  can  be  apparent  to  any  persrtn  who  has 
looked  only  at  the  form  of  the  process.  Whoever  has  assented  to  all 
that  was  said  in  the  last  Book  concerning  the  case  of  the  Composition 
of  Causes,  and  the  still  stronger  case  of  the  entire  supersession  of  one 
set  of  laws  by  another,  is  aware  that  geometry  and  algebra  are  the 
only  sciences  of  which  the  propositions  arc  categorically  true :  the 
general  propositions  of  all  other  sciences  are  true  only  hypothetically, 
sifj>j>os//ig  that  no  counteracting  cause  happens  to  interfere.  A  con- 
clusion, therefore,  however  correctly  deduced,  in  point  of  form,  from 
admitted  laws  of  nature,  will  have  no  other  than  a  hypothetical  cer- 
tainty. At  every  step  we  must  assure  ourselves  that  no  other  law  of 
nature  has  superseded,  oi-*!nterminglcd  its  operation  with,  those  which 
are  the  premisses  of  the  reasoning;  and  how  can  this  be  done  by 
merely  looking  at  the  words  ]  We  must  not  only  be  constantly  think- 
ing of  the  phenomena  themselves,  but  we  must  be  constantly  looking 
at  them;  making  ourselves  acquainted  with  the  peculiarities  of  every 
case  to  which  we  attempt  to  apply  our  general  principles. 

The  algebraic  notation,  viewed  as  a  philosophical  language,  is  per- 
fect in  its  adaptation  to  the  subjects  for  which  it  is  commonly  employed, 
namely  those  of  which  the  investigations  have  already  been  reduced 
to  the  ascertainment  of  a  relation  between  numbers.  But,  admirable 
as  it  is  for  its  own  purpose,  the  properties  by  which  it  is  rendered  such 
are  so  far  from  constituting  it  the  ideal  model  of  philosophical  language 
in  general,  that  the  more  nearly  the  language  of  any  other  branch  of 
science  approaches  to  it,  the  less  fit  that  language  is  for  its  own  proper 
functions.  On  all  other  subjects,  instead-  of  contrivances  to  prevent 
our  attention  from  being  distracted  by  thinking  of  the  meaning  of  our 
signs,  we  require  contrivances  to  make  it  impossible  that  we  should 
ever  lose  siglit  of  that  meaning  even  for  an  instant. 

With  this  view,  as  much  meaning  as  possible  should  be  thrown  into 
the  formation  of  the  word  itself;  the  aids  of  derivation  and  analogy 
being  made  available  to  keep  alive  a  consciousness  of  all  that  is  signi- 
fuid  by  it.  In  this  respect  those  languages  have  an  immense  advantage 
which  form  their  compounds  and  derivatives  from  native  roots,  like 
the  (Terman,  and  not  from  those  of  a  foreign  or  a  dead  language,  as  is 
so  much  the  case  with  English,  French,  and  Italian  :  and  the  best  are 
those  which  foiTn  them  according  to  fixed  analogies,  corresponding  to 
the  relations  between  the  ideas  to  be  expressed.  All  languages  do 
this  more  or  less,  but  especially,  among  modem  European  languages, 
the  German  :  while  even  that  is  inferior  to  the  Greek,  in  which  the 
relation  between  the  meaning  of  a  derivative  word  and  that  of  its  prim- 
itive, is  in  general  clearly  marked  by  its  mode  of  formation  ;  except  in 
the  case  of  words  compounded  with  prepositions,  which,  it  nmst  be 
acknowledged,  are  often,  in  both  those  languages,  extremely  anomalous. 

But  all  that  can  be  done,  by  the  mode  of  constructing  words,  to 
prevent  them  fi-om  degenerating  into  sounds  passing  through  the  mind 
without  any  distinct  apprehension  of  what  they  signify,  is  far  too  little 
for  the  necessity  of  the  case.  Words,  however  well  constructed  origi- 
nally, are  always  tending,  like  coins,  to  have  their  inscription  worn  off 
by  passing  from  hand  to  hand;  and  the  only  possible  mode  of  reviving 


432  OBSERVATIONS    SUBSIDIARY    TO    INDUCTION. 

it  is  to  be  ever  stamping  it  afresh,  by  living  in  the  habitual  contempla- 
tion of  the  phenomena  themselves,  and  not  resting  in  our  familiarity 
with  the  words  that  express  them.  If  any  one,  having  possessed  him- 
self of  the  laws  of  phenomena  as  recorded  in  words,  whether  delivered 
to  him  originally  by  others  or  even  found  out  by  himself,  is  content 
from  thenceforth  to  live  in  the  midst  of  these  fomiulas,  to  think  exclu- 
sivelv  of  them,  and  of  applying  them  to  cases  as  they  arise,  without 
keeping  up  his  acquaintance  with  the  realities  from  which  these  laws 
were  collected — not  only  will  he  continually  fail  in  his  practical  efforts, 
because  he  Avill  apply  his  foiTnulce  without  duly  considering  whether, 
in  this  case  and  in  that,  other  laws  of  nature  do  not  modify  or  super- 
sede them ;  but  the  fornuite  themselves  will  progressively  lose  their 
meaning  to  him,  and  he  will  cease  at  last  even  to  be  capable  of  recog- 
nizing with  certainty  whether  a  case  falls  within  the  contemplation  of 
his  fomiula  or  not.  It  is,  in  short,  as  ne(?bssary,  on  all  subjects  not 
mathematical,  that  the  things  on  which  we  reason  should  be  conceived 
by  us  in  tlie  concrete,  and  "clothed  in  circumstances,"  as  it  is  in  alge- 
bra that  we  should  keep  all  individualizing  peculiarities  sedulously  out 
of  view. 

With  this  remark  we  shall  close  our  observations  on  the  Philosophy 
of  Language. 


CHAPTER  VII. 

OF   CLASSIFICATION,   AS  SUBSIDIARY  TO   INDUCTION. 

§  1.  There  is,  as  we  have  frequently  remarked  in  this  work,  a  classi- 
fication of  things,  which  is  inseparable  from  the  fact  of  giving  them 
general  names.  Every  name  which  connotes  an  attribute,  divides,  by 
that  very  fact,  all  things  whatever  into  two  classes,  those  which  have 
the  attribute  and  those  which  have  not;  those  of  which  the  name  can 
be  predicated,  and  those  of  which  it  cannot.  And  the  division  thus 
made  is  not  merely  a  division  of  such  things  as  actually  exist,  or  are 
kno\\Ti  to  exist,  but  of  all  such  as  may  hereafter  be  discovered,  and 
even  of  all  such  as  can  be  imagined. 

On  this  kind  of  Classification  we  have  nothing  to  add  to  what  has 
previously  been  said.  The  Classification  "which  requires  to  be  dis- 
cussed as  a  separate  act  of  the  mind,  is  altogether  different.  In  the 
one,  the  arrangement  of  objects  in  groups,  and  distribution  of  them  into 
compartments,  is  a  mere  incidental  effect  consequent  upon  the  use  of 
names  given  for  another  purpose,  namely,  that  of  simply  expressing 
som.e  of  their  qualities.  In  the  other,  the  an-angement  and  distribution 
are  the  main  object,  and  the  naming  is  secondary  to,  and  purj)0sely 
conforms  itself  to,  instead  of  governing,  that  more  important  operation. 

Classification,  thus  regarded,  is  a  contrivance  for  the  best  possible 
ordering  of  the  ideas  of  objects  in  our  minds ;  for  causing  the  ideas  to 
accompany  or  succeed  one  another  in  such  a  way  as  shall  give  us  the 
greatest  command  over  our  knowledge  already  acquired,  and  lead  most 
directly  to  the  acquisition  of  more.      The  general  problem  of  Classifi- 


CLASSIFICATION.  433 

cation,  in  reference  to  tlicse  pui-poses,  may  be  stated  as  ft)llo\vs :  To 
provide  that  tilings  shall  be  thought  of  in  such  groups,  and  those  gTOups 
m  such  an  order,  as  ^vill  best  conduce  to  the  remembrance  and  to  tlie 
ascertainment  of  tlieir  laws. 

Classification  thus  considered,  diffei-s  from  classification  in  the  wider 
sense,  in  having  rcfei'cnce  to  real  objects  exclusively,  and  not  to  all 
that  are  imagijuible :  its  object  being  the  due  coordination  in  oui'  minds 
of  those  things  only,  wth  tlic  properties  of  which  wc  have  actually  , 
occasion  to  make  ourselves  acquainted.  But  on  the  other  hand  it  em- 
braces all  really  existing  objects.  We  cannot  constitute  any  one  class 
properly,  exce^Jt  in  reference  to  a  general  division  of  the  whole  of 
natui-e;  we  cannot  determine  the  group  in  which  any  one  object  can 
most  conveniently  be  placed,  without  taking  into  consideration  all  the 
varieties  of  existing  objects,  all  at  least  which  have  any  degree  of  affinity 
with  it.  No  one  family  of  plants  or  animals  could  have  been  rationally 
constituted,  except  as  part  of  a  systematic  aiTangcment  of  all  plants  or 
animals;  nor  could  such  a  general  an-angemcnt  have  been  properly 
made,  without  first  determining  the  exact  place  of  plants  and  animals 
in  a  general  division  of  nature. 

The  theory  of  scientific  classification,  in  its  most  general  aspect,  is 
now  very  well  understood,  owing  chiefly  to  the  labors  of  the  distin- 
guished natm^alists  to  whom  science  is  indebted  for  what  are  called 
Natural  An-angements  or  Classifications,  especially  of  the  organized 
world.  jMr.  Whewell,  in  his  Philosoj^hij  of  the  Inductive  Sciences,  has 
systematized  a  portion  of  the  general  logical  principles  which  these 
classifications  exemplify ;  and  this  has  been  still  more  completely  done 
by  M.  Comte,  whose  view  of  the  philosophy  of  classification,  in  the 
third  volume  of  his  great  work,  is  the  most  complete  wath  which  I  am 
acquainted. 

§  2.  There  is  no  property  of  objects  which  may  not  be  taken,  if  we 
please,  as  the  foundation  for  a  classification  or  mental  gi-oujjing  of 
those  objects ;  and  in  our  first  attempts  we  are  liko-ly  to'select  for  that 
purpose  properties  which  are  simple,  easily  conceived,  and  perceptible 
on  a  first  view,  without  any  previous  process  of  thought.  Thus  Tour- 
nefort's  aiTangemont  of  plants  was  founded  on  the  shape  and  divisions 
of  the  corolla;  and  that  which  is  commonly  called  the  Linnaean  (though 
Linnaeus  also  suggested  another  and  more  scientific  an-angeraent)  was 
grounded  chiefly  upon  the  nimiber  of  the  stamens  and  pistils. 

But  these  classifications,  which  are  at  first  recommended  by  the 
facility  they  afford  of  ascertaining  to  what  class  any  individual  belongs, 
are  seldom  much  adapted  to  the  ends  of  that  Classification  which  is 
the  subject  of  our  present  remarks.  The  Linntean  arrangement  an- 
swers the  j)uii)06e  of  making  us  think  together  of  all  those  kinds  of 
plants  which  possess  the  same  number  of  stamens  and  j)istils  ;  but  to 
think  of  them  in  that  manner  is  of  little  use,  since  we  seldom  have 
anything  to  affinn  in  common  of  the  plants  which  have  a  given  number 
of  stamens  and  pistils.  If  plants  of  the  class  Pentandria,  order  .Mono- 
gynia,  agreed  in  any  other  properties,  the  habit  of  thhiking  and  speak- 
ing of  the  plants  under  a  common  designation  would  conduce  to  our 
remembering  those  common  properties  so  far  as  they  were  ascertained, 
and  would  dispose  us  to  be  on  the  look-out  for  such  of  them  as  are  not 
yet  known.  But  since  this  is  not  the  case,  the  only  purpose  of  thought 
31 


434  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

which  the  Liniiaean  classification  serves  is  that  of  causing  us  to  re- 
member, better  than  we  should  otherwise  have  done,  the  exact  number 
of  stamens  and  pistils  of  every  species  of  plants.  Now,  as  this  prop- 
erty is  of  little  importance  or  interest,  the  remembering  it  with  any 
particular  accm-acy  is  of  no  moment.  And  inasmuch  as,  by  habitually 
thinking  of  plants  in  those  groups,  we  are  prevented  from  habitually 
thinking  of  them  in  groups  which  have  a  greater  number  of  projierties 
in  common,  the  effect  of  such  a  classification,  when  systematically 
adhered  to,  upon  our  habits  of  thought,  must  be  regarded, as  mis- 
chievous. ' 

The  ends  of  scientific  classification  are  best  answered,  when  the 
objects  are  formed  into  groups  respecting  which  a  greater  number  of 
general  propositions  can  be  made,  arid  those  propositions  more  impor- 
tant, than  could  be  made  respecting  any  other  gi'oups  into  which  the 
same  things  could  be  distributed.  The  properties,  therefore,  according 
to  which  objects  are  classified,  shoidd,  if  possible,  be  those  which  are 
causes  of  many  other  properties  ;  or  at  any  rate,  which  are  sure  marks 
of  them.  Causes  are  preferable,  both  as  being  the  surest  and  most 
direct  of  marks,  and  as  being  themselves  the  properties  upon  which  it 
is  of  most  use  that  our  attention  should  be  strongly  fixed.  But  the 
property  which  is  the  cause  of  the  chief  peculiarities  of  a  class,  is 
unfortunately  seldom  fitted  to  serve  also  as  the  diagnostic  of  the  class. 
Instead  of  the  cause,  we  must  generally  select  some  of  its  more  prom- 
inent effects,  which  may  serve  as  marks  of  the  other  effects  and  of  the 
cause  itself. 

A  classification  thus  formed  is  properly  scientific  or  philosophical, 
and  is  commonly  called  a  Natural,  in  contradistinction  to  a  Technical 
or  Artificial,  classification  or  aiTangement.  The  phrase  Natural  Clas- 
sification seems  most  peculiarly  appropriate  to  such  an'angements  as 
con-espond,  in  the  groups  which  they  fonn,  to  the  spontaneous  tenden- 
cies of  the  mind,  by  placing  together  the  objects  most  similar  in  their 
general  aspect ;  in  opposition  to  those  technical  systems  which,  ar- 
ranging things  according  to  their  agreement  in  some  circumstance 
arbitrarily  selected,  often  throw  into  the  same  group  objects  which  in 
the  general  aggi'egate  of  their  properties  present  no  resemblance,  and 
into  different  and  remote  groups,  others  which  have  the  closest  simi- 
larity. It  is  one  of  the  most  valid  recommendations  of  any  classifica- 
tion to  the  character  of  a  scientific  one,  that  it  shall  be  a  natural 
classification  in  this  sense  also ;  for  the  test  of  its  scientific  character  is 
the  number  and  importance  of  the  jjroperties  which  can  be  asserted  in 
common  of  all  objects  included  in  a  group  ;  and  propertieson  which 
the  general  aspect  of  the  things  depends,  are,  if  only  on  that  ground, 
important,  as  well  as,  in  most  cases,  numerous.  But,  though  a  strong 
recommendation,  this  circumstance  is  not  a  sine  qud  non ;  since  the 
more  obvious  properties  of  things  may  be  of  ti-ifling  importance  com- 
pared with  others  that  are  not  obvious.  I  have  seen  it  mentioned  as  a 
great  absurdity  in  the  LinnEean  classification,  that  it  places  (which  by 
the  way  it  does  not)  the  violet  by  the  side  of  the  oak  :  it  certainly  dis- 
severs natural  afiinities,  and  brings  together  things  quite  as  unlike  as 
the  oak  and  the  violet  are.  But  the  difference,  apparently  so  wide, 
which  renders  the  juxtaposition  of  those  two  vegetables  so  suitable  an 
illustration  of  a  bad  aiTangement,  depends,  to  the  common  eye,  mainly 
upon  mere  size  and  texture ;  now  if  we  made  it  our  study  to  adopt 


CLASSIFICATION.  435 

the  classification  which  would  involve  the  least  peril  of  similar  rap- 
prochcmcns,  we  should  return  to  the  obsolete  division  into  trees,  shrubs, 
and  herbs,  which  although  of  jn-imary  importance  with  regard  to  mere 
general  aspect,  yet  (compared  even  with  so  petty  and  unobvious  a  dis- 
tinction as  that  into  dicotyledones  and  monocotyledones)  answers  to  so 
few  ditterenccs  in  the  other  properties  of  ])lants,  that  a  classification 
founded  on  it  (independently  of  the  indistinctness  of  the  lines  of 
demarkation,)  would  be  as  completely  artificial  and  technical  as  the 
Linneean. 

Our  natural  groups,  therefore,  must  often  be  founded  not  upon  the 
obvious,  but  upon  the  unobvious  properties  of  things,  when  these  are  of 
gi-eater  importance.  ,But  in  such  cases  it  is  essential  that  there  should 
be  some  other  property  or  set  of  properties,  more  readily  recognizable 
by  the  observer,  which  coexist  with,  and  may  be  received  as  marks  of, 
the  properties  which  are  the  real  groundwork  of  tlic  classification.  A 
natural  aiTangement,  for  example,  of  animals,  must  be  founded  in  the 
main  upon  their  internal  structure,  but  (as  M.  Comte  justly  remarks)  it 
would  be  absurd  that  we  should  not  be  able  to  determine  the  genus  and 
species  of  an  animal  uithout  first  killing  it.  On  this  ground,  M.  Comte 
gives  the  preference,  among  zoological  classifications,  to  that  of  INI.  de 
ElainWlle,  founded  upon  the  differences  in  the  external  integuments ; 
differences  which  conespond,  much  more  accurately  than  might  be  sup- 
posed, to  the  really  important  varieties,  both  in  the  other  parts  of  the 
structure,  and  in  the  habits  and  history  of  the  animals. 

This  shows,  more  strongly  than  ever,  how  extensive  a  knowledge  of 
the  properties  of  objects  is  necessary  for  making  a  good  classification 
of  them.  And  as  it  is  one  of  the  uses  of  such  a  classification  that  by 
drawing  attention  to  the  properties  on  which  it  is  foiinded,  and  which 
if  the  classification  be  good  are  marks  of  many  others,  it  facilitates  the 
discovery  of  those  others ;  we  see  in  what  manner  our  knowledge  of 
things,  and  our  classification  of  them,  tend  mutually  and  indefinitely  to 
the  improvement  of  one  another. 

We  said  just  now  that  the  classification  of  objects  should  follow 
those  of  their  propeities  which  indicate  not  oidy  the  most  numerous-, 
but  also  the  most  important  peculiarities.  \Vliat  is  here  meant  by 
importance  ?  It  has  reference  to  the  particular  end  in  view:  and  the 
same  objects,  therefore,  may  admit  with  })ro]iriety  of  several  different 
classifications.  Each  science  or  art  fi)rins  its  classification  of  things 
according  to  the  properties  which  fall  within  its  special  cognizance,  or 
of  which  it  must  take  account  in  order  to  accomplish  its  peculiar  prac- 
tical ends.  A  fanner  does  not  divide  plants,  like  a  botanist,  into 
dicotyledonous  and  monocotyledonoiLS,  but  into  useful  plants  and  weeds. 
A  geologist  divides  fossils,  not,  like  a  zoologist,  into  families  correspon- 
ding to  tliose  of  living  species,  but  into  fossil^  of  the  secondary  and  of 
the  tertiary  periods,  above  the  coal  and  below  the  coal,  &c.  Wliales 
are  or  are  not  fish,  according  to  the  purpose  for  which  we  are  consider- 
ing them.  "  If  we  are"  speaking  of  the  internal  structure  and  physiology 
of  the  animal,  we  must  not  call  them  fish ;  for  in  these  respects  they 
deviate  widely  from  fishes ;  tliey  have  warm  hlood,  and  produce  and 
suckle  their  young  as  land  quadrupeds  do.  l^ut  this  would  ncjt  prevent 
our  speaking  of  the  whale  fishery,  and  calling  such  animals  Jish  on  all 
occasions  connected  with  this  employment;  fJir  the  relations  thus  arising 
depend  upon  the  animal's  living  in  the  water,  and  being  caught  in  a 


436  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

manner  similar  to  other  fishes.  A  plea  that  human  laws  which  mention 
fish  do  not  apply  to  whales,  would  be  rejected  at  once  by  an  intelligent 
judge."* 

These  different  classifications  are  all  good,  for  the  purposes  of  their 
own  particular  departments  of  knowledge  or  practice.  But  when  we 
are  studying  objects  not  for  any  special  practical  end,  but  for  the  sake 
of  extending  our  knowledge  of  the  whole  of  their  properties  and  rela- 
tions, we  must  consider  as  the  most  important  attributes,  those  which 
contribute  most,  either  by  themselves  or  by  their  eft'ects,  to  render  the 
things  like  one  another,  and  unlike  other  things  ;  which  give  to  the  class 
composed  of  them  the  most  marked  individuality ;  whicli  fill,  as  it  were, 
the  largest  space  in  their  existence,  and  would  most  impress  the  atten- 
tion of  a  spectator  who  knew  all  their  properties  but  was  not  specially 
interested  in  any.  Classes  fbrmed  upon  this  principle  may  be  called, 
in  a  more  emjihatic  manner  than  any  others,  natural  groups. 

§  3.  On  the  subject  of  these  groups  Mr.  Wliewell  lays  down  a  theo- 
ry, grounded  on  an  important  truth,  whicli  he  has,  in  some  respects, 
expressed  and  illustrated  very  felicitously;  but  also,  as  it  appears  to 
me,  with  some  admixture  of  error.  It  will  be  advantageous,  for  both 
these  reasons,  to  extract  the  statement  of  his  doctrine  in  the  very 
words  he  has  used. 

"  Natural  groups,"  according  to  Mr.  Whewell,t  are  "  given  by 
Type,  not  by  Definition."  And  this  consideration  accounts  for  "  that 
indefiniteness  and  indecision  which  we  frequently  find  in  the  descrip- 
tions of  such  gi-oups,  and  which  must  appear  so  strange  and  incon- 
sistent to  any  one  who  does  not  suppose  these  descriptions  to  assume 
any  deeper  ground  of  connexion  than  an  arbitrary  choice  of  the 
botanist.  Thus  in  the  family  of  the  rose-tree,  we  are  told  that  the 
ovules  are  very  rarely  erect,  the  stigmata  usually  simple.  Of  what 
use,  it  might  be  asked,  can  such  loose  accounts  be  1  To  which  the 
answer  is,  that  they  are  not  inserted  in  order  to  distinguish  the  species, 
but  in  order  to  describe  the  family,  and  the  total  relations  of  the  ovules 
and  the  stigmata  of  the  family  are  better  known  by  this  general  state- 
ment. A  similar  obsei-vation  may  be  made  with  regard  to  the  Anom- 
alies of  each  gi'oup,  which  occur  so  commonly,  that  Mr.  Lindley,  in  his 
Introduction  to  the  Natural  System  of  Botany,  makes  the  'Anomalies' 
an  article  in  each  family.  Thus,  part  of  the  chairacter  of  the  Rosacege 
is,  that  they  have  alternate  stipulate  leaves,  and  x\\?it  the  alhumen  is 
obliterated ;  but  yet  in  Lowea,  one  of  the  genera  of  this  family,  the 
stipulae  are  absent;  and  the  albumen  is  present  in  another,  Neillia. 
This  irnplies,  as  we  have  already  seen,  that  the  artificial  character  (or 
diagnosis,  as  Mr.  Lindley  calls  it),  is  imperfect.  It  is,  though  very 
nearly,  yet  not  exactly,  commensurate  with  the  natural  gi'oup  :  and 
hence  in  certain  cases  this  character  is  made  to  yield  to  the  general 
weight  of  natural '  affinities. 

"  Tliese  views, — of  classes  determined  by  characters  which  cannot 
be  expressed  in  words, — of  propositions  which  state,  not  what  hap- 
pens in  all  cases,  but  only  usually, — of  particulars  which  are  included 
in  a  class,  though  they  transgress  the  definition  of  it,  may  probably 

*  Aphorisms  concerning  the  Language  of  Science,  in  Mr.  Whewell's  Philosophy  of  the 
Inductive  Sciences,  vol.  i.,  p.  Ixxv. 
■t  Phil.  Ind.  Sc,  i.,  476-7. 


CLASSIFICATION.  437 

surprise  the  reader.  They  are  so  contrary  to  many  of  the  received 
opinions  respecting  the  use  of"  definitions,  and  the  nature  of  scicntitic 
propositions,  that  they  will  probably  appear  to  many  persons  highly 
illogical  and  unphilosophical.  But  a  disposition  to  such  a  judgment 
arises  in  a  great  measure  from  this,  tliat  the  mathematical  and 
mathematico-physical  sciences  have,  in  a  great  degree,  determined 
men's  views  of  the  general  nature  and  fonii  of  scientific  truth  ;  while 
Natural  Histoiy  has  not  yet  had  time  or  opportunity  to  exert  its  due 
influence  upon  the  current  habits  of  philosophizing.  The  ajiparent 
indefiniteness  and  inconsistency  of  the  classifications  and  definitions  of 
Natural  History  belongs,  in  a  far  higher  degree,  to  all  other  except 
mathematical  speculations ;  and  the  modes  in  which  approximations 
to  exact  distinctions  and  general  truths  have  been  made  in  Natural 
History,  may  be  worthy  our  attention,  even  for  the  light  they  throw 
upon  the  best  modes  of  pursuing  ti-uth  of  all  kinds." 

"  Though  in  a  Natural  group  of  objects  a  definition  can  no  longer 
be  of  any  use  as  a  regulative  principle,  classes  are  not  therefore  left 
quite  loose,  without  any  certain  standard  or  guide.  The  class  is 
steadily  fixed,  though  not  precisely  limited ;  it  is  given,  though  not 
circumscribed;  it  is  determined,  not  by  a  boundary  line  without,  but 
by  a  central  pointwit  hin;  not  by  what  it  strictly  excludes,  but  by  what  it 
eminently  includes  ;  by  an  example,  not  by  a  precept ;  in  short,  instead 
of  Definition  we  have  a  Type  for  our  director. 

"  A  Type  is  an  example  of  any  class,  for  instahee  a  species  of  a' 
genus,  which  is  considered  as  eminently  possessing  the  character  of 
the  class.  All  the  species  which  have  a  greater  afHnity  with  this  tyye- 
species  than  with  any  others,  form  the  genus,  and  are  ranged  about 
it,  deviating  froni  it  in  various  directions  and  different  degrees.  Thus 
a  genus  may  consist  of  several  species  which  approach  very  near  tlie 
type,  and  of  which  the  claim  to  a  place  with  it  is  obvious;  while  there 
may  be  other  species  which  straggle  further  from  this  central  knot,  and 
which  yet  are  clearly  more  connected  with  it  than  with  any  other. 
And  even  if  there  should  be  some  species  of  which  the  place  is  dubi- 
ous, and  which  appear  to  be  equally  bound  to  two  generic  types,  it  is 
easily  seen  that  this  would  not  destroy  the  reality  of  the  generic 
groups,  any  more  than  the  scattered  trees  of  the  intervening  plain 
prevent  our  speaking  intelligibly  of  the  distinct  forests  of  two  sep- 
arate hills. 

"  The  type-species  of  every  genus,  the  type-genus  of  every  family, 
is,  then,  one  which  possesses  all  the  characters  and  properties  of  the 
genus  in  a  marked  and  prominent  manner.  The  type  of  the  Rose 
family  has  alternate  stipulate  leaves,  wants  tlie  albumen,  has  the  ovules 
not  erect,  has  the  stigmata  simple,  and  besides  these  features,  which 
distinguish  it  from  the  exceptions  or  varieties  of  its  class,  it  has  the 
features  which  make  it  prominent  in  its  class.  It  is  one  of  those  which 
possess  clearly  several  leading  attributes ;  and  thus,  though  wo  cannot 
say  of  any  one  genus  that  it  7nu.'st  be  the  type  of  the  family,  or  of  any 
one  species  that  it  must  be  tlie  type  of  the  genus,  we  are  still  not 
wholly  to  seek ;  the  type  must  be  connected  by  many  affinities  with 
most  of  the  others  of  its  group ;  it  must  be  near  the  centi'e  of  the 
crowd  and  not  one  of  the  stragglers." 

In  this  passage  (the  latter  part  of  which  especially  I  cannot  help  no- 
ticing as  an  admirable  example  of  philosophic  style,)  Mr,  WlieweU 


438  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

has  stated  very  clearly  and  forcibly,  but  (I  think)  without  making  all 
necessary  distinctions,  one  of  the  principles  of  a  Natural  Classification. 
What  this  principle  is,  what  are  its  limits,  and  in  what  manner  Mr. 
Whewell  seems  to  me  to  have  overstepped  them,  will  appear  when 
we  have  laid  down  another  and  more  fundamental  rule  of  Natural 
Arrangement,  entitled  to  precedency  over  that  which  Mr.  Whewell 
has  here  in  view. 

§  4.  The  reader  is  by  this  tiine  familiar  with  the  general  truth 
(which  I  restate  so  often  on  account  of  the  great  confusion  in  which  it 
is  commonly  involved),  that  there  are  in  nature  distinctions  of  Kind ; 
distinctions  not  consisting  in  a  given  number  of  definite  properties, 
fhis  the  effects  which  follow  from  those  properties,  but  running  through 
the  whole  nature,  through  the  attributes  generally,  of  the  things  so 
distinguished.  Our  knowledge  of  the  properties  of  a  Kind  is  never 
complete.  We  are  always  discovering,  and  expecting  to  discover, 
new  ones.  Where  the  distinction  between  things  is  not  one  of  kind, 
we  expect  to  find  their  properties  alike,  except  where  there  is  some 
reason  for  their  being  different.  On  the  contrary,  when  the  distinction 
is  in  kind,  we  expect  to  find  the  projjerties  different  unless  there  be 
some  cause  for  their  being  the  same.  All  knowledge  of  a  Kind  must 
be  obtained  by  observation  and  experiment  upon  the  Kind  itself;  no 
inference  respecting  its  properties  from  the  properties  of  things  not 
connected  with  it  by  kind,  goes  for  more  than  the  sort  of  presumption 
usually  characterized  as  an  analogy,  and  generally  in  one  of  its  faint.er 
degrees. 

Since  the  common  properties  of  a  true  Kind,  and  consequently  the 
general  assertions  which  can  be  made  respecting  it,  or  which  are  cer- 
tain to  be  made  hereafter  as  our  knowledge  extends,  are  indefinite  and 
inexhaustible  ;  and  since  the  very  first  principle  of  natural  classification 
is  that  of  forming  the  classes  so  that  the  objects  composing  each  may 
have  the  gi'eatest  number  of  properties  in  common ;  this  principle 
prescribes  that  every  such  classification  shall  recognize  and  adopt  into 
itself  all  distinctions  of  Kind,  which  exist  among  the  objects  it  pro- 
fesses to  classify.  To  pass  over  any  distinctions  of  Kind,  and  substitute 
definite  distinctions,  which,  however  considerable  they  may  be,  do  not 
point  to  ulterior  unknown  differences,  would  be  to  replace  classes  with 
more  by  classes  with  fewer  attributes  in  common ;  and  would  be  sub- 
versive of  the  Natural  Method  of  Classification. 

Accordingly  all  natural  arrangerrients,  whether  the  reality  of  the 
distinction  of  Kinds  was  felt  or  not  by  their  framers,  have  been  led,  by 
the  mere  pursuit  of  their  own  proper  end,  to  conform  themselves  to 
the  distinctions  of  Kind,  so  far  as  these  had  been  ascertained  at  the 
time.  The  Species  of  Plants  are  not  only  real  Kinds,  but  are  prob- 
ably,* all  of  them,  real  lowest  Kinds,  or  Infimas  Species  ;  which  if  we 
were  to  subdivide,  as  of  course  it  is  open  to  us  to  do,  into  sub-classes, 

*  I  say  probably,  not  certainly,  because  tliis  is  not  the  consideration  by  which  a  botanist 
determines  what  shall  or  shall  not  be  admitted  as  a  species.  In  natural  history  those 
objects  belong  to  the  same  species,  which  are,  or  consistently  with  experience  might  have 
been,  produced  from  the  same  stock.  But  tliis  distinction  in  most,  and  probably  in  all 
cases,  happily  accords  with  the  other.  It  seems  to  be  a  law  of  physiology,  that  animals 
and  plants  do  really,  in  the  philosophical  as  well  as  the  popular  sense,  propagate  their  kind  ; 
transmitting  to  their  descendants  all  the  distinctions  qf  Kind  (down  to  the  most  special  0? 
lowest  Kind),  which  they  themselves 


CLASSIFICATION.  439 

the  sul)ilivi.sion  would  necessarily  be  founded  upon  definite  disllnttiona, 
not  poiiitintT  (apiut  from  what  may  be  known  of  their  causes  or  effects) 
to  any  dift'erenco  beyond  themselves. 

In  so  far  as  the  natural  dassitication  is  grounded  upon  real  Kinds, 
its  jj^'oups  are  certainly  not  conventional  ;  INIr.  Wliewell  is  quite  right 
in  atlirming  that  they  do  not  depend  upon  an  arbitrary  choice  of  the 
naturalist.  But  it  does  not  follow,  nor,  I  conceive,  is  it  true,  that 
these  classes  are  determined  by  a  type,  and  not  by  characters.  To 
determine  them  by  a  type  would  be  as  sure  a  way  of  missing  the  Kind, 
as  if  we  were  to  select  a  set  of  characters  arbitrarily.  They  are  deter- 
mined by  characters,  but  which  are  not  arbitrary.  The  problem  is,  to 
find  a  k\v  definite  characters  which  point  to  the  multitude  of  indefinite 
ones.  Kinds  are  Classes  between  which  there  is  an  impassil)lc  bar- 
rier ;  and  what  we  have  to  seek  is,  marks  whereby  we  may  determine 
on  which  side  of  the  banier  an  object  takes  its  place.  The  characters 
which  will  best  do  this  are  what  should  be  chosen  :  if  they  are  also 
important  in  themselves,  so  much  the  better.  When  we  have  selected 
the  characters,  we  parcel  out  the  objects  according  to  those  characters, 
and  not,  as  Mr.  Wliewell  seems  to  suppose,  according  to  resemblance 
to  a  type.  We  do  not  compose  the  species  Ranunculus  acris,  of  all 
plants  which  bear  a  satisfactory  degree  of  resemblance  to  a  model-but- 
tercup, but  of  tliose  which  possess  certain  characters  selected  as  marks 
by  which  we  might  recognize  the  possibility  of  a  common  parentage ; 
and  the  enumeration  of  those  characters  is  the  definition  of  the  species. 

The  question  next  arises,  whether,  as  all  Kinds  must  have  a  place 
among  the  classes,  so  all  the  classes  in  a  natural  arrangement  must 
be  Kinds  ]  And  to  this  I  answer,  certainly  not.  The  distinctions 
of  Kind  are  not  numerous  enough  to  supply  the  whole  basis  of 
a  classification.  Very  few  of  the  genera  of  plants,  or  even  of  the 
famiUes,  can  be  pronounced  with  certainty  to  be  Ivinds.  The  gi'cat 
distinctions  of  Vascular  and  Cellular,  Dicotyledonous  or  Exogenous 
and  Monocotyledonous  or  Endogenous,  are  perhaps  differences  of 
Kind :  the  lines  of  demarkation  which  divide  those  classes  seem  (though 
even  on  this  I  would  not  pronounce  positively)  to  go  through  the 
whole  nature  of  the  plants.  But  the  different  species  of  a  genus,  or 
genera  of  a  family,  usually  have  in  common  only  a  limited  number  of 
characters.  A  Rosa  does  not  seem  to  differ  from  a  Rubus,  or  the 
Umbcllifera3  fi-om  the  Ranunculacea?,  in  much  else  than  the  characters 
botanically  assigned  to  those  genera  or  those  families.  Unenumcratcd 
differences  certainly  do  exist  in  some  cases  ;  there  are  families  of 
plants  which  have  peculiarities  of  chemical  composition,  or  yield  pro- 
ducts having  peculiar  effects  on  the  animal  economy.  The  Cruciferai 
and  Fungi  contain  an  unusual  proportion  of  azote  ;  the  Labiata;  are  the 
chief  sources  of  essential  (fils,  the  Solancce  are  very  commonly  narcotic, 
&c.  In  these  and  similar  cases  there  are  possibly  distinctions  of  Kind  ; 
but  it  is  by  no  means  indispensable  that  there  should  be.  Genera  and 
Families  may  be  eminently  natural,  though  inarkcd  out  from  one 
another  by  properties  limited  in  number  ;  provided  those  ])ropertio8 
be  important,  and  the  objec^ts  contained  in  each  genus  or  family  re- 
semble each  other  more  than  they  resemble  anything  which  is  excluded 
from  the  genus  or  family. 

After  the  recognition  and  definition,  then,  of  the  infima  species,  the 
next  step  is  to  arrange  these  infirncc  sjjecies  into  larger  groups :  making 


440  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

those  gi'oups  con-espond  to  Kinds  wherever  it  is  possible,  but  in  most 
cases  without  any  such  guidance.  And  in  dohig  this  it  is  true  that  we 
are  naturally  and  properly  guided,  in  most  cases  at  least,  by  resem- 
blance to  a  type.  We  form  our  groups  round  certain  selected  Kinds, 
each  of  which  serves  as  a  sort  of  exemplar  of  its  group.  But  though 
the  groups  are  suggested  by  types,  I  calnnot  agree  with  Mr.  Whewell 
that  a  group  when  formed  is  determined  by  the  type ;  that  in  deciding 
whether  a  species  belongs  to  the  group,  a  reference  is  made  to  the 
type,  and  not  to  the  characters;  that  the  characters  "cannot  be  ex- 
pressed in  words."  This  assertion  is  inconsistent  with  Mr.  Wliewell's 
own  statement  of  the  fundamental  principle  of  classification,  namely, 
that  "  general  assertions  shall  be  possible."  If  the  class  did  not  possess 
any  characters  in  common,  what  general  assertions  would  be  possible 
respecting  it?  Except  that  they  all  resemble  each  other  more  than 
they  resemble  anything  else,  nothing  whatever  could  be  predicated  of 
the  class. 

The  truth  is,  on  the  contrary,  that  every  genus  or  family  is  framed 
with  distinct  reference  to  certain  characters,  and  is  composed,  first  and 
principally,  of  species  which  agree  in  jjossessing  all  those  characters. 
To  these  are  added,  as  a  sort  of  appendix,  such  other  species,  gener- 
ally in  small  number,  as  possess  nearly  all  the  properties  selected; 
wanting,  some  of  them  one  property,  some  another,  and  which,  while 
they  agree  with  the  rest  almost  as  much  as  these  agree  with  one 
another,  do  not  resemble  in  an  equal  degree  any  other  group.  Our 
conception  of  the  class  continues  to  be  grounded  on  the  characters; 
and  the  class  might  be  defined,  those  things  which  either  possess  that 
set  of  characters,  or  resemble  the  things  that  do  so,-  more  than  they 
resemble  anything  else. 

And  this  resemblance  itself  is  not,  like  resemblance  between  simple 
sensations,  an  ultimate  fact  unsusceptible  of  analysis.  Even  the  inferior 
degree  of  resemblance  is  created  by  the  possession  of  common  char- 
acters. Whatever  resembles  the  genus  Rose  more  than  it  resembles 
any  other  genus,  does  so  because  it  possesses  a  greater  number  of  the 
characters  of  that  genus,  than  of  the  characters  of  any  other  genus. 
Nor  can  there  be  the  smallest  difficulty  in  representing,  by  an  enumera- 
tion of  characters,  the  nature  and  degree  of  the  resemblance  which  is 
sti-ictly  sufficient  to  include  any  object  in  the  class.  There  are  always 
some  properties  common  to  all  things  which  are  included.  Others 
there  often  are,  to  which  some  things,  which  are  nevertheless  included, 
are  exceptions.  But  the  objects  which  are  exceptions  to  one  character 
ai'e  not  exceptions  to  another:  the  resemblance  which  fails  in  some 
particulars  must  be  made  up  for  in  others.  The  class,  therefore,  is 
constituted  by  the  possession  of  all  the  characters  which  are  universal, 
and  viost  of  those  which  admit  of  exceptions.  If  a  plant  had  the 
ovules  erect,  the  stigmata  divided,  the  albumen  not  obliterated,  and 
was  without  stijaules,  it  probably  would  not  be  classed  among  the 
RosaceEe.  But  it  may  want  any  one,  or  more  than  one  of  those  char- 
acters, and  not  be  excluded.  The  ends  of  a  scientific  classification  are 
better  answered  by  including  it.  Since  it  agrees  so  nearly,  in  its  known 
properties,  with  the  sum  of  the  characters  of  the  class,  it  is  likely  to 
resemble  that  class  more  than  any  other  in  those  of  its  properties  which 
are  still  undiscovered. 

Not  only,  therefore,  are  natural  groups,  no  less  than  any  artificial 


CLASSIFICATION.  441 

classes,  iletennincd  by  ('haract(!i\s ;  tlioy  arc  constituted  in  ccMiteinpla- 
tion  of,  and  by  reason  of,  characters.  But  it  is  in  contemplation  not  of 
those  characters  only  which  are  rigorously  common  to  all  the  objects 
included  in  the  group,  but  of  the  entire  body  of  characters,  all  of  which 
are  found  in  most  of  those  objects,  and  most  of  them  in  all.  And 
hence  our  conception  of  the  class,  the  image  in  our  minds  which  is 
representative  of  it,  is  that  of  a  specimen  complete  in  all  the  charac- 
ters ;  most  naturally  a  sjiecimen  which,  by  possessing  them  all  in  the 
greatest  degiee  in  which  they  are  ever  found,  is  the  best  fitted  to  ex- 
hibit clearly,  and  in  a  inarked  maimer,  what  they  arc.  It  is  by  a  mental 
referLMice  to  this  standard,  not  instead  of,  but  in  illustration  of,  the 
delinirion  of  the  class,  that  we  usually  and  advantageously  determine 
wliether  any  individual  or  species  belongs  to  the  class  or  not.  And 
this,  as  it  seems  to  me,  is  the  amount  of  truth  which  is  containe'd  in 
Mr.  Whewell's  doctrine  of  Types. 

We  shall  see  presently  that  where  the  classification  is  made  for  the 
express  purpose  oi  a  special  inductive  inquiry,  it  is  not  o[)tional,  but 
necessary  for  fulfilling  the  conditions  of  a  correct  Inductive  Method, 
that  we  should  establish  a  type-species  or  genus,  namely,  the  one  which 
exhibits  in  the  most  eminent  degree  the  particular  phenomenon  under 
investigation.  But  of  this  hereafter.  It  remains,  for  completing  the 
theory  of  natural  groups,  that  a  few  words  should  be  said  on  the 
principles  of  the  nomenclature  adapted  ta  them. 

§  5.  A  Nomenclature,  as  we  have  said,  is  a  system  of  the  names  of 
Kinds.  These  names,  like  other  class-names,  are  defined  by  the 
enumeration  of  the  characters  distinctive  of  the  class.  The  only  merit 
which  a  set  of  names  can  have  beyond  this,  is  to  convey,  by  the  mode 
of  their  construction,  as  much  information  as  possible  :  so  that  a  per- 
son who  knows  the  thing,  may  receive  all  the  assistance  which  the 
name  can  give  in  remembering  what  he  knows,  while  he  who  knows 
it  not,  may  receive  as  much  knowledge  respecting  it  as  the  case  admits 
of,  by  merely  being  told  its  name. 

There  are  two  modes  of  giving  to  the  name  of  a  kind  this  sort  of 
significance.  The  best,  but  which  unfortunately  is  seldom  practicable, 
is  when  the  word  can  be  made  to  indicate,  by  its  formation,  the  very 
properties  which  it  is  designed  to  connote.  The  name  of  a  kind  does 
hot,  of  course,  connote  all  the  properties  of  the  kind,  since  these  are 
inexhaustible,  bilt  such  of  tliem  as  are  sufficient  to  distinguish  it;  such 
as  are  sure  marks  of  all  the  rest.  Now,  it  is  very  rare  that  one 
property,  or  even  any  two  or  three  properties,  can  answer  this  pur- 
pose. To  distinguish  the  common  daisy  from  all  other  species  ot 
plants  would  require  the  specification  of  many  characters.  And  a 
name  cannot,  without  being  too  cumbrous  for  use,  give  indication,  by 
its  etymology  or  mode  of  constructicm,  of  more  than  a  very  small 
number  of  these.  The  possibility,  therefore,  of  an  ideally  perfect 
Nomenclature,  is  probably  confined  to  the  one  case  in  which  we  are 
happily  in  possession  of  something  lujiirly  approacliing  to  it;  1  refer  to 
the  Nomenclature  of  Chemistry.  Tlu;  substances,  whether  simple  or 
compound,  with  which  chemistry  is  conversant,  arc  Kinds,  and,  as 
such,  the  properties  which  distinguish  each  of  them  from  the  rest,  are 
innumerable  ;  but  in  the  case  of  compound  substances  (the  simple 
ones  are  not  numerous  enough  to  require  a  systematic  nomenclature), 
3K 


442  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

there  is  one  property,  the  chemical  composition,  which  is  of  itself 
sufficient  to  distinguish  the  Kind  ;  of  itself  a  sure  mark  of  all  the  other 
properties  of  the  compound.  All  that  was  needful,  therefore,  was  to 
make  the  name  of  every  compound  express,  on  the  first  hearing,  its 
chemical  composition ;  that  is,  to  form  the  name  of  the  compound,  in 
some  uniform  inanner,  from  the  names  of  the  simple  suhstances  which 
enter  into  it  as  elements.  This  was  done,  most  skillfully  and  success- 
fully, by  the  French  chemists.  The  only  thing  left  unexpressed  by 
them  was  the  exact  proportion  in  which  the  elements  were  combined; 
and  even  this,  since  the  establishment  of  the  atomic  theory,  it  has 
been  found  possible  to  express  by  a  simple  adaptation  of  their 
phraseology. 

But  where  the  characters  which  must  be  taken  into  consideration  in 
order  sufficiently  to  designate  the  Kind,  are  too  numerous  to  be  all 
signified  in  the  derivation  of  the  name,  and  where  no  one  of  them  is  of 
such  preponderant  importance  as  to  justify  its  being  singled  out  to  be 
so  indicated,  we  may  avail  ourselves  of  a  subsidiary  resource.  Though 
we  cannot  indicate  the  distinctive  properties  of  the  kind,  we  may  indi- 
cate its  nearest  natural  affinities,  by  incorporating  into  its  name  the 
name  of  the  proximate  natural  group  of  which  it  is  one  of  the  species. 
On  this  principle  is  founded  the  admirable  binary  nomenclature  of 
botany  and  zoology.  In  this  nomenclature  the  name  of  every  species 
consists  of  the  name  of  the  genus,  or  natural  group  next  above  it,  with 
a  word  added  to  distinguish  the  particular  species.  This  last  jjortion 
of  the  compound  name  is  sometimes  taken  from  some  one  of  the  pecu- 
liarities in  which  that  species  diffex's  from  others  of  the  genus ;  as  Cle- 
matis integrifolia,  Potentilla  alha,  Yio\ci  palustris,  Axtc\n\?,m  vulgaris  ; 
sometimes  from  a  circumstance  of  a  historical  nature,  as  Narcissus  ^oe- 
ticus,  Potentilla  tormcntilla  (indicating  that  the  plant  was  formerly 
known  by  the  latter  name),  Exacum  Candollii  (from  the  fact  that  De 
Gandolle  was  its  first  discoverer) ;  and  sometimes  the  word  is  purely 
conventional,  as  Thlaspi  bursa-pastoris,  Ranunculus  thora :  it  is  of  little 
consequence  which  ;  since  the  second,  or  as  it  is  usually  called  the  spe- 
cific name,  could,  at  most,  express,  independently  of  convention,  no 
more  than  a  very  small  portion  of  the  connotation  of  the  term.  But 
by  adding  to  this  the  name  of  the  superior  genus,  we  make  the  best 
amends  we  can  for  the  impossibility  of  so  contriving  the  name  as  to 
express  all  the  distinctive  characters  of  the  Kind.  We  make  it,  at  all 
events,  express  as  many  of  those  characters  as  are  common  to  the  prox- 
imate natural  gToup  in  which  the  Kind  is  included.  If  even  those 
common  characters  are  so  numerous  or  so  little  familiar  as  to  require  a 
further  extension  of  the  same  resource,  we  might,  instead  of  a  binary, 
adopt  a  ternary  nomenclature,  employing  not  only  the  name  of  the 
genus,  but  that  of  the  next  natural  group  in  order  of  generality  above 
the  genus,  commonly  called  the  Family.  This  was  done  in  the  mine- 
ralogical  nomenclature  proposed  by  Professor  Mohs.  "  The  names 
framed  by  him  were,"  says  Mr.  Whewell,*  "not  composed  of  two, 
but  of  three  elements,  designating  respectively  the  Species,  the  Genus, 
and  the  Order;  thus  he  has  such  species  as  PJioiyihohedral  Lime  Ha- 
loide,  Octahedral  Fluor  Haloide,  Prismatic  Hal  Baryte.'"  The  binary 
construction,  however,  has  been  found  sufficient  in  botany  and  zoology, 

*  Aphorisms  concerning  tlie  Language  of  Science,  p.  Ixiv. 


CLASSIFICATION    BY    SERIES.  448 

the  only  sciences  in  which  this  general  principle  has  hitherto  heensuc- 
cesslully  adopted  in  the  construction  of  a  nomenclature. 

Besides  the  advantage  Avhich  this  principle  ot'nomenclature  possesses, 
in  giving  to  tlje  names  of  species  the  greatest  quantity  of"  independent 
significance  wliiih  the  circumstances  of  the  case  admit  of,  it  answers 
the  further  end  of  innnensely  economizing  the  use  of  names,  and  pre- 
venting an  otherwise  intolerable  hiu-den  upon  the  memory.  When  the 
naiDes  of  species  become  extremely  numerous,  some  artifice  (as  Mr. 
W'hewell*  observes)  becomes  absolutely  necessary  to  make  it  possible 
to  recollect  or  apply  them.  "  The  known  species  of  plants,  for  ex- 
ample, were  ten  thousand  in  the  time  of  Linnaeus,  and  are  now  prob- 
ably sixty  thousand.  It  would  be  useless  to  endeavor  to  frame  and 
employ  separate  names  for  each  of  these  species.  The  division  of  the 
objects  into  a  subordinated  system  of  classification  enables  us  to  intro- 
duce a  Nomenclature  which  docs  not  require  this  enormous  immherof 
names.  Each  of  the  genera  has  its  name,  and  the  species  are  marked 
by  the  addition  of  some  epithet  to  the  name  of  the  genus.  In  this 
manner  about  seventeen  hundred  generic  names,  with  a  moderate 
number  of  specific  names,  were  found  by  Linnasus  sufticient  to  desig- 
nate with  precision  all  the  species  of  vegetables  known  at  his  time." 
And  though  the  number  of  generic  names  has  since  greatly  increased, 
it  has  not  increased  in  anything  like  the  proportion  of  the  multiplica- 
tion of  known  species. 


CHAPTER  VIII. 

OF  CLASSIFICATION   BY   SERIE.S. 


§  1.  Thus  far,  we  have  considered  the  principles  of  scientific  classi- 
fication so  far  only  as  relates  to  the  formation  of  natural  groups;  and 
at  this  point  most,  of  those  who  have  attempted  a  theory  of  natural  ar- 
rauffement,  including,  among  the  rest,  Mr.  Whewcll,  have  stopped. 
There  remains,  however,  another  and  a  not  less  important  pt)rtion  of 
the  thef)rv,  which  has  not  yet,  so  far  as  I  am  aware,  been  systemati* 
cally  treated  of  by  any  winter  except  M.  Comte.  This  is,  the  aiTange- 
ment  of  the  natural  gi-oups  into  a  natural  series. 

The  end  of  C'lassification,  as  an  instrument  for  the  investigation  of 
nature,  is  (as  before  stated)  to  make  us  think  of  those  objects  together, 
which  ha.ve  the  greatest  number  of  important  common  properties  ;  and 
which  therefore  we  have  oftenest  occasion,  in  the  course  of  our  induc- 
tions, fiir  taking  into  joint  consideration.  Our  ideas  of  objects  are  thus 
brought  into  the  order  most  conducive  to  the  successful  prosecution  of 
inductive  inquiries  generally.  But  when  the  purpose  is  to  facilitate 
some  particular  inductive  in(|uiry,  more  is  recpiired.  To  be  instru- 
mental to  that  purpose,  the  classification  must  bring  those  objects  to- 
gether, the  simultaneous  contemplation  of  which  is  likely  to  throw 
most  light  upon  the  particular  subject.     That  subject  being  the  laws 

♦  Philosophy  of  the  Inductive  Sciences,  i.,  p.  489. 


444  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

of  some  phenomenon,  or  some  set  of  connected  phenomena ;  the  very 
phenomenon  or  set  of  phenomena  in  question  must  be  chosen  as  the' 
groundwork  of  the  classification. 

The  requisites  of  a  classification  intended  to  facilitate  the  study  of  a 
particular  phenomenon,  are,  first,  to  bring  into  one  class  all  Kinds  of 
things  which  exhibit  that  phenomenon,  in  whatever  variety  of  fomis  or 
degi'ees,;  and  secondly,  to  arrange  those  Kinds  in  a  series  according 
to  the  degree  in  which  they  exhibit  it,  beginning  with  those  which 
exhibit  anost  of  it,  and  terminating  with  those  which  exhibit  least. 
The  principal  example,  as  yet,  of  such  a  classification,  is  afforded  by 
comparative  anatomy  and  physiology,  from  which,  therefore,  our  illus- 
trations shall  be  taken. 

§  2.  The  object  being  supposed  to  be,  the  investigation  of  the  laws 
of  animal  life  ;  the  first  step,  after  foraiing  a  distinct  conception  of  the 
phenomenon  itself,  is  to  erect  into  one  great  class  (that  of  animals)  all 
the  known  Kinds  of  beings  where  that  phenomenon  presents  itself;  in 
however  various  combinations  with  other  properties,  and  in  however 
different  degrees.  As'  some  of  these  Kinds  manifest  the  general  phe- 
nomenon of  animal  life  in  a  very  high  degi'ee,  and  others  in  an  insig- 
nificant degree,  barely  sufficient  for  recognition  ;  we  must,  in  the  next 
place,  arrange  the  various  Kinds  in  a  series,  following  one  another  ac- 
cording to  the  degrees  in  which  they  severally  exhibit  the  phenomenon  ; 
beginning,  therefore,  with  man,  and  ending  with  the  most  imperfect 
kinds  of  zoophytes. 

This  is  merely  saying  that  we  should  put  the  instances,  from  which 
the  law  is  to  be  inductively  collected,  into  the  order  which  is  implied 
in  one  of  the  four  Methods  of  Experimental  Inquiry  discussed  in  the 
preceding  Book  ;  the  fourth  Method,  that  of  Concomitant  Variations. 
As  we  formerly  remarked,  tjiis  is  often  the  only  method  to  which  re- 
course can  be  had,  with  assurance  of  a  true  conclusion,  in  cases  in 
which  we  have  but  limited  means  of  effecting,  by  artificial  experiments, 
a  separation  of  circumstances  usually  conjoined.  The  principle  of  the 
method  is,  that  facts  which  increase  or  diminish  together,  and  disappear 
together,  are  either  cause  and  effect,  or  effects  of  a  common  cause. 
When  it  has  been  ascertained  that  this  relation  really  subsists  between 
the  variations,  a  connexion  between  the  facts  themselves  may  be  con- 
fidently laid  down,  either  as  a  law  of  nature  or  only  as  an  empirical 
law,  according  to  circumstances. 

That  the  application  of  this  Method  must  be  preceded  by  the  forma- 
tion of  such  a  series  as  we  have  described,  is  too  obvious  to  need  being 
pointed  out;  and  the  mere  arrangement  of  a  set  of  objects  in  a  series, 
according  td  the  degrees  in  which  they  exhibit  some  fact  of  which  we 
are  seeking  the  law,  is  too  naturally  suggested  by  the  necessities  of 
our  inductive  operations,  to  require  any  lengthened  illustration  here. 
But  there  ai'e  cases  in  which  the  aiTangement  required  for  the  special 
purpose,  becomes  the  determining  principle  of  the  classification  of  the 
same  objects  for  general  puqwses.  This  will  naturally  and  pi-operly 
happen,  when  those  laws  of  the  objects  which  are  sought  in  the  special 
inquiry  enact  so  principal  a  part  in  the  general  character  and  histoiy 
of  those  objects  —  exercise  so  much  influence  in  determining  all  the 
phenomena  of  which  they  are  either  the  agents  or  the  theatre  —  that 
all  other  differences  existing  among  the  objects  are  fittingly  regarded  as 


CLASSIFICATION    BY    SERIES.  445 

mere  modifications  of  the  one  phenomenon  sought;  effects  (Iclermiiicd 
by  the  cooperation  ot"  some  iiicideutal  circumstance  with  the  hiws  of 
that  phenomenon.  Thus  in  the  case  of  animated  beings,  the  dilferences 
between  one  class  of  animals  and  another  may  reasonably  be  con- 
sidered as  mere  modifications  of  the  general  phenomenon,  animal  life; 
modifications  arising  cither  from  the  diflercnt  degrees  in  which  that 
phenomenon  is  manifested  in  different  animals,  or  fi-om  the  intermix- 
ture of  the  effects  of  incidental  causes  peculiar  to  the  nature  of  each, 
with  the  effects  produced  by  the  gcnel-al  laws  of  life ;  those  laws  still 
exercising  a  predominant  inlluence  over  the  result.  Such  being  the 
case,  no  other  inductive  incjuiry  respecting  animals  can  bo  successfully 
canied  on,  except  in  subordination  to  the  gi'eat  inquiry  into  the  uni- 
versal laws  of  animal  life.  And  the  classification  of  animals  best 
suited  to  that  one  purpose,  is  the  most  suitable  to  all  the  other  pur- 
poses of  zoological  science. 

§  3.  To  establish  a  classification  of  this  sort,  or  even  to  comprehend 
it  when  established,  requires  the  power  of  recognizing  the  essential 
similarity  of  a  phenomenon,  in  its  minuter  degrees  and  obscurer  forms, 
with  what  is  called  the  sa7nc  phenomenon  in  the  greatest  perfection  ot 
its  development ;  that  is,  of  identifying  with  each  other  all  phenomena 
which  difier  only  in  degree,  and  in  projierties  which  we  suppose  to  be 
caused  by  difference  of  degree.  In  order  to  recognize  this  identity, 
or  in  other  words,  this  exact  similarity  of  quality,  the  assumption  of  a 
type-species  is  indispensable.  We  must  consider  as  the  type  of  the 
class,  that  among  the  Kinds  included  in  it,  which  exhibits  the  projierties 
constitutive  of  the  class,  in  the  highest  degree ;  conceiving  the  other 
varieties  as  instances  of  degeneracy,  as  it  were,  fi-om  that  type;  devia- 
tions from  it  by  inferior  intensity  of  the  characteristic  ])roperty  or 
properties.  For  every  phenomenon  is  best  studied  [cceteris  j^aribus) 
where  it  exists  in  the  greatest  intensity.  It  is  there  that  the  effects 
which  either  depend  upon  it,  or  depend  upon  the  same  causes  with  it, 
will  also  exist  in  the  greatest  degree.  It  is  there,  consequently,  and 
only  there,  that  those  effects  of  it,  or  joint  effects  with  it,  can  become 
fully  known  to  us ;  so  that  we  may  learn  to  recognize  their  smaller 
degrees,  or  even  their  mere  rudimtnits,  iir  cases  in  which  the  direct 
study  would  have  been  difficult  or  even  impossible.  Not  to  mention 
that  the  phenomenon  in  its  higher  degrees  may  be  attended  by  effects 
or  collateral  circumstances  which  in  its  smaller  degrees  do  not  occur  at 
all,  requidng  for  their  production  in  any  sensible  amoimt  a  greater 
degree  of  intensity  of  the  cause  than  is  there  met  with.  In  man,  for 
example  (the  species  in  which  both  the  phenomenon  of  animal  and  that 
of  organic  life  exist  in  the  highest  degree),  many  subordinate  phe- 
nomena develop  themselves  in  the  course  of  his  animated  existence, 
which  the  inferior  varieties  of  animals  do  not  show.  The  knowledge 
of  these  properties  may  nevertheless  be  of  great  avail  towards  the 
discovery  of  the  conditions  and  laws  of  the  general  phenomenon  oi'  life, 
which  is  common  to  man  with  those  inferior  animals.  And  they  are, 
even,  rightly  considered  as  properties  of  animated  nature  itself; 
because  they  may  evidently  be  afiiliated  to  the  general  laws  of  ani- 
mated nature ;  because  we  may  fairly  presume  that  some  rudiments 
or  feeble  degrees  of  those  properties  would  be  recognized  in  all 
animals  by  more  perfect  organs,  or  even  by  more  perfect  instruments, 


446  OPERATIONS    SUBSIDIARY    TO    INDUCTION. 

than  one  ;  and  because  those  may  be  correctly  termed  properties  of  a 
class,  which  a  thing-  exhibits  exactly  in  proportion  as  it  belongs  to  the 
class,  that  is,  in  proportion  as  it  possesses  the  main  attributes  con- 
stitutive of  the  class. 

§  4.  It  remains  to  consider  how  the  internal  distribution  of  the  series 
may  most  properly  take  place  :  in  what  manner  it  should  be  divided 
into  Orders,  Families,  and  Genera. 

The  main  principle  of  division  must  of  course  be  natural  affinity  ; 
the  classes  formed  must  be  natural  groups :  and  the  formation  of  these 
has  already  been  sufficiently  treated  of.  But  the  principles  of  natural 
gi-ouping  must  be  applied,  in  subordination  to  the  principle  of  a  natural 
series.  The  groups  must  not  be  so  constituted  as  to  place  in  the  same 
gi-oup  things  which  ought  to  occupy  different  points  of  the  general 
scale.  The  precaution  necessary  to  be  observed  for  this  purpose  is, 
that  the  frimary  divisions  must  be  grounded  not  upon  all  distinctions 
indiscriminately,  but  upon  those  which  correspond  to  variations  in  the 
degree  of  the  main  phenomenon.  The  series  of  Anirriated  Nature 
should  be  broken  into  parts  at  the  exact  points  where  the  variation  in 
the  degree  of  intensity  of  the  main  phenomenon  (as  marked  by  its 
principal  characters.  Sensation,  Thought,  Voluntary  Motion,  &c.)  be- 
gins to  be  attended  by  conspicuous  changes  in  the  miscellaneous  prop- 
erties of  the  animal.  Such  well  marked  changes  take  place,  for 
example,  where  the  class  Mammalia  ends  ;  at  the  points  where  Fishes 
are  separated  from  Insects,  Insects  from  Mollusca,  &c.  Wlien  so 
formed,  the  primary  natural  groups  vnll  compose  the  series  by  mere 
juxtaposition,  without  redistribution  ;  each  of  them  corresponding  to 
a  definite  division  of  the  scale.  In  like  manner  each  family  should,  if 
possible,  be  so  subdivided,  that  one  portion  of  it  shall  stand  higher  and 
the  other  lower,  though  of  course  contiguous,  in  the  general  scale  ; 
and  only  when  this  is  impossible  is  it  allowable  to  ground  the  remain- 
ing subdivisions  upon  characters  having  no  determinable  connexion 
with  the  main  phenomenon. 

Where  the  principal  phenomenon  so  far  transcends  in  importance  all 
other  properties  on  which  a  classification  could  be  grounded,  as  it  does 
in  the  case  of  animated  existence,  any  considerable  deviation  from  the 
rule  last  laid  down  is  in  general  sufliciently  guarded  against  by  the  first 
principle  of  a  natural  arrangement,  that  of  foi-ming  the  groups  ac- 
cording to  the  most  important  characters.  All  attempts  at  a  scientific 
classification  of  animals,  since  first  their  anatomy  and  physiology  were 
successfully  studied,  have  been  fi-amcd  with  a  certain  degree  of  in- 
stinctive reference  to  a  natural  series,  and  have  accorded,  in  many 
more  points  than  they  have  differed,  with  the  classification  which 
would  most  naturally  have  been  grounded  upon  such  a  series.  But 
the  accordance  has  not  always  been  complete,  and  it  still  is  often  a 
matter  of  discussion  which  of  several  classifications  best  accords  with 
the  true  scale  of  intensity  of  the  main  phenomenon.  M.  Comte,  for 
example,  blames  Cuvier  for  having  formed  his  natural  groups  with  an 
undue  degree  of  reference  to  the  mode  of  alimentation,  a  circumstance 
directly  connected  only  with  organic  life,  and  leading  to  an  ari^mge- 
ment  most  inappropriate  for  the  pui-poses  of  an  investiga:tion  of  the 
laws  of  animal  life,  since  both  carnivorous  and  herbivorous  or  frugivo- 
rous  animals  are  found '  at  almost  every  degree  in  the  scale  of  animal 


CLASSIFICATION    BY    SERIES,  447 

pei-fection.  M.  Comte,  with  much  apparent  reason,  gives,  on  these 
grounds,  gi-catly  the  preference  to  the  classification  framed  by  M.  de 
Blainville  ;  as  representing  correctly,  by  the  mere  order  of  the  groups, 
the  successive  degeneracy  of  animal  nature  from  its  highest  to  its  most 
imperfect  exemplification. 

§  5.  A  classification  of  any  large  portion  of  the,  field  of  nature,  in  con- 
formity to  the  foregoing  principles,  has  hitherto  been  found  practicable 
only  in  one  great  instance,  that  of  animals.  In  the  case  even  of  vege- 
tables, the  natural  arrangement  has  not  been  carried  beyond  the  forma- 
tion of  natural  groups.  Naturalists  have  found  and  probably  will 
continue  to  find  it  impossible  to  form  those  gi-oups  into  any  series,  the 
terms  of  which  correspond  to  real  gi'adations  in  the  phenomenon  of 
vegetative  or  organic  life.  Such  a  difference  of  degree  may  be  traced 
between  the  class  of  Vascular  Plants  and  that  of  Cellular,  which 
includes  lichens,  algre,  and  other  substances  whose  organization  is 
simpler  and  more  rudimentary  than  that  of  the  higher  order  of  vegeta- 
bles, and.  which  therefore  approach  nearer  to  mere  inorganic  nature. 
But  when  we  rise  much  above  this  point,  we  do  not  find  any  recogniz- 
able difference  in  the  degree  in  which  different  plants  possess  the 
properties  of  organization  and  life.  The  dicotylcdones  and  the  mono- 
cotyledones  are  distinct  natural  groups,  but  it  cannot  be  said,  even  by 
a  metaphor,  that  the  former  are  more  or  less  plants  than  the  latter. 
The  palm-tree  and  the  oak,  the  rose  and  the  tulip,  are  organized  and 
vegetate  in  a  different  manner,  but  certainly  not  in  a  different  degree. 
The  natural  classification  of  vegetables  must  therefore  continue  to  be 
made  without  reference  to  any  scale  or  series;  and  the  whole  vegetable 
kingdom  must  form,  as  it  does  in  M.  Comte's  arrangement,  one  single 
step  or  gradation,  the  lowest  of  all  in  the  series  of.  organized  beings, 
scientifically  constructed  for  the  purpose  of  facilitating  the  investiga- 
tion of  the  laws  of  organic  life. 

Although  the  scientific  arrangements  of  organic  nature  affiird  as  yet 
the  only  complete  example  of  the  true  principles  of  rational' classifica- 
tion, whether  as  to  the  formation  of  gi'oups  or  of  series,  those  principles 
are  applicable  to  all  cases  in  which  mankind  are  called  upon  to  bring 
the  various  parts  of  any  extensive  subject  into  mental  coordination. 
They  are  as  much  to  the  point  when  objects  are  to  be  classed  for 
pui-poses  of  ait  or  business,  as  for  those  of  science.  The  proper 
an-angement,  for  example,  of  a  code  of  laws,  depends  upon  the  same 
scientific  conditions  as  the  classifications  in  natural  history;  nor  could 
there  be  a  better  preparatory  discipline  for  that  important  function, 
than  the  study  of  the  pi-inciples  of  a  natural  arrangement,  not  only  in 
the  abstract,  but  in  their  actual  application  to  the  class  of  phenomena 
for  which  they  were  first  elaborated,  and  which  are  still  the  best  school 
for  learning  their  use.  Of  this  the  gi-eat  authority  on  codification, 
Bentham,  was  perfectly  aware  :  and  his  early  Fragment  on  Government, 
the  admirable  introduction  to  a  scries  of  writings  unequalcd  in  their 
peculiar  department,  contains  clear  and  just  views  (as  far  as  they  go) 
on  the  meaning  of  a  natural  arrangement,  such  as  could  scarcely  have 
occuiTcd  to  any  one  who  lived  anterior  to  iho  ago  of  Linnaeus  and 
Bernard  de  Jussieu. 


BOOK  V. 

ON  FALLACIES. 


'  11  leur  semble  qu'il  n'y  a  qu'ii  douter  par  fantaisie,  et  qu'ii  n'y  a  qu'^  dire  en  gen6ral 
que  notre  nature  est  infirme  ;  que  notre  esprit  est  plain  d'aveuglement ;  qu'il  faut  avoir  un 
grand  soin  de  se  defaire  de  ses  prejuges,  et  autres  choses  semblables.  lis  pensent  que  cela 
suffit  pour  ne  plus  se  laisser  seduire  a  ses  sens,  et  pour  ne  plus  se  tromper  du  tout.  11  ne 
sufiit  pas  de  dire  que  I'esprit  est  foible,  il  faut  lui  faire  sentir  ses  foiblesses.  Ce  n'est  pas 
assez  de  dire  qu'il  est  sujet  a  I'erreur,  il  faut  lui  decouvrir  en  quoi  consistent  ses  erreurs." 
— Malebranche,  Recherche  de  la  Verite. 

"  Errare  non  modo  afErmando  et  negando,  sed  etiam  sentiendo,  et  in  tacita  hominum 
cogitatione  contingit." — Hobbes,  Computatio  sive  Legica,  eh.  v. 


CHAPTER  I. 

OF  FALLACIES  IN  GENERAL. 


§  1.  It  is  a  maxim  of  tlie  schoolmen,  that  "  contrarioinim  eadem  est 
scientia :"  we  never  really  know  what  a  tiling  is,  unless  we  are  also 
able  to  give  a  sufficient  account  of  its  opposite.  Conformably  to  this 
maxim,  one  considerable  section,  in  most  treatises  on  Logic,  is  devoted 
to  the  subject  of  Fallacies;  and  the  practice  is  too  well  worthy  of 
observance,  to  allow  of  our  departing  from  it.  The  jjhilosophy  of  rea- 
soning, to  be  complete,  ought  to  comprise  the  theory  of  bad  as  well  as 
of  good  reasoning. 

We  have  endeavored  to  ascertain  the  principles  by  which  the  suffi- 
ciency of  any  proof  can  be  tested,  and  by  which  the  nature  and  amount 
of  evidence  needful  to  prove  any  given  conclusion  can  be  determined 
beforehand.  If  these  principles  were  adhered  to,  then  although  the 
number  and  value  of  the  truths  ascertained  would  be  limited  by  the 
opportunities,  or  by  the  industry,  ingenuity,  and  patience,  of  the  indi- 
vidual inquirer,  at  least  error  would  not  be  embraced  instead  of  truth. 
But  the  general  consentof  mankind,  founded  upon  all  their  experience, 
vouches  for  their  being  far  indeed  from  even  this  negative  kind  of 
perfection  in  the  employment  of  their  reasoning  powers. 

In  the  conduct  of  life — in  the  ordinary  business  of  mankind — UTong 
inferences,  incorrect  interpretations  of  experience,  unless  after  much 
culture  of  the  thinking  faculty,  are  absolutely  ine^-itable  :  and  with 
most  people  after  the  highest  degree  of  culture  they  ever  attain  (unless 
where  the  events  of  their  daily  life  supply  an  immediate  con-ective), 
such  erroneous  inferences  are  as  fi-equent  if  not  more  frequent  than 
coiTect  inferences,  correct  intei-pretations  of  experience.  Even  in  the 
speculations  to  which  the  highest  intellects  systematically  devote  them- 
selves, and  in  reference  to  Avhich  the  collective  mind  of  the  scientific 
world  is  always  at  hand  to  aid  the  efforts  and  control  the  aberrations 


FALLACIES    IN    GENERAL.  449 

of  indiviJuab,  it  is  only  from  the  more  perfect  sciences,  from  those  of 
which  the  subject  matter  is  the  least  complicated,  ihat  opinions  not 
resting  upon  a  correct  induction  have  at  length,  generally  speaking, 
been  expelled.  In  the  departments  of  inquiiy  relating  to  the  more 
complex  phenomena  of  the  universe,  and  especially  those  of  which  the 
subject  is  man,  whether  as  a  moral  and  intellectual,  a  social,  or  even 
as  a,  physical  being ;  the  diversity  of  opinions  still  prevalent  among 
instructed  persons,  and  the  equal  confidenco  with  which  those  of  the 
most  contrary  ways  of  thinking  cling  to  their  respective  tenets,  are  a 
pi'oof  not  only  that  right  modes  of  philosophizing  are  not  yet  generally 
adopted  on  those  subjects,  but  that  wrong  ones  are;  that  j)hilosophcrs 
have  not  only  in  general  missed  the  truth,  but  have  often  embraced 
en-or;  that  even  the  most  cultivated  portion  of  our  species  have  not 
yet  learned  to  abstain  from  drawing  conclusions  for  -which  the  evidence 
is  insufficient. 

The  only  complete  safeguard  against  reasoning  ill,  is  the  habit  of 
reasoning  well ;  familiarity  with  the  principles  of  cctrrect  reasoning, 
and  practice  in  applying  those  principles.  It  is,  however,  not  unim- 
portant to  consider  what  are  the  most  common  modes  of  bad  reasoning ; 
by  what  appearances  the  mind  is  most  liliely  to  be  seduced  from  the 
observance  of  true  principles  of  induction  ;  what,  in  short,  are  the  most 
common  and  most  dangerous  varieties  of  Apparent  Evidence,  whereby 
men  are  misled  into  opinions  for  which  there  does  not  exist  evi- 
dence really  conclusive. 

A.  catalogue  of  the  varieties  of  apparent  evidence , which  are  not  real 
evidence,  is  an  enumeration  of  Fallacies.  Without  such  an  enumera- 
tion, therefore,  the  present  work  would  be  wanting  in  an  essential 
point.  And  while  writers  who  included  in  their  theory  of  reasoning 
nothing  more  than  ratiocination,  have,  in  ponsistency  with  this  limita- 
tion, confined  their  remarks  to  the  fallacies  which  have  their  seat  in 
thit  portion  of  the  process  of  investigation  ;  we,  who  profess  to  treat 
of  the  whole  process,  must  add  to  our  directions  for  perfonning  it 
rightly,  warnings  against  performing  it  AVi-ong  in  any  of  its  parts : 
whether  the  ratiocinative  or  the  experimental  portion  of  it  be  in 
fault,  or  the  fault  lie  in  dispensing  with  ratiocination  and  induction 
altogether. 

§  2.  In  considering  the  sources  of  unfounded  inference,  it  is  un- 
necessary to  r&ckon  the  errors  which  arise,  not  from  a  wrong  method, 
or  even  from  ignorance  of  the  right  one,  but  from  a  casual  lapse, 
through  hurry  or  inattention,  in  the  application  of  the  true  principles 
of  induction.  Such  eiTors,  like  the  accidental  mistakes  in  casting  up 
a  sum,  do  not  call  for  philosophical  analysis  or  classification ;  theo- 
retical considerati(jns  can  throw  no  light  upon  the  means  of  avoiding 
tliem.  In  the  present  treatise  oui'  attention  is  required,  not  to  mere 
inexpertness  in  perfonning  the  operation  in  the  right  way,  (the  only 
remedies  for  which  are  increased  attention  and  mm-o  sedulous  prac- 
tice,) but  to  the  modes  of  performing  it  in  a  way  fundamentally 
wrong ;  the  conditions  under  which  the  human  mind  persuades  itself 
that  it  has  sufficient  grounds  for  a  conclusion  which  it  ha.s  n(jt  arrived 
at  by  any  of  the  legitimate  methods  of  induction — which  it  has  not, 
even  carelessly  or  overhastily,  endeavored  to  test  by  those  legitimate 
methods. 

3  L 


450  FALLACIES. 

§  3.  There  is  another  branch  of  what  may  be  called  the  Philosophy 
of  Error,  which  must  be  mentioned  here,  though  only  to  be  excluded 
from  our  subject.  The  sources  of  erroneous  opinions  are  two-fold, 
moral  and  intellectual.  Of  these,  the  moral  do  not  fall  within  the  com- 
pass of  this  work.  They  may  be  classed  under  two  general  heads ; 
Indifference  to  the  attainment  of  truth,  and  Bias :  of  which  last  the 
most  common  case  is  that  in  which  we  are  biased  by  our  wishes ;  but 
the  liability  is  almost  as  gi'eat  to  the  undue  adoption  of  a  conclusion 
which  is  disagi-eeable  to  us  as  of  one  which  is  agreeable,  if  it  be  of  a 
nature  to  bring  into  action  any  of  the  stronger  passions.  Persons  of 
timid  character  are  the  more  predisposed  to  believe  any  statement,  the 
more  it  is  calculated  to  alarm  them.  Indeed,  it  is  a  psychological  law, 
deducible  from  the  most  general  laws  of  the  mental  constitution  ot 
man,  that  any  strong  passion  renders  us  credulous  as  to  the  existence 
of  objects  suitable  to  excite  it. 

But  the  moral  causes  of  our  opinions,  though  real  and  most  powerful, 
are  but  remote  causes  :  they  do  not  act  immediately,  but  by  means  ot 
the  intellectual  causes  ;  to  which  they  bear  the  same  relation  that  the 
circumstances  called,  in  the  theory  of  medicine,  predisposing  causes, 
bear  to  exciting  causes.  Indifference  to  tiaith  cannot,  in  and  by  itself, 
produce  erroneous  belief;  it  operates  by  preventing  the  mind  fi-om 
collecting  the  proper  evidences,  or  from  applying  to  them  the  test  of  a 
legitimate  and  rigid  induction  ;  by  which  omission  it  is  exposed  unpro- 
tected to  the  influence  of  any  species  of  apparent  evidence  which 
occurs  spontaneously,  or  which  is  elicited  by  that  smaller  quantity  of 
trouble  which  the  mind  may  be  not  unwilling  to  take.  As  little  is 
Bias  a  direct  source  of  wrong  conclusions.  We  cannot  believe  a 
proposition  only  by  wishing,  or  only  by  dreading,  to  believe  it.  The 
most  violent  inclination  to  find  a  set  of  propositions  true  will  not  enable 
the  weakest  of  mankind  to  believe  them  without  a  vestige  of  intel- 
lectual grounds,  without  any,  even  apparent,  evidence.  It  can  only 
act  indirectly,  by  placing  the  intellectual  grounds  of  belief  in  an  in- 
complete or  distorted  shape  before  his  eyes.  It  makes  him  shrink 
from  the  irksome  labor  of  a  rigorous  induction,  when  he  has  a  mis- 
giving that  its  result  may  be  disagi'ceable ;  and  in  such  examination  as 
he  does  institute,  it  makes  him  exert  that  which  is  in  a  certain  measure 
voluntary,  his  attention,  unfairly,  giving  a  larger  share  of  it  to  the 
evidence  which  seems  favorable  to  the  desired  conclusion,  a  smaller 
to  that  which  seems  unfavorable.  And  the  lilve  when  the  bias  arises 
not  from  desire  but  fear.  Although  a  person  afraid  of  ghosts  believes 
that  he  has  seen  one  on  evidence  wonderfully  inadequate,  he  does  not 
believe  it  altogether  without  evidence  ;  he  has  perceived  some  unusual 
appearance,  while  passing  through  a  chiirch-yard  :  he  saw  something 
start  up  near  a  gi-ave,  which  looked  white  in  the  moonshine.  Thus 
eveiy  erroneous  inference,  though  originating  in  moral  causes,  involves 
the  intellectual  operation  of  admitting  insufficient  evidence  as  sufficient; 
and  whoever  was  on  his  guard  against  all  kinds  of  inconclusive  evidence 
which  can  be  mistaken  for.- conclusive,  would  be  in  no  danger  of  being 
led  into  eiTor  even  by  the  strongest  bias.  There  have  been  minds  so 
strongly  fortified  on  the  intellectual  side,  that  they  could  not  blind 
themselves  to  the  light  of  truth,  however  really  desirous  of  doing  so  ; 
they  could  not,  with  all  the  inclination  in  the  world,  pass  off"  upon 
themselves  bad  arguments  for  good  ones.     If  the  sophistry  of  the  in- 


CLASSIFICATION    OF    FALLACIES.  451 

tellect  coukl  be  Tendered  impossible,  that  of  the  feelings,  having  no 
instiannent  to  work  with,  would  be  jiowerless.  A'  comprehensive 
classification  of  all  those  things  which,  not  being  evidence,  ai-e  liable 
to  appear  such  to  the  understanding,  will,  therefore,  include  all  enors 
of  juilgnient  arising  Irom  moral  causes,  to  the  exclusion  only  of  errors 
of  practice  committed  against  better  knowledge. 

To  examine,  then,  the  various  kinds  of  apparent  evidence  which  are 
not  evidence  at  all,  and  of  apparently  conclusive  evidence  which  do  not 
really  amount  to  conclusiveness,  is  the  object  of  that  part  of  our  inquiry 
into  which  we  are  about  to  enter. 

The  subject  is  not  beyond  the  compass  of  classification  and  compre- 
hensive surVey.  The  things,  indeed,  which  are  not  evidence  of  any 
given  conclusion,  are  manifestly  endless,  and  this  negative  property, 
having  no  dependence  upon  any  positive  ones,  cannot  be  made  the 
gi'oundwork  of  a  real  classification.  But  the  things  which,  not  being 
evidence,  are  susceptible  of  being  mistaken  for  it,  are  capable  of  a 
classification  having  reference  to  the  positive  property  which  they 
possess,  of  appearing  to  be  evidence.  We  may  arrange  them,  at  our 
choice,  on  either  of  two  prljiciples  ;  according  to  the  cause  which  mak^s 
them  appear  evidence,  not  being  so  ;  or  according  to  the  particular 
kind  of  evidence  which  they  simulate.  The  Classification  of  Fallacies 
which  will  be  uttemped  in  the  ensuing  chapter,  is  founded  upon  these 
considerations  jointly. 


CHAPTER  II. 

CLASSIFICATION   OF  FALLACIES. 


§  1.  In  attempting  to  establish  certain  general  distinctions  which  shall 
mark  out  from  one  another  the  various  kinds  of  Fallacious  Evidence, 
we  propose  to  ourselves  an  altogether  different  aim  from  that  of  sev- 
eral eminent  thinkers,  who  have  .given,  under  the  name  of  Political  or 
other  Fallacies,  a  mere  enumeration  of  a  certain  number  of  erroneous 
opinions;  false  general  propositions  which  happen  to  be  often  met  w^th; 
loci  conwuine.i  of  l)ad  arguments  on  some  {)articular  subject.  Logic  is 
not  concerned  with  the  false  opinions  which  men  happen  to  entertain, 
but  with  the  manner  in  which  they  come  to  entertain  them.  The  ques- 
tion fin-  us  is  not,  what  facts  men  have  at  any  time  en-oneously  supj)oseJ 
to  be  proof  of  certain  other  facts,  but  what  property  in  the  facts  it  was 
which  led  them  to  this  mistaken  suppctsition. 

When  a  fact  is  supposed,  altJiough  incorrectly,  to  be  evidentiary  of, 
or  a  maik  of,  sf)me  other  fact,  there  must  be  a  cause  of  the  error ;  the 
supposed  evidentiary  fact  must  be  connected  in  some  particular  manner 
vnth  the  fact  of  which  it  is  deemed  evidentiary,  must  stand  in  some 
particular  relation  to  it,  without  which  relation  it  would  not  be  regarded 
m  that  light.  The  relation  may  either  be  one  resulting  from  the  simple 
contemplati(jn  of  the  two  facts  side  l)y  side  with  one  another,  or  it  may 
dopend  upon  some  process  «f  our  own  mhid,  by  which  a  previous  a.s30- 
ciation  has  been  established  between  them.  Some  peculiarity  of  i-ela- 
tionj  however,  there  must  be;  the  fact  which  can,  even  by  the  wildest 


452  FALLACIES. 

aberration,  be  supposed  to  prove  another  fact,  must  stand  in  some 
special  position  with  regard  to  it;  and  if  we  could  ascertain  and  define 
that  special  position,  we  should  perceive  the  origin  of  the  error. 

We  cannot  regard  one  fact  as  evidential^  of  another  unless  we 
believe  that  the  two  are  always,  or  in  the  majority  of  cases,  conjoined. 
If  we  believe  A  to  be  evidentiary  of  B,  if  when  we  see  A  we  are 
inclined  to  infer  B  fi'om  it,  the  reason  is  because  we  believe  that  where- 
ever  A  is,  B  also  either  always  or  for  the  most  part  exists,  either  as  an 
antecedent,  a  consequent,  or  a  concomitant.  If  when  we  see  A  we  are 
inclined  not  to  expect  B,  if  we  believe  A  to  be  evidentiary  of  the  absence 
of  B,  it  is  because  we  believe  that  where  A  is,  B  either  is  never,  or  at 
least  seldom,  found.  Erroneous  conclusions,  in  short,  no  less  than 
coiTect  conclusions,  have  an  invariable  relation  to  a  general  formula, 
either  expressed  or  tacitly  implied.  When  we  infer  some  fact  from 
some  other  fact  which  does  not  really  prove  it,  we  either  have  admitted, 
or  if  we  maintained  consistency,  ought  to  admit,  some  groundless  gen- 
eral proposition  respecting  the  conjunction  of  the  two  phenomena. 

For  every  property,  therefore,  in  facts,  or  in  our  mode  of  considering 
facts,  which  leads  us  to  believe-that  they  are  habitually  conjoined  when 
they  are  not,  or  that  they  are  not  when  in  reality  they  are,  there  is  a 
corresponding  kind  of  Fallacy;  and  an  enumeration  of  Fallacies  would 
consist  in  a  specification  of  those  properties  in  facts,  and  those  pecu- 
liarities in  our  mode  of  considering  them,  which  give  rise  to  this  eri'o- 
neous  opinion. 

§  2.  To  begin,  then ;  the  supposed  connexion,  or  repugnance,  between 
the  two  facts,  may  either  be  a  conclusion  from  evidence  (that  is,  from 
some  other  proposition  or  propositions)  or  may  be  admitted  without 
any  such  ground;  admitted,  as  the  phrase  is,  on  its  own  evidence  :  em- 
bra,ced  as  self-evident,  as  an  axiomatic  truth.  This  gives  rise  to  the  first 
great  distinction,  that  between  Fallacies  of  Inference,  and  Fallacies  of 
Simple  Inspection.  In  the  latter  division  must  be  included  not  only 
all  cases  in  which  a  proposition  is  believed  and  held  for  true,  literally 
without  any  extrinsic  evidence,  either  of  specific  experience  or  general 
reasoning ;  but  those  more  frequent  cases  in  which  simple  inspection 
creates  ?i  presumption  in  favor  of  a  proposition;  not  sufficient  for  belief, 
but  sufficient  to  cause  the  strict  principles  of  a  regular  induction  to  be 
dispensed  with,  and  creating  a  predisposition  to  believe  it  on  evidence 
which  would  be  seen  to  be  insuflScient  if  no  such  presumption  existed. 
This  class,  comprehending  the  whole  of  what  may  be  termed  ,  Natural 
Prejudices,  and  which  I  shall  call  indiscriminately  Fallacies  of  Simple 
Inspection  or  Fallacies  a  priori.,  shall  be  placed  at  the  head  of  our  list. 

Fallacies  of  Inference,  or  eiToneous  conclusions  from  supposed 
evidence,  must  be  subdivided  according  to  the  nature  of  the  apparent 
evidence  from  which  the  conclusions  are  drawn  ;  or  (what  is  the  same 
thing,)  according  to  the  particular  kind  of  sound  argument  which  the 
fallacy  in  question  simulates.  But  there  is  a  distinction  to  be  first 
drawn,  which  does  not  answer  to  any  of  the  divisions  of  sound  argu- 
ments, but  arises  out  of  the  nature  of  bad  ones.  We  may  know 
exactly  what  our  evidence  is,  and  yet  draw  a  false  conclusion  from  it; 
we  may  conceive  precisely  what  our  premisses  are,  what  alleged  mat- 
ters of  fact,  or  general  principles,  are  the  foundation  of  our  inference ; 
and  yet,  because  the  premisses  are  false,  or  because  we  have  inferred 


CLASStflCATlOX    OP    FALLACIES.  453 

from  them  what  they  will  not  support,  our  conclusion  may  be  cito- 
noous.  But  a  case,  j^orhaps  c,\c.ii  more  iroquent,  is  that  in  which 
the  error  arises  from  not  conceivinjr  our  pri'misses  with  due  clearness, 
that  is,  (as  shown  in  the  preceding  book,*)  witli  due  fixity :  forminfr 
one  conception  of  our  evidence  whon  we  collect  or  receive  it,  ami 
another  wlien  we  make  use  of  it ;  or  unadvisedly  and  in  general  un- 
consciously substituting,,  as  we  proceed,  difltjrent  premisses  in  the 
})lace  of  Uiose  with  which  we  set  out,  or  a  different  conclusion  for  that 
which  we  undertook  to  prove.  This  gives  existence  to  a  class  of  fal- 
lacies which  may  be  justly  termed  Fallacies  of  Confusion  ;  compre- 
hending, among  others,  all  those  which  have  their  source  in  language; 
whether  arising  frohi  £he  vagueness  or  ambiguity  of  oui*  terras,  or  from 
casual  associations  with  them. 

When  the -fallacy  is  not  one  of  Confusion,  that  is,  when  the  propo- 
sition believed,  and  the  evidence  on  which  it  is  believed,  are  steadily 
apprehended  and  unambiguously  expressed,  there  remain  to  be  made 
two  cross  divisions,  giving  rise  to  four  classes.  The  Apparent  Evidence 
may  be  either  particular  facts,  or  foregone  generalizations  ;  that  is, 
the  process  may  simulate  either  simple  Induction,  6t  Deduction  :  and 
again,  the  evidence,  whether  consisting  of  facts  or  general  propositions, 
may  be  false  in  itself,  or,  being  true,  may  fail  to  beai*  out  the  conclu- 
sion attempted  to  be  founded  upon  it.  This  gives  us,  first.  Fallacies 
of  Induction  and'  Fallacies  of  Deduction,  and  thou  a  subdivision  of 
each  of  these,  according  as  the  supposed  evidence  is  false,  or  true  but 
inconclusive. 

Fallacies  of  Induction,  where  the  facts  upon  which  the  induction 
proceeds  are  erroneous,  may  be  termed  Fallacies  of  Observation.  The 
tenn  is  not  strictly  accurate,  or  rather,  not  accurately  coextensive  with 
the  class  of  fallacies  which  I  propose  to  designate  by  it.  Induction  is 
not  always  grounded  upon  facts  immediately  observed,  but  sometimes 
upon  facts  inferred :  and  when  these  last  are  erroneous,  the  error  is  not, 
in  the  literal  sense  of  the  term,  an  instance  of  bad  observation,  but  of 
bad  inference.  It  will  be  convenient,  however,  to  make  only  one  class 
of  all  the  inductions  of  which  the  error  lies  in  not  sufliciently  ascer- 
taiiung  tlie  facts  on  which  the  theory  is  grounded ;  whether  the  cause 
of  failure  be  raal-observation,  or  simple  non-observation,  and  whether 
the  mal-obsen'ation  be  direct,  or  by  means  of  intermediate  marks 
which  do  not  prove  what  they  are  suj)posed  to  prove.  And  in  the 
absence  of  any  comprehensive  term  to  denote  the  asceitainment,  by 
whatever  means,  of  the  facts  on  which  an  induction  is  grounded,  1  will 
venture  to  retain  for  this  class  of  fallacies,  under  the  explanation  already 
given,  the  title,  Fallacies  of  Observation. 

The  other  class  of  inductive  fallacii^s,  in  which  the  facts  are  correct, 
but  the  conclusion  not  wan-anted  by  them,  are  properly  denominated 
Fallacies  of  Generalization :  and  these,  again,  fall  into  various  subor- 
dinate classes,  or  natural  groups,  some  of  which  will  be  enumerated 
in  their  pro{)cr  place. 

When  we  now  turn  to  Fallacies  of  Deduction,  namely,  those  modes 
of  incorrect  argumentation  in  wliicli  the  jiremisses,  or  some  of  them,  are 
general  j)ropositions,  and  the  argument  a  ratiocination  ;  we  may  of 
coUree  subdivide  these  also  into  two  species,  similar  lo  the  twopreced- 

•  Supra,  p.  300. 


454 


FALLACIES. 


ino-,  namely,  those  which  proceed  on  false  premisses,  and  those  of 
■which  the  premisses,  though  true,  do  not  support  the  conclusion.  But 
of  these  species,  the  first  must  necessarily  fall  within  some  one  of  the 
heads  already  enumerated.  For  the  error  must  be  either  in  those 
premisses  which  are  general  propositions,  or  in  those  which  assert 
individual  facts.  In  the  former  case  it  is  an  Inductive  Fallacy,  of  one 
or  the  other  class  ;  in  the  latter  it  is  a  Fallacy  of  Observation  :  unless, 
in  either  case,  the  erroneous  premiss  has  been  assumed  on  simple 
inspection,  in  which  case  the  fallacy  is  a  priori.  Or,  finally,  the  prem- 
isses, of  whichever  kind  they  are,  may  never  have  been  conceived  in 
so  distinct  a  manner  as  to  produce  any  clear  consciousness  by  what 
means  they  were  aiTived  at ;  as  in  the  case  of  what  is  called  reasoning 
in  a  circle :  and  then  the  fallacy  is  of  Confusion. 

There  remains,  therefore,  as  the  only  class  of  fallacies  having  prop- 
erly their  seat  in  deduction,  those  m  which  the  premisses  of  the  ratio- 
cination do  not  bear  out  its  conclusion  ;  the  various  cases,  in  short, 
of  vicious  argumentation,  provided  against  by  the  rules  of  the  syllogism. 
We  shall  call  these.  Fallacies  of  Ratiocination. 

We  have  thus  five  distinguishable  classes  of  fallacy,  which  may  be 
expressed  in  the  following  synoptic  table  : — 
■  of  Simple  Inspection 


Fallacies  i 


'from  evidence 
distinctly  con- 
ceived 

from  evidence 
indistinctly 
conceived 


Inductive 
Fallacies 


Deductive  i 
Fallacies 


1.  Fallacies  a  priori. 

2.  Fallacies  of  Observation. 


Fallacies  of  Generalization. 


4.  Fallacies  of  Ratiocination. 


5.  Fallacies  of  Confusion. 


§  3.  We  must  not,  however,  expect  to  find  that  men's  actual  errors 
always,  or  even  commonly,  fall  so  unmistakably  under  some  one  of 
these  classes,  as  to  be  incapable  of  being  referred  to  any  other.  Erro- 
neous arguments  do  not  admit  of  such  a  sharply  cut  division  as  valid 
arguments  do.  An  argument  fully  stated,  with  all  its  steps  distinctly 
set  out,  in  language  not  susceptible  of  misunderstanding,  must,  if  it  be 
erroneous,  be  so  in  some  one,  and  one  only,  of  these  five  modes;  or 
indeed  of  the  first  four,  since  the  fifth,  on  such  a  supposition,  would 
vanish.  But  it  is  not  in  the  nature  of  bad  reasoning  to  express  itself 
thus  unambiguously.  When  a  sophist,  whefher  he  is  imposing  upon 
himself  or  attempting  to  impose  upon  others,  can  be  constrained  to 
throw  his  sophistry  into  so  distinct  a  form,  it  needs,  in  a  large  propor- 
tion of  cases,  no  further  exposure. 

In  all  arguments,  everywhere  but  in  the  schools,  some  of  the  links 
are  suppressed  ;  a  fortiori  when  the  arguer  either  intends  to  deceive, 
or  is  a  lame  and  inexpert  thinker,  little  accustomed  to  bring  his  rea- 
soning processes  to  any  test :  and  it  is  in  those  steps  of  the  reasoning 
which  are  made  in  this  tacit  and  half-conscious,  or  even  wholly  uncon- 
scious manner,  that  the  error  oftenest  lurks.  In  order  to  detect  the 
fallacy,  the  proposition  thus  silently  assumed  must  be  supplied  ;  but  the 
reasoner,  most  likely,  has  never  really  asked  himself  what  he  wa.«  as- 
suming :  his  confuter,  if  unable  to  extort  it  from  him  by  the  Socratic 
mode  of  interrogation,  must  himself  judge  what  the  suppressed  ])jemiss 
ought  to  be  in  order  to  support  the  conclusion.  And  hence,  in  the 
words  of  Archbishop  Whately,  "  it  must  be  often  a  matter  of  doubt,  or 


CLASSIFICATION  OF  FALLACIES.  455 

rather  of  arbitrary  clioicr,  not  only  to  which  genus  each  kind  of  lallacy 
should  ho  referred,  but  even  to  which  kind  to  roFer  any  one  indiridual 
fallacy  ;  for  siiice,  in  any  course  of  argument,  One  premiss  is  usually 
suppressed,  it  freipuMitly  happens  in  the  case  of  a  fallacy,  that  the  hear- 
ers are  left  to  the  alieniative  uf  supplying  <v7/<tr  a  jireniiss  which  is  7iot 
true,  or  else,  one  which  docs  not  jirorc  the  conclusion:  e.g.,  if  a  man 
expatiates  on  the  distress  of  the  country,  and  thence  argues  that  the 
government  is  tyrannical,  we  must  suppose  him  to  assume  eit/icr  that 
'every  distressed  country  is  under  a  tyranny,'  which  is  a  manifest 
falsehood,  or,  merely  that '  every  ct>untry  under  a  lynmny  is  distressed,' 
which,  however  true,  proves  nothing,  the  middle  term  being  undis- 
tributed." The  former  wonld  be  ranked,  in  our  distribution,  among 
fallacies  of  generalization,  the  latter  among  those  of  ratiocination, 
**  Which  arc  we  to  suppose  the  speaker  meant  us  to  understand  1 
Surely"  (if  he  understood  himself)  "just  whichever  each  of  his  hearers 
might  hapjien  to  prefer:  some  might  assent  to  the  false  prcnjiss  ; 
others  allow  the  unsound  syllogism." 

Almost  all  fallacies,  therefore,  might  in  strictness  be  brought  under 
our  tifth  class,  Fallacies  of  Confusion.  A  fallacy  can  seldom  be  abso- 
lutely referred  to  any  of  the  other  classes ;  we  can  only  say,  tliat  if  all 
the  links  were  filled  up  which  should  be  capable  of  being  supplied  in 
a  valid  argument,  it  would  either  stand  thus  (forming  a  fallacy  of  one 
class),  or  thus  (a  fallacy  of  another) ;  or  at  furthest  we  may  say,  that 
tlie  conclusion  is  most  likeli/  to  have  originated  in  a  fallacy  of  such 
and  such  a  class.  Thus  in  Archbishop  Whately's  illustration,  the 
error  committed  may  be  traced  with  most  probability  to  a  falla(-y  of 
generalization;  that  of  mistaking  an  uncertain  mark,  or  piece  of  evi- 
dence for  a  certain  one  ;  concluding  from  an  effect  to  some  one  of  its 
possible  causes,  when  there  are  others  which  would  have  been  equally 
capable  of  producing  it. 

Yet,  though  tlie  five  classes  run  into  each  other,  and  a  particular 
error  often  seems  to  be  arbitrarily  assigned  to  one  of  them  rathor  than 
to  any  of  the  rest,  there  is  considerable  use  in  so  distinguishing  them. 
We  shall  find  it  convenient  to  set  apart,  as  Fallacies  of  Confusion, 
those  of  which  confusion  is  the  most  obvious  characteristic  ;  in  which 
no  other  cause  can  be  assigned  for  the  mistake  committed,  than  neg- 
lect or  inability  to  state  the  (piestion  properly,  and  to  aj)preliend  the 
evidence  with  definiteness  and  precision.  In  the  remaining  four 
classes  I  shall  place  not  only  the  comparatively  few  cases  in  which  the 
evidence;  is  clearly  seen  to  be  what  it  is,  and  yet  a  wrong  conclusion 
drawn  from  it,  but  also  tlutse  in  which,  although  there  be  confusion, 
the  confusion  is  not  the  sole  cause  of  the  error,  but  there  is  some 
shadow  of  a  ground  for  it  in  the  nature  of  the  evidence  itself.  And  in 
distributing  these  cases  of  partial  ccjufusion  among  the  four  classes,  I 
shall,  when  there  can  be  any  hesitation  as  to  the  jirecise  seat  of  the 
falla<y,  suppose  it  to  be  in  that  part  cjf  the  process  in  which  from  the 
nature  of  the  case,  and  the  known  infirmities  of  the  human  mind,  an 
error  would  in  the  particular  circumstances  be  the  most  prcjbable. 

After  these  obsen'ations  w<!  shall  ])roceed,  without  further  pream- 
ble, to  consider  the  five  classes  in  tlieir  order. 


456  FALLACIES. 

CHAPTER  III. 

FALLACIES   OF   SIMPLE   INSPECTION ;    OR  A  PRIORI  FALLACIES. 

§  1.  The  tiibe  of  errors  of  which  we  are  to  treat  in  the  first  instance, 
are  those  in  which  no  actual  inference  takes  place  at  all ;  the  proposi- 
tion (it  cannot  in  such  cases  be  called  a  conclusion)  being  embraced, 
not  as  proved,  but  as  requiring  no  proof;  as  a  self-evident  truth ; .  or 
else  as  having  such  intrinsic  verisimilitude,  that  external  evidence  not 
in  itself  amounting  to  proof,  is  sufficient  in  aid  of  the  antecedent  pre- 
sumption. 

An  attempt  to  treat  this  subject  comprehensively  would  be  a  trans- 
gression of  the  bounds  prescribed  to  this  work,  since  it  would  necessi- 
tate the  inquiry  which,  more  than  any  other,  is  the  grand  question  of 
transcendental  metaphysics,  viz.,  What  are  the  propositions  which  may 
reasonably  be  received  without  proof  1  That  there  must  be  some  such 
propositions  all  are  agreed,  since  there  cannot  be  an  infinite  series  of 
proof,  a  chain  suspended  from  nothing.  But  to  determine  what  these  . 
propositions  are,  is  the  opus  magnum  of  the  higher  mental  philosophy. 
Two  principal  divisions  of  opinion  on  the  subject  have  divided  the 
schools  of  philosophy  from  its  first  dawn.  The  one  recognizes  no 
ultimate  premisses  but  the  facts  of  our  subjective  consciousness ;  our 
sensations,  emotions,  intellectual  states  of  mind,  and  volitions.  These, 
and  whatever  by  the  strict  rules  of  Induction  can  be  derived  fi-om  these, 
it  is  possible,  according  to  this  theory,  for  us  to  know ;  of  all  else  we 
must  remain  in  ignorance.  The  opposite  school  hold  that  there  are  other 
existences  suggested  indeed  to  our  tninds  by  these  subjective  phenom- 
ena, but  not  nifen-ible  from  them,  by  any  process  either  of  deduction 
or  of  induction ;  which,  however,  w^e  must  by  the  constitution  of  our 
omental  nature,, recognize  as  realities;  and  realities,  too,  of  a  higher 
order  than  the  phenomena  of  our  consciousness,  being  the  efficient 
causes  and  necessary  substrata  of  all  Phenomena.  Among  these  en- 
tities they  reckon  Substances,  whether  matter  or  spirit;  from  the 
dust  under  our  feet  to  the  soul,  and  fi-om  that  to  the  Deity.  All  these 
according  to  them  are  preternatural  or  supei-natural  beings,  having  no 
likeness  in  expei"ience,  although  experience  is  entirely  a  manifestation 
of  their  agency.  Their  existence,  together  with  more  or  less  of  the 
laws  to  which  they  conform  in  their  operations,  are,  on  this  theory, 
apprehended  and  recognized  as  real  by  the  mind  itself,  intuitively : 
experience  (whether  in  the  form  of  sensation,  or  of  mental  feeling) 
having  no  other  part  in  the  matter  than  as  affording  a  multitude  of  facts, 
which  are  consistent  with  these  necessary  postulates  of  reason,  and 
which  are  explained  and  accounted  for  by  them. 

As  it  is  foreign  to  the  purpose  of  the  present  treatise  to  determine 
on  which  side  the  truth  lies  as  between  these  theories,  we  are  pre- 
cluded from  inquiring  into  the  existence,  or  defining  the  extent  and 
limits,  of  knowledge  a  priori,  and  from  characterizing  the  kind  of  cor- 
rect assumption  (if  any  such  there  be),  whicli  the  fallacy  of  incorrect 
assumption,  now  under  consideration,  simulates.  Yet  since  it  is  allowed 
on  both  sides  that  such  assumptions  are  occasionally  made  improperly, 
we  may  find  it  practicable,  without  entering  into  the  ultimate  raeta- 


FALLACIES    OF    SIMPLE    INSPECTION.  457 

physical  grounds  of  the  discussion,  to  state  some  speculative  pn^posi- 
tions,  and  suggest  some  practical  cautions  (not  absolutely  inconsistent 
with  either  vrew  of  the  philosophicitl  (piestion)  respecting  the  forms  in 
which  such  unwari'anted  assumptions  are  most  likely  to  be  made. 

§  2.  In  the  cases  in  which,  according  to  the  philosophers  of  the  onto- 
logical  school,  the  mind  apprehends,  by  intuitittn,  things,  and  the  laws 
of  things,  not  cognizable  by  our  sensitive  faculty;  those  intuitive,  or 
supposed  intuitive,  perceptions  are  undistinguisliable  from  wliat  the 
opposite  school  are  accustomed  to  call  ideas  of  the  mind.  WIumi  they 
themselves  say  that  they  perceive  the  things  by  an  immediate  act  of 
a  faculty  given  for  that  purj)0se  at  their  creation^  it  would  be  said  of 
them  by  their  opponents  that  they  find  an  idea  or  conception  in  their 
own  minds,  and  from  the  idea  or  conception  infer  the  existence  of 
a  corresponding  objective  reality.  Nor  would  this  be  an  mifair  state- 
ment, but  a  mere  version  into  other  words  of  the  account  given  by 
themselves ;  and  one  to  which  the  more  clear-sighted  of  them  might, 
and  generally  do,  without  hesitation  subscribe.  Since,  tlierefore,  in  the 
cases  which  lay  the  strongest  claim  to  be  examples  of  knowledge  a 
priori,  the  mind  proceeds  from  the  idea  of  a  thing  to  the  reality  of  the 
tiling  itself,  we  cannot  be  surjnised  by  finding  thai  illicit  assumjitions 
a  priori,  consist  in  doing  the  same  thing  erroneously :  in  mistaking 
subjective  facts  for  objective,  laws  of  the  percipient  mind  for  laws  of 
the  perceived  object,  properties  of)  the  ideas  or  conceptions  for  pi-op- 
erties  of  the  things  conceived. 

Accordingly,  a  large  proportion  of  the  erroneous  thinking  which  exists 
in  the  world  proceeds  ujjon  a  tacit  assumption,  that  the  same  order 
must  obtain  among  the  objects  in  nature  which  obtains  among  our 
ideas  of  them.  That  if  we  always  think  of  two  things  together,  the 
two  things  must  always  exist  together.  That  if  one  thing  makes  us 
think  of  another  as  preceding  or  following  it,  that  othdr  must  precede 
it  or  follow  it  in  actual  fact.  And  conversely,  that  when  we  cannot 
conceive  two  things  together  they  cannot  exist  together  and  that  their 
combination  may,  with(jut  further  evidence,  be  rejected  from  the  list 
of  possible  occurrences. 

Few  persons,  1  am  inclined  to  think,  have  reflected  upon  the  great 
extent  to  which  this  fallacy  has  prevailed,  and  prevails,  in  the  actual 
beliefs  and  actions  of  mankind.  For  a  first  illustration  of  it,  we  may 
refer  to  a  lar^e  class  of  popular  suspt^rstitions.  If  any  one  will 
examine  in  what  circumstance  most  of  those  things  agree,  which  in 
different  ages  and  by  different  portions  t)f  the  human  race  have  been 
considered  as  omens  or  progrK»stics  of  some  interesting  event,  whether 
calamitous  or  fortunate  ;  ho  will  find  them  very  generally  characterized 
by  this  peculiarity,  that  they  cain^e  the  mind  to  think  of  that,  of  which 
they  are  therefore  supposed  to  forebode  the  actual  occuiTence.  "  Talk 
of  the  devil,  and  he  will  appear,"  has  passed  into  a  proverb.  Talk  of 
the  devil,  that  is,  raise  the  idea,  and  the  reality  will  follow.  In  tinier 
wluni  the  ap{)earance  of  tliat  personage  in  a  visible  foiin  was  thought 
to  be  no  uncommon  occurrence,  it  lias  doubtless  often  hajipened  toper- 
sons  of  vivid  imagination  and  suscei)tible  nerves,  that  talking  of  the 
devil  has  caused  them  to  fancy  they  saw  him  ;  as,  even  in  our  incred- 
ulous days,  listening  to  ghost  stories  predisposes  us  to  see  ghosts : 
and  thus,  as  a  prop  to  ihe  d  priori  iillacy,  there  might  come  to  be 
3M 


458  FALLACIES. 

added  an  auxiliary  fallacy  of  mal-observation,  with  one  of  false  genera- 
lization grounded  upon  it.  Fallacies  of  different  orders  often  herd  or 
cluster  together  in  this  fashion.  But  the  origin  of  the  superstition  is 
evidently  that  which  we  have  assigned.  In  like  manner  it  has  been 
universally  considered  unlucky  to  speak  of  misfortune.  The  day  on 
which  any  calamity  happened  has  been  considered  an  unfortunate  day, 
and  there  has  been  a  feeling  everywhere,  and  in  some  nations  a 
religious  obligation,  against  transacting  any  important  business  on 
that  day.  For  on  such  a  day  our  thoughts  are  likely  to  be  of  misfor- 
tune. For  a  similar  reason,  any  untoward  occurrence  in  commencing 
an  undertaking  has  been  considered  ominous  of  failure  ;  and  often, 
doubtless,  has  really  contributed  to  it,  by  putting  the  persons  engaged 
in  the  enterprise  more  or  less  out  of  spirits :  but  the  belief  has  etjually 
prevailed  where  the  disagi-eeable  circumstance  was,  independently  of 
superstition,  too  insignificant  to  depress  the  spirits  by  any  influence  of 
its  own.  All  know  the  story  of  Caesar's  accidentally  stumbling  in  the 
act  of  landing  on  the  African  coast ;  and  the  presence  of  mind  with 
which  he  converted  the  direful  presage  into  a  favorable  one  by  ex- 
claiming, "Africa,  I  embrace  thee  !"  Such  omens,  it  is  true,  were  of- 
ten conceived  as  warnings  of  the  future,  given  by  a  friendly  or  a  hostile 
deity  :  but  this  very  superstition  grew  out  of  a  preexisting  tendency  ; 
the  god  was  supposed  to  send,  as  an  indication  of  what  was  to  come, 
something  which  men  were  already  inclined  to  consider  in  that  light. 
So  in  the  case  of  lucky  or  unlucky  names.  Herodotus  tells  how  the 
Greeks,  on  the  way  to  Mycale,  were  encouraged  in  their  enterprise  by 
the  arrival  of  a  deputation  from  Samos,  one  of  the  members  of  which 
was  named  Hegesistratus,  the  leader  of  armies. 

Cases  may  be  pointed  out  in  which  something  which  could  have  no 
real  effect  but  to  make  pei-sons  think  of  misfortune,  was  regarded  not 
merely  as  a  prognostic  but  as  something  approaching  to  an  actual 
cause  of  it.  The  kv<^i]\iEi  of  the  G  reeks,  and  favete  Unguis,  or  bona 
verba  quceso,  of  the  Romans,  evince  the  care  with  which  they  endeav- 
ored to  repress  the  utterance  of  any  word  expressive  or  suggestive 
of  ill  fortune  ;  not  from  notions  of  delicate  politeness,  to  which  their 
general  mode  of  conduct  and  feeling  had  very  little  reference,  but  from 
bona  fide  alarm  lest  the  event  so  suggested  to  the  imagination  should  in 
fact  occur.  Some  vestige  of  a  similar  superstition  has  been  known  to 
exist  among  uneducated  persons  even  in  our  own  day  :  it  is  thought  an 
unchristian  thing  to  talk  of,  or  suppose,  the  death  of  any  person  while 
he  is  alive.  It  is  known  how  careful  the  Romans  were  to  avoid,  by  an 
indirect  mode  of  speech,  the  utterance  of  any  word  directly  expressive 
of  death  or  other  calamity  :  how  instead  oi  mortuus  est  they  said  vixit ; 
and  "be  the  event  fortunate  or  otherwise"  instead  of  a Jrer^e.  The 
name  Maleventum,  of  which  Salmasius  so  sagaciously  detected  the 
Thessalian  origin  (MaAoei^,  yiakoevToc;),  they  changed  into  the  highly 
propitious  denomination,  Beneventum  ;  and  Epidamnus,  a  name  so 
pleasant  in  its  associations  to  the  reader  of  Thucydides,  they  ex- 
changed for  Dyrrhachium,  to  escape  the  perils  of  a  word  suggestive 
of  damnum  or  detriment. 

"  If  a  hare  cross  the  highway,"  says  Sir  Thomas  Browne,*  "  there 
are  few  above  threescore  that  are  not  perplexed  thereat;  which  not- 

*  Vulgar  Errors,  book  v.,    hap.  21. 


FALLACinS    OF    SIMPLE    INSPF.CTION.  459 

withstanding  is  but  an  augurial  terror,  according  to  tliat  received  ex- 
pression, Inauspicatum  dat  iter  ohUittis  /rpu.s.  And  the  ground  of  the 
conceit  was  prt)l)aV)ly  no  greater  than  tliis,  tlmt  a  fearful  animal  pjussing 
by  us  portended  unto  us  something  to  be  feared ;  as  upon  tli«^  Uke 
consideration  the  meeting  of  a  fox  presaged  some  future  imposture," 
Such  superstitions  as  these  last  must  be  the  result  of  stutly;  they  are 
too  recondite  for  natural  or  spontaneous  growth.  But  when  the  at- 
tempt w:is  once  made  to  construct  a  science  of  predicticms,  any  asso- 
ciation, though  never  so  faint  or  remote,  by  which  an  object  could  bo 
connected  in  however  far-fetched  a  manner  with  ideas  either  of  pros- 
perity or  of  danger  and  misfortune,  was  enough  to  determine  its  being 
classed  among  good  or  evil  omens. 

An  example  of  rather  a  different  kind  from  any  of  these,  but  falling 
under  the  same  principle,  is  the  famous  attempt,  on  which  so  much 
labor  and  ingenuity  were  expended  by  the  alchemists,  to  make  gold 
potable.  The  motive  to  this  was  a  conceit  that  potable  gold  could  be 
no  other  than  the  universal  medicine  :  and  why  gold  ?  Because  it  was 
so  precious.  It  must  have  all  marvelous  properties  as  a  physical 
substance,  because  the  mind  was  already  accustomed  to  marvel  at  it. 

From  a  similar  feeling,  "  every  substance,"  says  Dr.  Paris,*  "  whose 
origin  is  involved  in  mysterj',  has  at  different  times  been  eagerly  ap- 
plied to  the  purposes  of  medicine.  Not  long  since,  one  of  those 
showers  which  are  now  known  to  consist  of  the  excrements  of  insects, 
fell  in  the  north  of  Italy ;  the  inhabitants  regarded  it  as  manna,  or 
some  supernatural  panacea,  and  they  swallowed  it  with  such  avidity, 
that  it  was  only  by  extreme  address  that  a  small  quantity  was  obtained 
for  a  chemical  examination."  The  superstition,  in  this  instance,  though 
doubtless  partly  of  a  religious  character,  probably  in  part  also  arose 
from  the  prejudice  that  a  woiidedul  thing  must  of  course  have  wonder- 
ful properties. 

§  3.  The  instances  of  d  priori  fallacy  which  we  have  hitherto  cited, 
belong  to  the  class  of  vulgar  errors,  and  do  not  now,  nor  in  any  but  a 
rude  age  ever  could,  impose  upon  minds  of  any  consideraV»le  attain- 
ments. But  those  to  which  we  are  about  to  proceed,  have  been,  and 
still  are,  all  but  universjdly  prevalent  evi;n  among  philosophers.  The 
same  disposition  to  give  objectivity  to  a  law  of  the  mind — to  suppose 
that  what  is  true  of  our  ideas  of  things  must  be  true  of  th(>  things  them- 
selves— exhibits  itself  in  many  of  the  most  accredited  modes  of  philo- 
sophical investigation,  both  on  physical  and  on  metaphysical  subjects. 
In  one  of  its  most  undisguised  manifestations,  it  embodies  itself  in  two 
maxims,  wliicb  lay  claim  to  axiomatic  truth  :  Tiling*  which  we  cannot 
tliink  of  together,  cannot  coexist  ;  and,  Things  which  we  cannot  help 
thinking  of  together,  must  coexist.  I  am  not  sure  that  the  maxims 
were  ever  expressed  in  the.se  precise  words,  but  the  history  Ixjth  of 
philosophy  and  of  popular  opinions  abounds  with  exemplifications  of 
both  forms  of  the  doctrine. 

To  begin  with  the  latter  of  them  :  Things  which  we  cannot  think  of 
except  together,  must  exist  together.  This  is  assumed  in  the  many 
reasonings  of  philosophers  which  conclude  that  A  must  accomi)any  B 
in  point  of  fact,  because  "  it  is  involved  in  the  idea."     Such  thinkers 

*  Pharmacologia,  Historical  Introduction,  p.  16 


460  FALLACIES. 

do  not  reflect  that  the  idea,  being  a  result  of  abstraction,  ought  to 
conform  to  the  facts,  and  cannot  make  the  facts  conform  to  it.  The 
argument  is  at  most  admissible  as  an  appeal  to  authority ;  a  surmise, 
that  what  is  now  part  of  the  idea  must,  before  it  became  so,  have  been 
found  by  previous  inquirers  in  the  facts.  Nevertheless,  the  j^hiloso- 
pher  who  more  than  all  others  has  made  profession  of  rejecting  author- 
ity, Descartes,  constructed  his  philosophical  system  on  this  very  basis. 
His  favorite  device  for  arriving  at  truth,  even  in  regai'd  to  outward 
things,  was  by  looking  into  his  own  mind  for  it.  "  Credidi  me,"  says 
his  celebrated  maxim,  "  pro  regula  generali  sumere  posse,  omne  id 
quod  valdi^  dilucide  et  distincte  concipiebam,  verum  esse  :"  whatever 
can  be  very  clearly  conceived,  must  certainly  exist;  that  is,  as  he  af- 
terwards explains  it,  if  the  idea  includes  existence.  And  upon  this 
ground  he  infers  that  geometrical  figures  really  exist,  because  they 
can  be  distinctly  conceived.  Wlienever  existence  is  "  involved  in  an 
idea,"  a  thing  conformable  to  the  idea  must  really  exist ;  which  is  as 
much  as  to  say,  whatever  the  idea  contains  must  have  its  equivalent  in 
the  thing ;  and  what  we  are  not  able  to  leave  out  of  the  idea  cannot 
be  absent  from  the  reality.  This  assumption  pervades  the  philosophy 
not, only  of  Descartes,  but  of  all  the  thinkers  who  received  their  im- 
pulse mainly  from  him,  in  particular  the  two  most  remarkable  among 
them,  Leibnitz  and  Spinosa,  from  whom  the  modern  Gennan  meta- 
physical philosophy  is  essentially  an  emanation.  The  esteemed  author 
of  one  of  the  Bridgewater  Treatises  (which  for  its  accumulation  of 
scientific  facts,  and  even  for  some  of  its  generalizations,  is  worthy  of 
all  praise)  has  fallen,  as  it  seems  to  rne,  into  a  similar  fallacy  when, 
after  arguing  in  rather  a  curious  way  to  prove  that  matter  may  exist 
without  any  of  the  known  properties  of  matter,  and  may  therefore  be 
changeable,  he  concludes  that  it  cannot  be  eternal,  because  "  etenial 
(passive)  existence  necessarily  involves  incapability  of  change."  I 
beUeve  it  would  be  difficult  to  point  out  any  other  connexion  betw^een 
the  facts  of  eternity  and  unchangeableness,  than  a  strong  association 
between  the  two  ideas. 

The  other  fonn  of  the  fallacy ;  Things'  which  we  cannot  think  of 
together  cannot  exist  together — inchiding  as  one  of  its  branches,  that 
what  we  cannot  think  of  as  existing,  cannot  exist  at  all — may  be  thus 
briefly  expressed  :  Whatever  is  inconceivable  must  be  false. 

Against  this  prevalent  doctrine  I  have  sufficiently  argued  in  a  former 
Book,*  and  nothing  is  required,  in  this  place,  but  examples.  It  was 
long  held  that  Antipodes  were  impossible,  because  of  the  difficulty 
which  men  found  in  conceiving  persons  with  their  heads  in  the  same 
direction  as  our  feet.  And  it  was  one  of  the  received  arguments 
against  the  Copernican  system,  that  we  cannot  conceive  so  great  a 
void  space  as  that  system  supposes  to  exist  in  the  celestial  regions. 
When  men's  imaginations  had  always  been  used  to  conceive  the  stars 
as  firmly  set  in  solid  spheres,  they  naturally  found  much  difficulty  in 
imagining  them  in  so  different,  and,  as  it  doubtless  appeared  to  them, 
so  unsafe  a  situation.  But  men  had  no  right  to  mistake  the  limitation 
(whether  natural,  or,  as  it  in  fact  proved,  only  artificial)  of  their  own 
faculties,  for  an  inherent  limitation  of  the  possible  modes  of  existence 
in  the  universe. 

*  Supra,  pp,  ]  56-161. 


FALLACIES    OF   SIMPLE   INSPECTION.  461 

It  rany  be  said  in  objection,  that  tlic  error  in  these  cases  was  in  the 
minor  premiss,  not  the  major;  an  error  of  fact,  not  of  principle;  that 
it  did  not  consist  in  snpposing  that  what  is  inconceivable  cannot  be 
true,  but  in  supposing  Antipodes  to  be  inconceivable,  when  present 
experience  so  fully  proves  that  they  can  be  conceived.  Even  if  this 
objection  were  allowed,  and  tlio  proposition  that  what  is  inconceivfvble 
cannot  be  true  were  suflered  to  remain  unquestioned  as  a  ajreculative 
ti'utli,  it  would  be  a  truth  upon  which  no  practical  consequence  could 
ever  bo  founded,  since,  upon  tliis  showing,  it  is  ini])ossible  to  affimi'  of 
any  proposition,  not  being  a  contradiction  in  terms,  that  it  is  inconceiva- 
ble. Antipodes  were  really,  not  fictitiously,  inconceivable  to  our 
ancestors:  they  are  indeed  conceivable  to  us ;  and  as  the  limits  of  Our 
power  of  conception  have  been  so  largely  extended,  by  the  extension 
of  our  experience  and  the  more  varied  exercise  of  our  imagination,  so 
may  posterity  find  many  combinations  perfectly  conceivable  to  them 
which  are  inconceivable  to  us.  But,  as  beings  of  limited  experience, 
we  must  always  and  necessarily  have  limited  conceptivc  powers ;  while 
it  does  not  by  any  means  follow  that  the  same  limitation  obtains  in  the 
possibilities  of  nature,  nor  even  in  her  actual  manifestations. 

Rather  more  than  a  century  and  a  half  ago  it  was  a  philosophical 
maxim,  disputed  by  no  one,  and  which  no  one  deemed  to  require  any 
proof,  that  "  a  thing  cannot  act  where  it  is  not."  With  this  weapon 
the  Cartesians  waged  a  formidable  war  against  the  theory  of  gravita- 
tion, which,  according  to  them,  involving  so  obvious  an  absurdity, 
must  be  rejected  in  limine ;  the  sun  could  not  possibly  act  upon  the 
earth,  not  laeing  there.  It  was  not  surprising  that  the  adherents  of  the 
old  systems  of  astronomy  should  urge  this  objection  against  the  new ; 
but  the  false  assumption  imposed  equally  upon  Newton  hin\self,  who 
in  order  to  turn  the  edge  of  the  objection,  imagined  a  subtle  ether 
which  filled  up  the  space  between  the  sun  and  the  earth,  and  by  its 
intermediate  agency  was  the  proximate  cause  of  the  phenomena  of 
gravitation.  "  It  is  inconceivable,"  said  Newton,  in  one  of  his  letters 
to  Dr.  Bentley,*  "  that  inanimate  brute  matter  should,  without  the 
mediation  of  something  else,  which  is  not  material,  operate  upon  and 

aflect  other  matter  ^cithout  mutual  contact That  gravity  should  be 

innate,  inherent,  and  essential  to  matter,  so  that  one  body  may  a(-t  on 
another,  at  a  distance,  through  a  vacuum,  without  the  mediation  of 
anythiiig  else,  by  and  througli  which  their  action  and  force  may  be 
conveyed  from  one  to  another,  is  to  me  so  great  an  absurdity,  that  I 
believe  no  man,  who  in  philosophical  mattei's  has  a  competent  faculty 
of  thinking,  can  ever  fall  into  it."  This  passage  should  be  hung  >ip  in 
the  cabinet  of  every  man  of  science  who  is  ever  tempted  to  pronounce 
a  fact  impossible  because  it  appears  to  him  inconceivable.  In  our  own 
day  one  would  be  more  inclined,  though  with  equal  injustice,  to  reverse 
the  concluding  observation,  and  consider  the  seeing  any  absurdity  at 
all  in  a  thing  so  simple  and  natural,  to  be  vyhat  really  marks  the  ab- 
sence of  "  a  competent  faculty  of  thinking."  No  one  now  feels  any 
difficulty  in  conceiving  gravity  to  Ix;,  as  much  as  any  other  pi-ojierty 
is,  "innate,  inherent,  and  essential  to  matter,"  nor  finds  the  compre- 
hension of  it  facilitated  in  the  smallest  degree  by  the  supposition  of 
an  ether ;  nor  thinks  it  at  all  incredible  that  the  celestial  bodies  can 

*  I  quote  this  passage  from  Playfair's  celebrated  Dissertation  on  the  Progress  of  Mathemat- 
ical and  Physical  Science. 


462  FALLACIES. 

and  do  act  where  they,  in  actual  hodily  presence,  are  not.  To  us  it  is 
not  more  wonderful  that  bodies  should  act  upon  one  another  "  without 
mutual  contact,"  than  that  they  should  do  so  when  in  contact :  we  are 
familiar  with  both  these  facts,  aitd  we  find  them  equally  inexplicable, 
but  equally  easy  to  believe.  To  Newton  the  one,  because  his  imagi- 
nation was  familiar  with  it,  appeared  natural  and  a  matter  of  course, 
while  the  other,  for  the  contrary  reason,  seemed  too  absurd  to  be  cred- 
ited. If  a  Newton  could  err  thus  gi'ossly  in  the  use  of  such  an  argu- 
ment, who  else  can  trust  himself  with  it  ] 

It  is  strange  that  any  one,  after  such  a  warning,  should  rely  implicitly 
upon  the  evidence,  d  priori,  of  such  propositions  as  these,  that  matter 
cannot  think  ;  that  space,  or  extension,  is  infinite  ;  that  nothing  can  be 
made  out  of  nothing  [ex  nihilo  nihil  Jit).  Whether  these  propositions 
are  true  or  no  this  is  not  the  place  to  determine,  nor  even  whether  the 
questions  are  soluble  by  the  human  faculties.  But  such  doctrines  are 
no  more  self-evident  truths,  than  the  ancient  maxim  that  a  thing  cannot 
act  where  it  is  not,  which  probably  is  not  now  believed  by  any  educated 
person  in  Europe.  Matter  cannot  think ;  why  1  because  we  cannot 
conceive  thought  to  be  annexed  to  any  arrangement  of  material  parti- 
cles. Space  is  infinite,  because  having  never  known  any  part  of  it 
which  had  not  other  parts  beyond  it,  we  cannot  conceive  an  absolute 
termination.  Ex  nihilo  nihil  Jit.,  because  having  never  known  any 
physical  product  without  a  preexisting  physical  material,  we  cannot,  or 
think  we  cannot,  imagine  a  creation  out  of  nothing.  But  these  things 
may  in  themselves  be  as  conceivable  as  gravitation  without  an  inter- 
vening medium,  which  Newton  thought  too  great  an  absurdity  fin-  any 
man  of  a  competent  faculty  of  philosophical  thinking  to  admit :  and 
even  supposing  them  not  conceivable,  this,  for  aught  we  know,  may  be 
merely  one  of  the  limitations  of  our  very  limited  minds,  and  not  in 
nature  at  all. 

t  Coleridge  has  attempted,  with  his  usual  ingenuity,  to  establish  a  dis- 
tinction which  would  save  the  credit  of  the  common  mode  of  thinking 
on  this  subject,  declaring  that  the  ■unimaginable,  indeed,  may  possibly 
be  true,  but  that  the  inconceivable  cannot :  and  he  would  probably  have 
said  that  the  three  supposed  impossibilities  last  spoken  of  are  not  cases 
of  mere  unimaginableness,  but  of  actual  inconceivableness ;  while  the 
action  of  the  sun  upon  the  earth  without  an  intervening  medium,  was 
merely  unimaginable.  I  am  not  aware  that  Coleridge  has  anywhere 
attempted  to  define  the  distinction  between  the  two  ;  and  I  am  per- 
suaded that,  if  he  had,  it  would  have  broken  down  under  him.  But  if 
by  unimaginableness  he  meant,  as  seems  likely,  mere  inability  on  our 
part  to  represent  the  phenomenon,  like  a  picture  of  sometliing  visible, 
to  tlie  internal  eye,  antipodes  were  not  unimaginable.  They  were 
capable  of  being  imaged ;  capable  even  of  being  drawn,  or  modeled 
in  plaster.  They  were,  however,  inconceivable :  the  imagination  could 
paint,  but  the  intellect  could  not  recognize  them  as  a  believable  thing. 
Things  may  be  inconceivable,  then,  witnout  being  incredible  :  and 
Coleridge's  distinction,  whether  it' have  any  foundation  or  not,  will  in 
no  way  help  the  maxim  out. 

No  philosopher  has  more  directly  identified  himself  with  the  fallacy 
now  under  consideration,  or  has  embodied  it  in  more  distinct  terms, 
than  Leibnitz.  In  his  view,  unless  a  thing  was  not  merely  conceivable, 
but  even  explainable,  it  could  not  exist  in  nature.     All  natural  phe- 


FALLACIES    OF    SIMPLE    INSPECTION.  463 

noniona,  accordinu^  to  liim,  must  bo  susceptible  of  bcinp;  accounli-J  for 
d  J)/ tori.  Tlio  «)nly  facts  of  whicb  no  explanation  could  be  given  but 
the  will  of  God,  "were  miracles  jiropeily  so  called.  "  Je  reconnais," 
says  he,*  "  qu'il  n'est  pas  permis  do  nier  ce  «pi'ou  n'entend  j)as  ;  inais 
j'ajoute  qu'ou  a  droit  de  nier  (au  moins  dans  I'ordre  naturel)  ce  qui 

absolument  n'est  point  intelligible  ni  explicable.     Je  soutiens  aussi 

qu'entin  la  conception  dcs  creatures  n'est  pas  la  mcsurc  du  pouvoir  de 
Dieu,  mais  que  leur  conceptivite,  ou  force  do  conccvoii*,  est  la  mesuro 
du  pouvoir  de  le  nature,  tout  co  qui  est  conforme  a  I'ordro  naturel 
pouvant  etre  con^u  ou  entendu  par  cjuelque  creature." 

Not  content  with  assuming  that  nothing  can  be  true  which  wc  are 
unable  to  conceive,  philosophers  have  frequently  given  a  still  further 
extension  to  the  doctrhie,  and  contended  that,  even  of  things  not  alto- 
gether  inconceivable,  that  which  wc  can  conceive  with  the  greatest 
ease  is  likeliest  to  be  true.  It  was  long  an  admitted  axiom,  and  is  not 
yet  entirely  discredited,  that  "  nature  always  acts  by  the  simplest 
means,"  i.  c.  by  those  which  arc  most  easily  conceivable.  A  large  pro- 
portion of  all  the  eiTors  ever  committed  in  the  investigation  of  the 
laws  of  nature,  have  arisen  fix)m  the  assumption  that  the  most  familiar 
explanation  or  hypothesis  must  be  the  truest.  One  of  the  most  in- 
structive facts  in  scientific  history  is  the  pertinacity  with  which  the 
human  mind  clung  to  the  belief  that  the  heavenly  bodies  must  move 
in  circles,  or  be  carried  round  by  the  revolution  of  spheres ;  merely 
because  those  were  in  themselves  the  simplest- suppositions  :  although, 
to  make  them  accord  witU  the  facts  which  were  ever  contradicting 
them  more  and  more,  it  became  necessary  to  add  sphere  to  sphere  and 
circle  to  circle,  until  the  original  simplicity  was  converted  into  almost 
inextricable  complication. 

§  4.  We  pass  to  another  d  priori  fallacy  or  natural  prejudice,  allied 
to  the  former,  and  originating  as  that  does,  hi  the  tendency  to  pre- 
sume an  exact  correspondence  between  the  laws  of  the  mind  and  those 
of  things  external  to  it.  The  fallacy  may  be  enunciated  in  this  general 
form — Whatever  can  be  thought  of  apart  exists  apart:  and  its  most 
remarkable  manifestaticm  consists  in  the  personification  of  abstractions. 
Mankind  in  all  agos  have  had  a  strong  propensity  to  conclude  that 
wherever  there  is  a  name,  there  must  be  a  distinguishable  separate 
entity  corresponding  to  tlie  name  ;  and  every  complex  idea  which  the 
mind  has  fonned  for  itself  by  operating  upon  its  conceptions  of  indi- 
vidual things,  was  considered  to  have  an  outward  objective  reality 
answering  to  it.  Fate,  Chance,  Nature,  Time,  Space,  were  real 
beings,  nay,  even  gods.  If  the  analysis  of  qualities  in  the  earlier  j)art 
of  tliis  work  be  con-ect,  names  of  qualities  and  names  of  substances 
stand  for  the  very  same  sets  of  facts  or  phenomena;  whiteness  and  a 
white  thing  are  only  different  phrases,  required  by  convenienco  ftr 
speaking,  under  different  circumstances,  of  the  same  external  fact. 
Not  such,  however,  was  the  notion  which  this  verbal  distinction  sug- 
gested of  old,  either  to  the  vulgar  or  to  philo8oj)hers.  Whiteness  was 
an  entity,  inhering  or  sticking  in  the  white  substance :  and  so  of  all 
other  qualities.  So  far  was  this  cairicd,  tliat  even  concrete  gi^neral 
terms  were  supposed  to  be,  not  names  of  indefinite  numbers  of  indi- 

*  Nouvea-nx  Essais  sur  F Entendcmerti  JIumain — Avanlpropos.  ((Euvrcs,  Paris  cd.  1842, 
voL  i.,  p.  19.) 


464  FALLACIES. 

vidual  -substances,  but  names  of  a  peculiar  kind  of  entities  termed 
Universal  Substances.  Because  we  can  think  and  speak  of  man  in 
g'eneral,  that  is,  of  all  men  in  so  far  as  j)ossessing  the  common,  attri- 
butes of  the  species,  without  fastening  our  thoughts  pemianently  on 
some  one  individual  man  ;  therefore  man  in  general  was  supposed  to 
be,  not  an  aggregate  of  individual  men,  but  an  abstract  or  universal 
man,  distinct  from  these. 

It  may  be  imagined  what  havoc  metaphysicians  trained  in  these 
babits  made  with  philosophy,  when' they  came  to  the  largest  generali- 
zations of  all,  Substantice  SecundcB  of  any  kind  were  bad  enough,  but 
such  Substantiae  Secundae  as  to  bv,  for  example,  and  to  ev,  standing  for 
peculiar  entities  supposed  to  be  inherent  in  all  things  which  exist,  or 
which  are  said  to  be  one,  were  enough  to  put  an  end  to  all  intelligible 
discvission ;  especially  since,  with  a  just  perception  that  the  truths 
whicli  philosophy  pursues  are  general  truths,  it  was  soon  laid  down 
that  these  general  substances  were  the  only  objects  of  science,  being 
immutable,  while  individual  substances  cognizable  by  the  senses, 
being  in  a  perpetual  flux,  could  not  be  the  subject  of  real  knowledge. 
This  misapprehension  of  the  import  of  general  language  constitutes 
Mysticism,  a  word  so  much  oftener  written  and  spoken  than  under- 
Stood.  Whether  in  the  Vedas,  in  the  Platonists,  or  in  the  Hegelians, 
mysticism  is  neither  more  nor  less  than  ascribing  objective  existence  to 
the  subjective  creations  of  the  mind's  own  faculties,  to  mere  ideas  of 
the  intellect ;  and  believing  that  by  watching  and  contemplating  these 
ideas  of  its  own  making,  it  can  read  in  them  what  takes  place  in  the 
world  without. 

§  5.  Proceeding  with  the  enumeration  of  a  priori  fallacies,  and 
endeavoring  to  arrange  them  with  as  much  reference  as  possible  to 
their  natural  affinities,  we  come  to  another,  which  is  also  nearly  allied 
to  the  fallacy  preceding  the  last,  standing  in  the  same  relation  to  one 
variety  of  it  as  the  fallacy  last  mentioned  does  to  the  other.  This,  too, 
represents  nature  as  bound  to  conform  herself  to  the  incapacities  of 
our  intellect;  but  instead  of  only  asserting  that  nature  cannot  do  a 
thing  because  we  caimot  conceive  it  done,  goes  the  still  greater  length 
of  averring  that  nature  does  a  particular  thing,  on  the  sole  ground 
that  we  can  see  no  reason  why  she  should  not.  Absurd  as  this  seems 
when  so  plainly  stated,  it  is  a  received  principle  among  philosophers 
for  demonsti-ating  a  priori  the  laws  of  physical  phenomena.  A  phe- 
nomenon must  follow  a  certain  law,  because  we  see  no  reason  why  it 
should  deviate  from  that  law  in  one  way  father  than  in  another.  This 
is  called  the  principle  of  the  Sufficient  Reason ;  and  by  means  of  it 
philosophers  often  flatter  themselves  that  they  are  able  to  establish, 
without  any  appeal  to  experience,  the  most  general  tinaths  of  experi- 
mental physics. 

Take,  for  example,  two  of  the  most  elementary  of  all  laws,  the  law 
of  inertia  and  the  first  law  of  motion.  A  body  at  rest  canjiot,- it  is 
affirmed,  begin  to  move  unless  acted  upon  by  some  external  force : 
because,  if  it  did,  it  must  either  move  up  or  down,  forward  or  back- 
ward, and  so  forth ;  but  if  no  outward  force  acts  upon  it,  there  can  be 
no  reason  for  its  moving  up  rather  than  down,  or  down  rather  than 
up,  &c.,  ergo  it  will  not  move  at  all.     Q.  E.  D. 

This  reasoning  I  conceive  to  be  entirely  fallacious,  as  indeed  Dr. 


FALLACIES    OF    SIMPLE    IXSPECTION.  465 

Brouni,  in  liis  ti-eatise  on  Cause  and  Effect,  has  sliowii  Avitli  great 
acuteness  and  justness  of  thouG;ht.  We  have  before  remarked,  ihat 
almost  every  fallacy  may  be  refeircd  to  diHbrcnt  genera  by  diilerent 
modes  of  hlling  up  the  suppressed  steps,  and  this  particular  one  may, 
at  our  ojition,  be  bi'uught  under  jK'titio  2>/'i>i'''J'i'.  It  supposes  that 
nothing  can  be  a  "  sufKcicnt  reason"  for  a  body's  moving  in  one  par- 
ticulai-  dii-ectiiin,  except  some  external  force.  But  this  is  the  -very 
thing  to  be  proved.  Wliy  not  some  internal  force  ]  Why  hot  the  law 
of  the  thing's  own  nature  1  Since  these  philosophers  think  it  neces- 
Bai^y  to  prove  the  law  of  inertia,  they  of  course  do  not  suppose  it  to  be 
sell'-evident ;  they  must,  therefore,  be  of  opinion  that,  ])rcviously  to  all 
jnoof,  the  8Ui)position  of  a  body's  moving  by  internal  impulse  is  an 
admissible  hypothesLj  r  but  if  so,  why  is  not  the  hypothesis  also  admis- 
sible, that  the  internal  impidsc  acts  naturally  in' some  one  paiticular 
direction,  not  in  another  I  If  spontaneous  motion  might  have  been 
the  law  of  matter,  why  not  spontaneous  motion  towards  the  sun, 
towards  the  earth,  or  towards  the  zenith  \  A\'hy  not,  as  the  ancients 
supposed,  towards  a  particular  place  in  the  universe,  appropriated  to 
each  particular  kind  of  substance  1  Surely  it  is  not  allowable  to  say 
that  spontaneity  of  motion  is  credible  in  itself,  but  not  credible  if  sup- 
posed to  take  place  in  any  determinate  directitm. 

Indeed,  if  any  one  chose  to  assert  that  all  bodies  when  uncontrolled 
set  out  in  a  direct  line  towards  the  north  pole,  he  might  ecpially  prove 
his  point  by  the  principle  of  the  Sufficient  Reason.  By  what  right  is 
it  assumed  that  a  state  of  rest  is  the  particular  state  which  camiot  be 
deviated  from  without  special  cause  ?  Why  not  a  state  of  motion,  and 
of  some  particular  sort  of  motion  ]  Why  may  we  not  say  that  the 
natural  state  of  a  horse  left  to  himself  is  to  amble,  because  otherwise 
he  must  either  trot,  gallop,  or  stand  still,  and  because  \\e  know  no 
reason  why  he  should  do  one  of  these  rather  than  another  (  If  this  is 
to  be  called  an  unfair  use  of  the  "  sufficient  reason,"  and  the  other  a 
fair  one,  there  must  be  a  tacit  assumption  that  a  state  of  rest  is  raorc 
natural  to  a  horse  than  a  state  of  ambling.  If  this  means  tliat  it  is  the 
;state  which  the  animal  will  assume  when  lel'c  to  himself,  that  is  the 
vei,y  point  to  be  proved ;  and  if  it  does  iu>\.  moan  this,  it  can  only  mean 
that  a  state  of  rest  is  the  simplest  state,  and  therefore  the  most  likely 
to  prevail  in  nature,  which  is  one  of  the  i'allacies  or  natural  i)rejudices 
we  have  already  examined. 

So  again  of  the  First  Law  of  Motion ;  that  a  body  once  moving 
Avill,  if  left  to  itself,  contuuie  to  move  unifonnly  in  a  straight  line.  An 
attempt  is  made  to  prove  this  law  by  saying,  that  if  not,  the  body  must 
deviate  either  to  the  right  or  to  the  left,  and  that  there  is  no  reason 
why  it  should  do  one  more  than  the  other.  But  who  could  jcnow,  an- 
tecedently to  experience,  whether  there  was  a  reason  or  not  ]  Might 
it  not  be  the  nature  of  bodies,  or  of  some  particular  bodies,  to  deviate 
towards  the  right  '.  or  if  the  supposition  is  preferred,  towaids  the  east, 
or  south  ?  It  wa.s  long  thought  that  l>odie.'*,  tencistrial  ones  at  least, 
had  a  natural  tendency  to  deflect  downwards ;  and  there  is  no  shadow 
of  anything  objectionable  in  the;  supj)osilion,  except  tliat  it  is  not  true. 
The  pretended  proof  of  the  law  of  motitm  is  oven  more  manifestly  un- 
tenable than  that  of  the  law  of  ineitia,  for  it  is  flagiaiitly  inconsistent ; 
it  assumes  that  the  continuance  of  motion  in  the  direction  first  taken  is 
more  natural  than  deviation  either  to  the  right  or  to  the  left,  but  denies 
3N 


466  FALLACIES. 

that  one  of  these  caii  possibly  be  more  natural  than  the  other.  All 
these  fancies  of  the  possibility  of  knowing  what  is  natural  or  not  natural 
by  any  other  means  than  experience,  are,  in  truth,  entirely  futile.  The 
real  and  only  proof  of  the  laws  of  motion,  or  of  any  other  law  of  the 
universe,  is  experience  ;  it  is  simply  that  no  other  suppositions  explain 
or  are  consistent  with  the  facts  of  universal  nature. 

Geometers  have,  in  all  ages,  been  open  to  the  imputation  of  en- 
deavoring to  prove  the  most  general  facts  of  the  outward  world  by 
sophistical  reasoning,  in  order  to  avoid  appeals  to  the  senses.  Archi- 
medes, says  Professor  Playfair,*  established  some  of  the  elementary 
propositions  of  statics  by  a  process  in  which  he  "boiTows  no  pi-inciple 
from  experiment,  but  establishes  his  conclusion  entirely  by  reasoning 
d  priori.  He  assumes,  indeed,  that  equal  bodies,  at  the  ends  of  the 
equal  arms  of  a  lever,  "vvill  balance  one  another ;  and  also  that  a  cylin- 
der or  parallelepiped  of  homogeneous  matter,  wall  be  balanced  about 
its  centre  of  magnitude.  These,  however,  are  not  inferences  from 
experience ;  they  are,  properly  speaking,  conclusions  deduced  from 
the  principle  of  the  Sufficient  Reason."  And  to  this  day  there  are 
few  geometers  who  would  not  think  it  far  more  scientific  to  establish 
these  or  any  other  premisses  in  this  way,  than  to  rest  their  evidence 
upon  that  familiar  experience  which  in  the  case  in  question  might  have 
been  so  safely  appealed  to. 

§  6.  Another  natural  prejudice,  of  most  extensive  prevalence,  and 
which  lay  at  the  root  of  the  errors  fallen  into  by  the  ancient  philoso- 
phers in  their  physical  inquiries,  was  this:  That  the  differences  in 
nature  must  con-espond  to  our  received  distinctions ;  that  effects  which 
we  are  accustomed,  in  popular  language,  to  call  by  different  names, 
and  aiTange  in  different  classes,  must  be  of  difterent  natures,  and  have 
different  causes.  This  prejudice,  so  evidently  of  the  same  origin  with 
those  already  treated  of,  marks  more  especially  the  earliest  stage  of 
science,  when  it  has  not  yet  broken  loose  from  the  trainmels  of  every- 
day phraseology.  The  extraordinary  prevalence  of  the  fallacy  among 
the  Greek  philosophers  may  be  accounted  for  by  theii'  generally  know- 
ing no  other  language  than  their  own ;  from  which  it  was  a  consequence 
that  their  ideas  followed  the  accidental  or  arbitrary  combinations  of 
that  language,  more  completely  than  can  happen  among  the  modems 
to  any  but  illiterate  persons.  They  had  gi'eat  difl[iculty  in  distinguish- 
ing between  things  which  their  language  confounded,  or  in  putting 
mentally  together  things  which  it  distinguished  ;  and  could  hardly  com- 
bine the  objects  in  nature  into  any  classes  but  those  which  were  made 
for  them  by  the  popular  phrases  of  their  own  country ;  or  at  least 
could  not  help  fancying  those  classes  to  be  natural,  and  all  others 
arbitrary  and  artificial.  Accordingly,  as  is  remarked  by  Mr.  Whewell, 
scientific  investigation  among  the  Greek  philosophers  and  their  fol- 
lowers in  the  middle  ages,  was  little  more  than  a  mere  sifting  and 
analyzing  of  the  notions  attached  to  common  language.  They  thought 
that  by  determining  the  meaning  of  words,  they  could  become  ac- 
quainted with  facts.  "  They  took  for  granted,"  says  Mr.  Whewell, t 
"that  philosophy  must  result  from  the  relations  of  those  notions  which 
are  involved  in  the  common  use  of  language,  and  they  proceeded  to 

*  Dissertation,  ut  supra,  pp.  298-9. 

t  History  of  the  Inductive  Sciences,  Book  i.,  chap.  1. 


FALLACIES    OF   SIMPLE    INSPECTION.  467 

seek  it  by  studying  such  notions."  In  his  next  chapter  Mr.  WIiowcll 
has  so  well  illustiated  and  exemplitied  this  error,  that  we  shall  take 
the  liberty  of  quoting  him  at  some  length. 

"The  propensity,"  says  he,  "to  seek  for  principles  in  the  common 
usages  of  language,  may  be  discerned  at  a  very  early  period.  Thus 
we  have  an  example  of  it  in  a  saying  which  is  reported  of  Thales,  the 
founder  of  Greek  philosophy.  When  he  was  asked,  'What  is  the 
greatest  thing?'  he  replied  'Plate;  for  all  other  thhigs  arc  i«  the 
world,  but  the  world  is  //*  it.'  In  Aristotle  we  have  the  consummation 
of  this  mode  of  speculation.  The  usual  point  from  which  he  starts  in 
his  inquiries  is,  that  wc  say  thus  or  thus  in  conmion  language.  Thus, 
when  he  has  to  discuss  the  ([uestion  whether  tliere  be,  in  any  part  of 
the  universe,  a  void,  or  space  in  which  there  is  nothing,  he  incpiires  first 
in  how  many  senses  we  say  that  one  thing  is  in  another.  He  enumer- 
ates many  of  these  ;  we  say  the  part  is  in  the  whole,  as  the  finger  is  in 
the  hand ;  again  we  say,  the  species  is  in  the  genus,  as  man  is  included 
in  animal;  again,  the  government  of  Greece  is  in  the  king;  and  various 
other  senses  are  described  and  exemplified,  but  of  all  tliesc  the  most 
proper  is  when  we  say  a  thing  is  in  a  vessel,  and  generally  in  place. 
He  next  examines  what  j^l^ic*^  is,  and  comes  to  this  conclusion,  that  '  if 
about  a  body  there  be  another  body  including  it,  it  is  in  place,  and  if 
not,  not.'  A  body  moves  when  it  changes  its  place ;  but  he  adds,  that 
if  water  be  in  a  vessel,  the  vessel  being  at  rest,  the  parts  ofs^he  water 
may  still  move,  for  they  are  included  by  each  other;  so  that  while  the 
whole  does  not  change  its  place,  the  parts  may  change  their  place  in  a 
circular  order.  Proceeding  then  to  the  question  of  a  void,  he  as  usual 
examines  the  different  senses  in  which  the  term  is  used,  and  adopts,  aa 
the  most  proper,  ^^ace  without  matter;   with  no  Useful  result." 

"  Again,  in  a  question  concerning  mechanical  action,  he  says,  '  When 
a  man  moves  a  stone  by  pushing  it  with  a  stick,  wc  say  both  that  the 
man  moves  the  stone,  and  that  the  stick  moves  the  stone,  but  the  latter 
more  properly.^ 

"Again,  we  find  the  Greek  philosophers  applying  themselves  to  ex- 
tract their  dogmas  from  the  most  general  and  abstract  notions  which 
they  could  detect ;  for  example,  from  the  conception  of  the  Universe 
as  One  or  as  Many  things.  They  D-ied  to  determine  how  far  we  may, 
or  must,  combine  with  these  conceptions  that  of  a  whole,  of  parts,  of 
number,  of  limits,  of  place,  of  begiiming  or  end,  of  full  or  void,  of  rest 
or  motion,  of  cause  and  effect,  and  the  like.  The  analysis  of  such  con- 
ceptions with  such  a  view,  occupies,  for  instance,  almost  the  whole  of 
Aristotle's  Treatise  on  the  Heavens." 

The  following  paragraph  merits  particular  attention  :  —  "Another 
mode  of  reasoning,  very  widely  applied  in  these  attempts,  was  the  doc- 
trine of  contrarieties,  in  which  it  was  assumed,  that  adjectives  or  sub- 
stantives which  are  in  common  language,  or  in  some  abstract  mode  of 
conception,  opposed  to  each  other,  nmst  point  at  some  fundamental 
antithesis  in  nature,  which  it  is  important  to  study.  Thus  Aristotle 
says,  that  the  Pythagoreans,  from  the  contntsts  whi<-h  number  sug- 
gests, collected  ten  principles — Limited  and  JJnIimitetl,  Odd  and  Kven, 
One  and  Many,  Right  and  Left,  Male  find  Female,  iii'st  and  Motion, 
Straight  and  Curved,  Light  and  Darkness,  Good  and  Evil,  Square  and 
Oblong ....  Aristotle  himself  deduced  the  doctrine  of  four  elements  and 
6ther  dogmas  by  oppositions  of  the  same  kind." 


468  FALLACIES. 

Of  the  manner  in  which,  fi-om  premisses  obtained  in  this  Way,  the 
ancients  attempted  to  deduce  laws  of  nature,  one  example  is  given  by- 
Mr.  Whewell  a  few  pages  further  on.  "Aristotle  decides  that  there  is 
no  void,  on  such  arguments  as  this.  In  a  void  there  could  be  no  dif- 
-ference  of  up  and  down  ;  for  as  in  nothing  there  are  no  differences,  so 
there  are  none  in  a  privation  or  negation  ;  but  a  void  is  merely  a  priva- 
tion or  negation  of  matter ;  therefore,  in  a  void,  bodies  could  not  move 
up  and  down,  which  it  is  in  their  nature  to  do.  It  is  easily  seen"  (Mr. 
Whewell  very  justly  adds)  "  that  such  a  mode  of  reasoning  elevates 
the  familiar  forms  of  language,  and  the  intellectual  connexions  of  tenns, 
to  a  supremacy  over  facts ;  making  truth  depend  upon  whether  terms 
are  or  are  not  privative,  and  whether  we  say  that  bodies  fall  naUirally" 

The  propensity  to  assume  that  the  same  relations  obtain  between 
objects  themselves,  which  obtain  between  our  ideas  of  them,  is  here 
seen  in  the  extreme  stage  of  its  development.  For  the  mode  of  phi- 
losophizing, exemplified  in  the  foregoing  instances,  assumes  no  less 
than  that  the  proper  way  of  arriving  at  knowledge  of  nature,  is  to 
study  nature  herself  subjectively  ;  to  apply  our  observation  and  anal- 
ysis not  to  the  facts,  but  to  the  common  notions  entertained  of  those 
facts. 

Many  other  equally  striking  examples  may  be  given  of  the  tendency 
to  assume  that  things  which  for  the  convenience  of  common  life  are 
placed  in  different  classes,  must  differ  in  every  respect.  Of  this  nature 
was  the  universal  and  deeply-rooted  prejudice  of  antiquity  and  the  mid- 
dle ages,  that  celestial  and  ten^estrial  phenomena  must  be  essentially 
different,  and  could  in  no  manner  or  degree  depend  upon  the  same 
laws.  Of  the  same  kind,  also,  was  the  prejudice  against  which  Bacon 
contended,  that  nothing  produced  by  nature  could  be  successfully 
imitated  by  man:  "  Calorem  solis  et  ignis  toto  genere  differre ;  ne 
scilicet  homines  putent  se  per  opera  ignis,  aliquid  simile  iis  qua3  in 
Natura  fiunt,  educere  et  formare  posse  :"  and  again,  "  Compositionem 
tantum  opus  Hominis,  Mistionem  vero  opus,  solius  Naturee  esse  :  ne 
scilicet  homines  sperent  aliquam  ex  arte  Corporum  naturalium  genera- 
tionem  aut  transformationem."  *  The  grand  distinction  in  the  ancient 
philosophy,  between  natural  and  violent  motions,  though  not  without 
a  plausible  foundation  in  the  appearances  themselves,  was  doubtless 
greatly  recommended  to  adoption  by  its  conformity  to  this  prejudice. 

§  7.  From  the  fundamental  error  of  the  scientific  inquirers  of  anti- 
quity, we  p^ss,  by  a  natural  association,  to  a  scarcely  less  fundamental 
one  of  their  gi-eat  rival  and  successor,  Bacon.  It  has  excited  the 
surprise  of  philosophers  that  the  detailed  system  of  inductive  logic, 
which  this  extraordinary  man  labored  to  construct,  has  been  turned  to 
so  little  direct  use  by  subsequent  inquirers,  having  neither  continued, 
except  in  a  few  of  its  generalities,  to  be  recognized  as  a  theory,  nor 
having  conducted  in  practice  to  any  great  scientific  results.  But  this, 
though  not  unfrequently  remarked,  has  scarcely  received  any  plausible 
explanation ;  and  some,  indeed,  have  prefeiTed  to  assert  that  all  rules 
of  induction  are  useless,  rather  than  suppose  that  Bacon's  rules  are 
gi-ounded  upon  an  insufficient  analysis  of  the  inductive  process.  Such, 
however,  will  be  seen  to  be  the  fact,  as  soon  as  it  is  considered,  that 

*  Nomm  Organum,  Aph.  75. 


FALLACIES    OF    SIMPLE    INSPECTION.  409 

Bacon  entirely  overlooked  Plurality  of  Causes.  All  his  rules  tacitly 
imply  the  assumption,  so  contrary  to  all  we  now  know  of  natui'e,  that 
a  phenomenon  cannot  have  more  tlian  one  cause. 

When  Bacon  is  inquiring  into  what  he  terms  the  forma  calidi  aut 
frigidi,  gravis  aut  Ici'is,  sicci  aut  hunndi,  and  tlic  like,  he  never  lor  an 
instant  doubts  that  there  is  some  one  thing,  some  invariable  condition 
or  set  of  conditions,  wliich  is  present  in  all  cases  of  heat,  or  of  cold,  or 
of  whatever  other  phenomenon  he  is  considering ;  tiic  only  ditiiculty 
being  to  find  what  it  is  ;  which  accorduigly  he  tries  to  do  by  a  process 
of  elimination,  rejecting  or  excluding,  by  negative  instances,  whatever 
is  not  the  Jonna  or  cause,  in  order  to  arrive  at  what  is.  Jiut,  tliat  this 
forma  or  cause  is  one  thing,  and  that  it  is  the  same  in  all  hot  objects, 
he  has  no  more  doubt  of,  than  another  person  has  that  tliere  is  always 
some  cause  or  other.  In  the  present  state  of  knowledge  it  could  not 
be  necessary,  even  if  we  had  not  already  treated  so  fully  of  the  question, 
to  point  out  how  widely  this  supjiosition  is  at  variance  with  the  truth. 
It  is  particularly  unfortunate  for  Bacon  that,  falling  into  this  error,  he 
should  have  fixed  almost  exclusively  upon  a  class  of  inquiries  in  which 
it  was  particularly  fatal ;  namely,  incjuiries  into  the  causes  of  the 
sensible  qualities  of  objects.  For  his  assumption,  groundless  in  every 
case,  is  false  in  a  peculiar  degree  with  respect  to  those  sensible  quali- 
ties. In  regard  to  scarcely  any  of  them  has  it  been  found  possible  to 
trace  any  unity  of  cause,  any  set  of  conditions  invariably  accompanying 
the  quality.  The  conjunctions  of  such  qualities  with  one  another 
constitute  the  vai'iety  of  Kinds,  in  ^vhich,  as  already  remarked,  it  has 
not  been  found  possible  to  trace  any  law.  Bacon  was  seeking  for 
what  did  not  exist.  The  phenomenon  of  which  he  sought  for  the  one 
cause  has  oftenest  no  cause  at  all,  and  when  it  has,  depends  (as  far  as 
hitherto  ascertained)  upon  an  unassignable  variety  of  distinct  causes. 

And  upon  this  rock  every  one  must  split,  who,  like  Bacon,  repre- 
sents to  himself  as  the  first  and  fundamental  problem  of  science  to 
ascertain  what  is  the  cause  of  a  given  effect,  rather  than  what  are  the 
effects  of  a  given  cause.  It  was  shown,  in  an  early  stage  of  our  in- 
quiry into  the  nature  of  Induction,*  how  much  more  ample  are  the 
resources  wliich  science  commands  for  the  latter  than  for  the  former 
inquiry,  since  it  is  upon  the  latter  only  that  we  can  throw  any  direct 
light  by  means  of  experiment ;  the  power  of  artificially  producing  an 
effect,  implying  a  previous  knowledge  of  at  least  one  of  its  causes.  If 
we  discover  the  causes  of  effects,  it  is  generally  by  having  previously 
discovered  the  effects  of  causes :  the  greatest  skill  in  devising  crucial 
instances  for  the  former  purpose  may  only  end,  as  Bacon's  physical 
inquiries  did,  in  no  result  at  all.  Was  it  that  his  eagerness  to  acquire 
the  power  of  producing  for  man's  benefit  effects  of  practical  importance 
to  human  life,  rendering  him  impatient  of  pursuing  that  end  by  a  cir- 
cuitous route,  made  even  him,  the  champion  of  experiment,  prefer  the 
direct  mode,  though  one  of  mere  ob-servation,  to  the  indirect,  in  which 
alone  experiment  was  possible?  Or  had  even  Bacon  not  entirely 
cleared  his  mind  from  the  notion  of  the  ancients,  that  "  rerum  cognos- 
cere  cau.saa'"  was  the  sole  object  of  j)hilosophy,  and  that  to  inquire  into 
the  effects  of  things  belonged  to  servile  and  mechanical  arts? 

It  is  worth  remarking  that,  whiU;  the  only  efficient  mode  of  cultivating 

♦  Supra,  p.  221, 


470  FALLACIES. 

speculative  science  was  missed  from  an  undue  contempt  of  manual 
operations,  the  false  speculative  views  thus  engendered  gave  in  their 
turn  a  false  direction  to  such  practical  and  mechanical  aims  as  were 
still  suflered  to  exist.  The  assumption  universal  among  the  ancients, 
and  in  the  middle  ages,  that  there  were  principles  of  heat  and  cold, 
dryness  and  moisture,  &c.,  led  directly  to  a  belief  in  alchemy ;  in  a 
transmutation  of  substances,  a  change  fiom  one  Kind  into  another. 
"Why  should  it  not  be  possible  to  make  gold  1  Each  of  the  charac- 
teristic properties  of  gold  had  its  forma,  its  essence,  its  set  of  condi- 
tions, which  if  we  could  discover,  and  learn  how  to  realize,  we  could 
superinduce  that  particular  property  upon  any  other  substance,  upon 
wood,  or  iron,  or  hme,  or  clay.  If,  then,  we  could  effect  this  with 
respect  to  every  one  of  the  essential  properties  of  the  precious  metals, 
we  should  have  converted  the  other  substance  into  gold.  Nor  did  this, 
if  once  the  premisses  were  granted,  appear  to  transcend  the  real  pow- 
ers of  man.  For  daily  experience  showed  that  almost  every  one  of 
the  distinctive  sensible  properties  of  any  object,  its  consistence,  its 
color,  its  taste,  its  smell,  its  shape,  admitted  of  being  totally  changed 
by  fire,  or  water,  or  some  other  chemical  agent.  The  fonnce  of  all 
those  qualities  seeming,  therefore,  to  be  within  human  power  either  to 
produce  or  to  annihilate,  not  only  did  the  transmutation  of  substances 
appear  absti'actedly  possible,  but  the  employment  of  the  power,  at  oui* 
choice,  for  practical  ends,  seemed  by  no  means  hopeless. 

A  prejudice  universal  in  the  ancient  world,  and  from  which  even 
Bacon  was  so  far  fi-om  being  free,  that  it  pen'aded  and  vitiated  the 
whole  practical  part  of  his  system  of  logic,  may  with  good  reason  be 
ranked  high  in  the  order  of  Fallacies  of  which  we  are  now  ti-eating. 

§  8.  There  remains  one  a  priori  fallacy  or  natural  prejudice,  the 
most  deeply-rooted,  perhaps,  of  all  which  we  have  enumei-ated  :  one 
which  not  only  reigned  supreme  in  the  ancient  world,  but  still  possesses 
almost  undisputed  dominion  over  many  of  the  most  cultivated  minds  ; 
and  some  of  the  most  remarkable  of  the  numerous  instances  by  which 
I  shall  think  it  necessary  to  exemplify  it,  will  be  taken  from  the  writings 
of  recent  philosophers.  This  is,  that  the  conditions  of  a  phenomenon 
must,  or  at  least  probably  wnll,  resemble  the  phenomenon  itself. 

Conformably  to  what  we  have  before  remarked  to  be  of  frequent 
occurrence,  this  fallacy  might  without  much  impropriety  have  been 
placed  in  a  different  class,  among  Fallacies  of  Generalization :  for 
experience  doe-s  afford  a  certain  degi'ee  of  countenance  to  the  assump- 
tion. The  cause  does,  in  very  many  cases,  resemble  its  effect ;  like 
produces  like.  Many  phenomena  have  a  direct  tendency  to  pei-jietuate 
their  own  existence,  or  to  give  rise  to  other  phenomena  similar  to  them- 
selves. Not  to  mention  forms  actually  moulded  upon  one  another,  as 
impressions  on  wax  and  the  like,  in  which  the  closest  resemblance 
between  the  effect  and  its  cause  is  the  very  law  of  the  phenomenon  ; 
all  motion  tends  to  continue  itself,  with  its  own  velocity,  and  in  its  own 
original  direction ;  and  the  motion  of  one  body  tends  to  set  others  in 
motion,  which  is  indeed  the  most  common  of  the  modes  in  which  the 
motions  of  bodies  originate.  We  need  scarcely  refer  to  contagion, 
fermentation,  and  the  like  ;  or  to  the  production  of  effects  by  the 
growth  or  expansion  of  a  germ  or  i-udiraent  resembling  on  a  smaller 
scale  the  completed  phenomenon— as  in  the  growth  of  a  plant  or  animal 


FALLACIES    OF    SIMPLE    INSPECTION.  471 

from  an  embryo,  that  eml)ryo  itself  deriving  its  origin  from  ant)lhor 
plant  or  animal  of  the  same  kind.  Again,  the  thoughts,  or  reminis- 
cences, which  are  effects  of  our  past  sensations,  resemble  those  seuBa- 
tions ;  feelings  produce  similar  Ibelings  by  way  of  sjnnpathy  ;  acts 
produce  similai  acts  by  invohuitary  or  voluntary  imitation.  With  so 
many  appearances  in  its  favor,  no  wonder  if  a  presumption  naturally 
giew  up  in  men's  minds,  that  causes  must  ncccssurdi/  resemble  their 
eH'ects,  and  that  like  could  only  be  produced  by  like. 

This  principle  of  fallacy  has  usually  presided  over  the  fantastical 
attempts  to  intluence  the  course  of  nature  by  conjectural  means,  the 
choice  of  which  was  not  directed  by  pievioits  obser\'ation  and  experi- 
ment. The  guess  almost  always  fixed  upon  some  means  which  pos- 
sessed features  of  real  or  apj)arent  resemblance  to  the  end  in  view. 
If  a  charm  was  wanted,  as  by  Ovid's  Medea,  to  prolong  life,  all  long- 
lived  animals,  or  what  were  esteemed  such,  were  collected  and  brewed 
into  a  broth  : — 

nee  defuit  illic 

Squamea  Cinyphii  tenuis  membrana  chclydri 

Vivacisque  jecur  cerv'i :  quibps  insuper  adiiit 

Ora  capuique  novem  cornicis  sajcula  passaj. 

A  similar  notion  was  eml)odied  in  the  celebrated  medical  theory 
called  the  "  Doctrine  of  Signatures,"  "  which  is  no  less,"  says  Dr. 
Paris,*  "  than  a  belief  that  every  natural  subtance  which  possesses 
any  medicinal  virtue,  indicates  by  an  obvious  and  well-marked  ex- 
ternal character  the  disease  for  which  it  is  a  remedy,  or  the  object 
for  which  it  should  be  employed."  This  outward  character  was 
generally  some  feature  of  rcsomblanco,  real  or  fantastical,  cither  to 
the  effect  it  was  supposed  t(j  produce,  or  to  the  phenomenon  over 
which  its  powqr  was  thought  to  be  exercised.  "  Thus  the  lungs 
of  a  fox  must  be  a  specific  for  asthma,  because  that  animal  is  re- 
markable for  its  strong  powers  of  resjiiration.  Turmeric  ha§  a 
briUiant  yellow  color,  which  indicates  that  it  has  the  power  of  curing 
the  jaundice  ;  for  the  same  reason  poppies  must  relieve  diseases  of  the 
head  ;  Agaricus  those  of  tlui  bladder ;  Cassia  Jistvfa  the  affections  of 
the  intestines,  and  Aristolochia  the  disorders  of  the  uterus:  the  polish- 
ed surface  and  stony  hardness  which  so  eminently  chiiracterize  the 
seeds  of  the  Llthospermum  ofliicinale  (common  gi'omwell)  were  deemed 
a  certain  indication  of  their  efficacy  in  calculous  and  gravelly  dis- 
orders :  for  a  similar  reason,  the  roots  of  the  Saxifraga  giamilata 
(white  saxifrage)  gained  reputation  in  the  cure  of  the  same  disease; 
and  the  Euphrasia  (eye-bright)  acquired  fame,  as  an  application  in 
complaints  of  the  eye,  because  it  exhibits  a  black  si)ot  in  its  corolla 
resembling  the  pupil.  The  blood-stone,  the  Heliotropium  of  the  an- 
cients, from  the  occasional  small  specks  or  points  of  a  blood-red  color 
exhibited  on  its  green  surface,  is  even  at  this  day  employed  in  many 
parts  of  England  and  Scotland,  to  stop  a  bleeding  from  the  nose;  and 
nettle  tea  continues  a  popular  remedy  for  the  cure  of  Urticaria.  It  is 
also  asserted  that  some  substances  bear  the  si  gnat  u  res  of  tlio  humors, 
as  the  petals  of  the  red  rose  that  of  the  blood,  and  the  roots  of  rhubarb 
and  the  flowers  of  saffron  that  of  the  bile." 

The  early  speculations  respecting  the  chemical  composition  of  bodies 
were  rendei-ed  abortive  by  no  circumstance  more,  than  by  their  inva- 

•  Pharmacologia,  ut  supra,  pp.  300-7. 


472  FALLACIES. 

riably  taking  for  granted  that  the  properties  of  the  elements  must  re- 
semble those  of  the  compounds  which  were  formed  from  them. 

To  descend  to  more  modern  instances  ;  it  was  long  thought  and  was 
stoutly  maintained  by  the  Cartesians  and  even  by  Leibnitz  against  the 
Newtonian  philosophy,  (nor  did  Newton  himself,  as  we  have  seen, 
contest  the  assumption,  but  eluded  it  by  an  arbitrary  hypothesis,)  that 
nothing  (of  a  physical  nature  at  least)  could  account  for  motion,  except 
previous  motion  ;  the  impulse  or  impact  of  some  other  body.  It  was 
very  long  before  the  scientific  world  could  prevail  upon  itself  to  admit 
attraction  and  repulsion  [I.e.  spontaneous  tendencies  of  particles  to  ap- 
proach or  recede  from  one  another)  as  ultimate  laws,  no  more  requiring 
to  be  accounted  for  than  impulse  itself,  if  indeed  the  latter  were  not, 
in  truth,  resolvable  into  the  former.  From  this  same  source  arose  the 
innumerable  hypotheses  to  explain  those  classes  of  motions  which  ap- 
peared more  mysterious  than  others  because  there  was  no  obvious 
mode  of  attributing  them  to  impulse,  as  for  example  the  voluntary  mo- 
tions of  the  human  body.  Such  were  the  interminable  systems  of 
vibrations  propagated  along  the  nerves,  or  animal  spirits  rushing  up 
and  down  between  the  muscles  and  the  brain  :  which,  if  the  facts 
could  have  been  proved,  would  710  doubt  have  been  an  important  ad- 
dition to  our  knowledge  of  physiological  laws  ;  but  the  mere  invention, 
or  arbitrary  supposition  of  them,  could  not  unless  by  the  strongest  de- 
lusion be  supposed  to  render  the  phenomena  of  animal  life  more  com- 
prehensible or  less  mysterious.  Nothing,  however,  seemed  satisfacto- 
ry, but  to  make  out  that  motion  was  caused  by  motion ;  by  something 
like  itself.  If  it  was  not  one  kind  of  motion  it  must  be  another.  In 
like  manner  it  was  supposed  that  the  physical  qualities  of  objects 
must  arise  from  some  similar  quality,  or  perhaps  only  some  quality 
bearing  the  same  name,  in  the  particles  or  atoms  of  which  the  objects 
were  composed  ;  that  a  sharp  taste,  for  example,  must  arise  from  shai-p 
particles.  And  reversing  the  inference,  the  effects  produced  by  a 
phenomenon  must,  it  was  supposed,  resemble  in  their  physical  attri- 
butes the  phenomenon  itself.  The  influences  of  the  planets  were  sup- 
posed to  be  analogous  to  their  visible  peculiarities :  Mars,  being  of  a 
red  color,  portended  fire  and  slaughter ;   and  the  like. 

Passing  from  physics  to  metaphysics,  we  may  notice  among  the  most 
remarkable  fruits  of  this  a  priori  fallacy,  two  closely  analogous  theories, 
employed  in  ancient  and  in  modern  times  to  bridge  over  the  chasm 
between  the  world  of  mind  and  that  of  matter:  the  species  sensihiles  of 
the  Epicureans,  and  the  modern  doctrine  of  perception  by  means  of 
ideas.  These  theories  are  indeed,  probably,  indebted  for  their  exist- 
ence not  solely  to  the  fallacy  in  question,  but  to  that  fallacy  combined 
with  another  natural  prejudice  already  adverted  to,  that  a  thing  cannot 
act  where  it  is  not.  In  both  doctrines  it  is  assumed  that  the  phenom- 
enon which  takes  place  in  us  when  we  see  or  touch  an  object,  and 
which  we  regard  as  an  effect  of  that  object,  or  rather  of  its  presence  to 
our  organs,  must  of  necessity  resemble  very  closely  the  outward  object 
itself  To  fulfill  this  condition,  the  Epicureans  supposed  that  objects 
were  constantly  projecting  in  all  directions  impalpable  images  of  them- 
selves, which  entered  at  the  eyes  and  penetrated  to  the  mind  :  while 
modem  philosophers,  though  they  rejected  this  hypothesis,  agi'eed  in 
deeming  it  necessary  to  suppose  that  not  the  object  itself,  but  a  mental 
image  or  representation  of  it,  was  the  direct  object  of  perception.    Dr. 


FALLACIES    OF    SIMPLE    IN3PECTI0X.  473 

Reid  had  to  employ  a  world  of  argument  and  illustration  to  faniiliarizo 
pieoplo  with  tlio  truth,  that  the  soiiisations  or  impressions  on  our  minds 
need  not  neccssaiily  be  copies  of,  or  have  any  reseuiblance  to,  the 
causes  wliich  produce  them;  in  opposition  to  the  iiutural  pn-judice 
which  led  men  to  assimihite  tiie  action  of  bodies  upon  our  senses,  and 
through  them  upon  our  minds,  to  the  transfer  of  a  given  form  from  one 
object  to  another  by  actual  moulding.  The  works  of  Ur,  Kei<l  are 
even  now  the  most  effectual  course  of  s^udy  for  detaching  the  mind 
fi-ora  the.  prejudice  of  which  this  was  an  example.  And  the  value  of 
the  service  wliich  he  thus  rendered  to  popular  [)hilosophy,  is  not  much 
diminislnjd  although  we  may  hold,  with  Brown,  that  he  went  too  for 
in  imputing  the  "  ideal  theory"  as  an  actual  tenet,  to  the  generality  of 
the  philosophers  who  preceded  him,  and  especially  to  Locke  and 
Hume  :  for  if  they  did  not  themselves  consciously  fall  into  the  error, 
unquestionably  they  often  led  their  readers  into  it. 

The  prejudice,  that  the  conditions  of  a  phenomenon  must  resemble 
the  phenomenon,  is  occasionally  exaggerated,  at  least  verbally,  into  a 
still  more  palpable  absurdity ;  the  conditions  of  the  thing  are  sj)oken 
of  as  if  they  ivere  the  very  thing  itself.  In  Bacon's  model-incjuiry, 
which  occupies  so  gi'eat  a  space  in  the  Novum  Organum,  the  hiquisitio 
informam  calidi,  the  conclusion  which  he  favors  is  that  heat  is  a  kind 
of  motion;  meaning  of  course  not  the  feeling  of  heat,  but  the  conditions 
of  the  feeling ;  meaning,  therefore,  only,  that  wherever  there  is  heat, 
there  must  first  be  a  particular  kind  of  motion  ;  but  he  makes  no  chs- 
tinction  in  his  language  between  these  two  ideas,  expressing  himself  as 
if  heat,  and  the  conditions  of  heat,  were  one  and  the  same  thing.  So 
Darwin,  in  the  beginning  of  his  7.oonomia,  says,  "  The  word  idea  has 
various  meanings  in  the  writers  of  metaphysics  :  it  is  here  used  simply 
for  those  notions  of  external  things  which  our  organs  of  sense  bring  us 
acquainted  with  originally"  (thus  far  the  proposition,  though  vague,  is 
unexceptionable  in  meaning),  "  and  is  defined  a  contractiim,  a  motion, 
or  configuration,  of  the  fibres  which  constitute  the  immediate  organ  of 
sense."  Om-  notions,  a  configuration  of  the  fibres !  What  kind  of 
philosopher  must  he  be  who  thinks  that  a  phenomenon  is  defined  to  he 
the  condition  on  which  he  su])poses  it  to  de{)end  \  Accordingly  he 
says  soon  after,  rtot  that  our  idt;as  are  caused  by,  or  consequent  uj\on, 
certain  organic  phenomena,  but  "  our  ideas  are  animal  motions  of  the 
organs  of  sense."  And  this  confusion  nms  through  the  four  volumes  of 
the  Zoonomia ;  the  reader  never  knows  whether  the  writer  is  speaking 
of  the  effect,  or  of  its  supposed  cause;  of  the  idea,  a  state  of  mental 
consciousness,  or  of  the  state  of  the  nerves  and  brain,  which  he  consid- 
ers it  to  presuppose. 

I  have  given  a  variety  of  instances  in  which  the  natural  ])rijudice, 
that  causes  and  their  eff*ects  must  resemble  one  another,  has  ojn-rated 
in  practice  so  as  to  give  rise  to  grievous  errors.  I  shall  now  go  further, 
and  produce  from  the  WTitings,  even  of  recent  philosophers,  instances 
in  which  the  prejudice  itseli"  is  laid  down  as  an  established  princijde. 
M.  Victor  Cousin,  in  the  last  of  his  very  remarkable  lectures  on  Locke 
(which  as  a  resume  of  the  objections  of  the  opj)ositc  school  to  that  yreat 
man's  doctrines,  is  a  work  of  eminent  merit),  enunciates  this  maxim  in 
the  following  unqualified  terms  :  "  Tout  ce  qui  est  vrai  de  reffl't  est 
vrai  de  la  cause."  A  doctiine  to  which,  unless  m  some  peculiar  and 
technical  meaning  of  the  words  cause  and  effect,  it  is  not  to  bo  ima- 
30 


474  FALLACIES. 

ginpd  that  any  person  would  literally  adhere :  hut  he  who  could  so 
write  must  he  far  enough  from  seeing,  that  the  very  reverse  might  be 
the  fact ;  that  there  is  nothing  impossible  in  the  supposition  that  no  one 
property  which  is  true  of  the  effect  might  be  true  of  the  cause.  AVithout 
going  quite  so  far  in  point  of  expression,  Coleridge,  in  his  Biographia 
Literaria*  affinns  as  an  "  evident  truth,"  that  "  the  law  of  causality 
holds  only  between  homogeneous  things,  i.  e.,  things  having  some 
common  property,"  and  therefore,  "  cannot  extend  from  one  world 
into  another,  its  opposite  :"  hence,  as  mind  and  matter  have  no  com- 
mon property,  mind  cannot  act  upon  matter  nor  matter  upon  mind. 
Wliat  is  this  but  the  a  priori  fallacy  of  which  we  are  speaking?  The 
doctiine,  like  many  others  of  Coleridge,  is  taken  from  Spinosa,  in  the 
first  book  of  whose  Ethica  [De  Deo)  it  stands  as  the  Third  Proposi- 
tion :  "  Q,u9e  res  nihil  commune  inter  se  habent,  earum  una  alterius 
causa  esse  non  potest,"  and  is  there  proved  from  two  so-called  axioms, 
equally  gi'atuitous  with  itself;  but  Spinosa,  ever  systematically  con- 
sistent, pvu'sued  the  doctrine  to  its  inevitable  consequence,  the  materi- 
ality of  God. 

The  same  conception  of  impossibility  led  the  ingenious  and  subtle 
mind  of  Leibnitz  to  his  celebrated  doctrine  of  a  preestablished  har- 
mony. He,  too,  thought  that  mind  could  not  act  upon  matter,  nor 
especially  matter  upon  mind,  and  that  the  two,  therefore,  must  have 
been  arranged  by  their  Maker  like  two  clocks,  which,  though  uncon- 
nected with  one  another,  strike  simultaneously,  and  always  point  to 
the  same  hour.  Malebranche's  equally  famous  theory  of  Occasional 
Causes  was  a  further  refinement  upon  this  conception  :  instead  of  sup- 
posing the  clocks  originally  arranged  to  strike  together,  he  held  that 
when  the  one  strikes,  God  interposes,  and  makes  the  other  sti-ike  in 
correspondence  with  it. 

Descartes,  in  like  manner,  whose  works  are  a  rich  mine  of  almost 
every  description  of  a  priori  fallacy,  says  that  the  Efficient  Cause  must 
at  least  have  all  the  perfections  of  the  effect,  and  for  this  singular 
reason:  "Si  enim  ponamus  aliquid  in  idea  reperiri  quod  non  fiierit  in 
ejus  caus§.,  hoc  igitur  habet  a  nihilo;"  of  which  it  is  scarcely  a  parody 
to  say,  that  if  there  be  pepper  in  the  soup  there  must  be  pepper  in  the 
cook  who  made  it,  since  otherwise  the  pepper  would  be  without  a 
cause.  A  similar  fallacy  is  committed  by  Cicero  in  his  second  book 
De  Finihus,  where,  speaking  in  his  own  pei'son  against  the  Epicureans, 
he  charges  them  -with  inconsistency  in  saying  that  the  pleasures  of  the 
mind  had  their  origin  from  those  of  the  body,  and  yet  that  the  former 
were  more  valuable,  as  if  the  effect  could  surpass  the  cause.  "  Animi 
voluptas  oritur  propter  voluptateni  corporis,  et  major  est  animi  voluptas 
quam  corporis?  ita  fit  ut  gratulator  lagtior  sit  quam  is,  cui  gratulatur." 
Even  that,  surely,  is  no  absolute  impossibility :  a  man's  good  fortune 
has  been  known  to  give  more  pleasure  to  others  than  it  gave  to  the 
man  himself 

Descartes,  with  no  less  readiness,  applies  the  same  principle  the 
converse  way,  and  infers  the  nature  of  the  effects  from  the  assumption 
that  they  must,  in  this  or  that  property,  or  in  all  their  properties, 
resemble  their  cause.  To  this  class  belong  his  speculations,  and  those 
of  so  many  others  after  him,  tending  to  infer  the  order  of  the  universe, 

*  Vol.  i.,  chap.  8. 


FALLACIES  OF  OBSERVATION.  475 

not  from  observation,  but  from  ibo  notion  we  think  oursolvos  alilo  to 
form  of  the  qiialiti(>s  of  the  G()ilhea<l.  This  sort  of  infi'rence  was 
probal)ly  never  eairied  to  a  i^reater  length  than  it  was  in  one  particular 
instance  by  Descartes,  when,  as  a  proof  of  one  of  his  physical  princi- 
ples, that  the  quantity  of  motion  in  the  universe  is  invariable,  he  had 
recourse  to  the  immutability  of  the  Divine  Nature.  Optimism,  in  all 
its  shapes,  is  an  examjile  of  the  same  sp(>cii's  of  fallacy:  (rod  is  per- 
fect, therefore  what  we  think  perfection  nmst  obtain  in  nature.  Even 
in  our  own  time  men  do  not  cease  to  oppose  the  divine  benevolence  to 
the  evidence  of  physical  facts,  to  the  principle  of  population  for  ex- 
ample. As  if  the  subjection  of  mankind  to  physical  sutt'erinir,  often 
entirely  unavoidable,  and,  when  capabli'  of  being  warded  oil',  capable 
only  by  means  of  forethought  and  self-restraint,  were  more  dithcult  to 
reconcile  with  the  ways  of  Providence  in  some  one  of  its  particular 
manifestations  than  in  so  many  others.  As  if,  in  so  far  as  j)ain  is  an 
imjierfection,  any  one  day's  experience  were  not  sufficient  to  con- 
vince the  devoutest  mind  that  imperfection,  in  that  sense,  in  the  work, 
entered  into  the  plans  of  the  Creator,  and  that  no  attribute  really 
incompatible  with  it  can  be  correctly  ascribed  to  him. 

Although  several  other  varieties  of  a  priori  fallacy  might  probably 
be  added  to  those  here  specified,  these  are  all  against  which  it  seems 
necessary  to  give  any  special  caution.  Our  object  is  to  open,  without 
attempting  or  aflecting  to  exhaust  the  subject.  Having  illustrated, 
therefore,  this  first  class  of  Fallacies  at  sufficient  length,  I  shall  pro- 
ceed to  the  second. 


CHAPTER  IV. 

FALLACIES  OF  OBSERVATION. 


§  1.  From  the  fallacies  which  are  properly  Prejudices,  or  presump- 
tions antecedent  to,  and  superseding,  proof,  we  pass  to  those  which  lie 
in  the  incorrect  performance  of  the  proving  process.  And  as  Proof, 
in  its  widest  extent,  embraces  oni^  or  more  or  all  of  three  processes, 
Observation,  Generalization,  and  Deduction;  we  shall  consider  in  their 
order  the  errors  capable  of  being  committed  in  these  three  operations. 
And.  first,  of  the  first  mentioned. 

A  fallacy  of  misobserv'ation  may  be  either  negative  or  positive ; 
either  Non-observation  or  Mal-obsei-vation.  It  is  non-observation, 
when  all  the  error  consists  in  overlooking,  or  neglecting,  facts  or  j)ar- 
ticulars  which  ought  to  have  been  observed.  It  is  mal-observation, 
when  something  is  not  simply  unseen,  but  seen  wrong;  when  the  fact 
or  phenomenon,  instead  of  being  recognized  for  what  it  is  in  reality, 
is  mistaken  for  something  else. 

§  2.  Non-observation  may  either  takc!  j)laco  by  overlooking  in.stances, 
or  by  overlooking  some  of  the  circumstances  of  a  given  instance.  If 
we  were  to  conclude  that  a  fiirlune-feller  was  a  true  propliet,  from  not 
adverting  to  the  cases  in  which  his  jnedictions  had  been  falsified  by 
the  event,  this  would  be  non-observation  of  instances :  but  if  we  ov^r- 


476  FALLACIES. 

looked  or  i-emainetl  ignorant  of  the  fact  that  in  cases  where  the  pre- 
dictions had  come  true,  he  had  been  in  collusion  with  some  one  who 
had  given  him  the  information  on  which  they  were  gi'ounded,  this 
would  be  non-obsei-vation  of  circumstances. 

The  former  case,  in  so  far  as  the  act  of  induction  from  insufficient 
evidence  is  concerned,  does  not  fall  under  this  second  class  of  Fallacies, 
but  under  the  third.  Fallacies  of  Generalization.  In  every  such  case, 
however,  there  are  two  defects  or  errors  instead  of  one :  there  is  the 
eiTor  of  treating  the  insufficient  evidence  as  if  it  were  sufficient,  which 
is  a  Fallacy  of  the  third  class ;  and  there  is  the  insufficiency  itself;  the 
not  having  better  evidence ;  which,  when  such  evidence,  or  m  other 
words,  when  other  instances,  were  to  be  had,  is  Non-observation  ;  and 
the  erroneous  inference,  so  far  as  it  is  to  be  attributed  to  this  cause,  is 
a  Fallacy  of  the  second  class. 

It  belongs  not  to  our  puiiiose  to  treat  of  non-observation  as  arising 
from  casual  inattention,  from  general  slovenliness  of  mental  habits,  want 
of  due  practice  in  the  use  of  the  obsei'ving  faculties,  or  insufficient  in- 
terest in  tlie  subject.  The  question  pertinent  to  logic  is — Grranting 
the  want  of  complete  competency  in  the  obsei-ver,  on  what  points 
is  that  insufficiency  on  his  paat  likely  to  lead  him  wrong  1  or  rather, 
what  sorts  of  instances,  or  of  circumstances  in  any  given  instance, 
are  most  likely  to  escape  the  notice  of  observers  generally ;  of  mankind 
at  large  1 

§  3.  First,  then,  it  is  evident  that  when  the  instances  on  one  side  of 
a  question  are  more  likely  to  be  remembered  and  recorded  than  those 
on  the  other ;  especially  if  there  be  any  strong  motive  to  preserve  the 
memory  of  the  hrst  but  not  of  the  latter ;  these  last  are  likely  to  be 
overlooked,  and  escape  the  observation  of  the  mass  of  mankind.  This 
is  the  recognized  explanation  of  the  credit  given,  in  spite  of  reason 
and  evidence,  to  many  classes  of  imjjosters ;  to  quack  doctors,  and  for- 
tune-tellers in  all  ages  ;  to  the  "  cimning  man"  of  modem  times,  and 
the  oracles  of  old.  Few  have  considered  the  extent  to  which  this 
fallacy  operates  in  practice,  even  in  the  teeth  of  the  most  palpable 
negative  evidence.  A  striking  example  of  it  is  the  faith  which  the 
uneducated  portion  of  the  agricultural  classes,  in  this  and  other  coun- 
tries, continue  to  repose  in  the  prophecies  as  to  weather  supplied  by 
almanac  makers :  although  every  season  affords  to  them  numerous 
cases  of  completely  erroneous  prediction ;  but  as  eveiy  season  also 
furnishes  some  cases  in  which  the  prediction  is  verified,  this  is  enough 
to  keep  up  the  credit  of  the  prophet,  with  people  who  do  not  reflect  on 
the  number  of  instances  requisite  for  what  we  have  called,  in  our  in- 
ductive temiinology,  the  Elimination  of  Chance  ;  since  a  certain  num- 
ber of  casual  coincidences  not  only  may  but  will  happen,  between  any 
two  unconnected  events. 

Coleridge,  in  one  of  the  essays  in  the  Friend,  has  very  happily 
illustrated  the  matter  we  are  now  considering,  in  discussing  the  origin 
of  a  proverb,  "  which,  differently  worded,  is  to  be  found  in  all  the 
languages  of  Europe,"  viz.,  "  Fortune  favors  fools."  This  proverb, 
says  he,  "  admits  of  various  explanations.  It  may  arise  from  pity,  and 
the  soothing  persuasion  that  Providence  is  eminently  watchful  over  the 
helpless,  and  extends  an  especial  care  to  those  who  are  not  capable  of 
caring  for  themselves.     So  used,  it  breathes  the  same  feeling  as  '  God 


FALLACIES    OF    OBSERVATION.  477 

-tempers  the  wind  to  the  shorn  lamh,'  or  the  more  sportive  ailage,  that 
*  the  fairies  take  care  of  chihlren  and  tij)sy  folk.'  "  So  far,  the  notion 
(■partakes  of  the  character  of  a  falhicy  of  Gonei-alization.  But  he  con- 
tinues, "  The  persuasion  itself,  in  addition  to  the  general  rchgious 
feeling  of  mankind,  and  the  scarcely  less  general  love  of  tlie  marvelous, 
may  be  accounted  for  from  our  tendency  to  exaggerate  all  effects,  that 
seem  disproportionate  to  their  visible  cause,  and  all  circumstances  that 
are  in  any  way  strongly  contrasted  with  our  notions  of  the  persons 
under  them."  Omitting  some  further  explanations  which  would  refer 
the  eiTor  to  mal-observation,  or  to  the  other  species  of  non-observation 
(that  of  circumstances),  I  take  up  the  «iin)tation  further  on.  "  Unfore- 
seen coincidences  may  have  greatly  helped  a  man,  yet  if  they  have 
done  for  him  only  what  jiossibly  fi-om  his  own  abilities  he  might  have 
effected  for  himself,  his  good  work  will  excite  less  attention,  and  the 
instances  be  less  remembered.  That  clever  men  should  attain  their 
objects  seems  natural,  and  we  neglect  the  circumstances  that  perhaps 
produced  that  success  of  themselves,  without  the  intervention  of  skill 
or  foresight ;  but  we  dwell  on  the  fact  and  remember  it,  as  something 
strange,  when  the  same  happens  to  a  weak  or  ignorant  man.  So  too, 
tliough  the  latter  should  fail  in  his  undertakings  from  concurrences 
that  might  have  happened  to  the  wisest  man,  yet  his  failure  being  no 
more  than  might  have  lieen  expected  and  accounted  f':>r  frt)m  his  folly, 
it  lays  no  hold  on  our  attention,  but  fleets  away  among  the  other  undis- 
tinguished waves  in  which  the  stream  of  ordinaiy  life  murmurs  by  us, 
and  is  forgotten.  Had  it  been  as  true  as  it  was  notoriously  false,  that 
those  all-embracing  discoveiies,  which  have  shed  a  dawn  oi science  on' 
the  art  of  chemistiy,  and  give  no  obscure  promise  of  some  one  gi-eat 
constitutive  law,  in  the  light  of  which  dwell  dominion,  and  the  power 
of  prophecy;  if  these  discoveries,  instead  of'having  been,  as  they  really 
were,  preconcerted  by  meditation,  and  evolved  out  of  his  own  intellect, 
had  occurred  by  a  set  of  lucky  accidents  to  the  illusti-ious  father  and 
founder  of  philosophic  alchemy ;  if  they  had  presented  themselves  to 
Professor  Davy  exclusively  in  consequence  of  his  luck  in  possessing  a 
particular  galvanic  battery;  if  this  battery,  as  far  as  Davy  was,  con- 
cerned, had  itself  been  an  accident,  and  not  (as  in  point  of  fact  it  was) 
desired  and  obtained  by  him  fur  the  purpose  f)f  insuring  the  testimony 
of  experience  to  his  prhiciples,  and  in  order  to  bind  down  material 
nature  under  the  inquisition  of  reason,  and  force  from  her,  as  by  tor- 
ture, unequivocal  answers  to  ^;re/>arfrZ  and  preconceived  questions, — 
yet  still  they  would  not  have  been  talked  of  or  described  as  instances 
of  hick,  but  as  the  natm-al  results  of  his  admitted  genius  and  known 
skill.  But  should  an  accident  have  disci ose<l' similar  discoveries  to  a 
mechanic  at  Binningham  or  Sheffield,  and  if  the  man  should  grow  rich 
in  consequence,  and  partly  by  the  envy  of  his  neighbors  and  partly 
with  good  reason,  be  considere<l  by  them  as  a  man  heloio  par  in  the 
general  powers  of  his  understanding;  then,  'O  what  a  lucky  fellow! 
AVell,  Fortune  docs  favor  fools — that's  for  certain! — It  is  always  so!' 
And  forthwith  the  exclaimer  relates  half  a  dozen  similar  instances. 
Thus  accumulating  the  one  sort  of  facts  and  never  collecting  the  other, 
we  do,  as  poets  in  their  diction,  and  quacks  of  all  denominations  do  in 
their  reasoning,  put  a  part  for  the  whole,  and  at  once  soothe  our  envy 
and  gratify  our  love  of  the  marvelous,  by  tho  sweeping  proverb, 
Fortune  favors  fools." 


478  FALLACIES. 

This  passage  very  happily  sets  forth  the  manner  in  which,  under  the 
loose  mode  of  induction  which  proceeds  jier  pnumerationeni  simplicem, 
not  seeking  for  instances  of  sucli  a  kind  as  to  be  decisive  of  the  ques- 
tion, but  generalizing  from  any  which  occur,  or  rather  which  are 
remembered,  opinions  grow  up  with  the  apparent  sanction  of  experi- 
ence, which  have  no  foundation  in  the  laws  of  nature  at  all.  "  Itaque 
recte  respondit  ille,"  (we  may  say  with  Bacon,*)  "qui  cum  suspensa 
tabula  in  templo  ei  monstraretur  eorum,  qui  vota  solverant,  quod 
naufragii  periculo  elapsi  sint,  atque  interrogando  premeretur,  anna 
tum  quidem  Deorum  numen  agnosceret,  quaesivit  denuo.  At  uhi  sunt 
illi  depicti  qui  post  vota  nuncupata  perieruntl  Eadem  ratio  est  fere 
omnis  superstitionis,  ut  in  Astrologicis,  in  Somniis,  Ominibus,  Neme- 
sibus,  et  hujusmodi ;  in  quibus,  homines  delectati  hujusmodi  vanitati- 
bus,  advertunt  eventus,  ubi  implentur ;  ast  ubi  fallunt,  licet  multo  fre- 
quentius,  tamen  negligunt,  et  praetereunt."  And  he  proceeds  to  say, 
that  independently  of  the  love  of  the  marvelous,  or  any  other  bias  in 
the  inclinations,  there  is  a  natural  tendency  in  the  intellect  itself  to  this 
kind  of  fallacy ;  since  the  mind  is  more  moved  by  affirmative  instances, 
altliough  negative  ones  are  of  most  use  in  philosophy :  "Is  tamen 
humano  intellectui  error  est  proprius  et  perpetuus,  ut  magis  moveatur 
et  excitetur  Affirmativis,  quam  Negativis ;  cum  rite  et  ordine  aequum 
se  utrique  praebere  debeat ;  quin  contra,  in  omni  Axiomate  vero  con- 
stituendo,  major  vis  est  instantiaj  negativee." 

But  the  greatest  of  all  causes  of  non-observation  is  a  preconceived 
opinion.  This  it  is  which,  in  all  ages,  has  made  the  whole  race  of 
mankind,  and  every  separate  section  of  it,  for  the  most  part  unobser- 
vant of  all  facts,  however  abundant,  even  v/hen  passing  under  their  own 
eyes,  which  are  contradictory  to  any  first  appearance,  or  any  received 
tenet.  It  is  worth  while  to  recall  occasionally  to  the  oblivious  memory 
of  mankind,  some  of  the  striking  instances  in  which  opinions  that  the 
simplest  experiment  would  have  shown  to  be  erroneous,  continued  to 
be  entertained  because  nobody  &ver  thought  of  trying  that  experiment. 
One  of  the  most  remarkable  of  these  was  exhibited  in  the  Copernican 
controversy.  The  opponents  of  Copernicus  argued  that  the  earth  did 
not  move,  because  if  it  did,  a  stone  let  fall  from  the  top  of  a  high  tower 
would  not  reach  the  gi'ound  at  the  foot  of  the  tower,  but  at  a  little  dis- 
tance from  it,  in  a  contrary  direction  to  the  earth's  course ;  in  the  same 
manner  (said  they)  as,  if  a  ball  is  let  drop  from  the  mast-head  while 
the  shijj  is  in  full  sail,  it  does  not  fall  exactly  at  the  foot  of  the  mast, 
but  nearer  to  the  stern  of  the  vessel.  The  Copernicans  would  hare 
silenced  these  objectors  at  once  if  they  had  tried  dropping  a  ball  from 
the  mast-head,  because  they  would  have  found  that  it  does  fall  exactly 
at  the  foot,  as  the  theory  requires:  but  no;  they  admitted  the  spurious 
fact,  and  struggled  vainly  to  make  out  a  difference  between  the  two 
cases.  "  The  ball  was  no  ^;ar^  of  the  ship — and  the  motion  forward 
was  not  natural,  either  to  the  ship  or  to  the  ball.  The  stone,  on  the 
other  hand,  let  fall  from  the  top  of  the  tower,  was  n.  part  of  the  earth; 
and  therefore,  the  diurnal  and  annual  revolutions  which  were  natural 
to  the  earth,  were  also  natural  to  the  stone ;  the  stone  would,  there- 
fore, retain  the  same  motion  with  the  tower,  and  strike  the  ground  pre- 
cisely at  the  bottom  of  it."t 

*  Nvo.  Org.,  Aph.  46.  t  Playfaie's  Dissertation,  sect.  4. 


FALLACIES    OF    OBSERVATION.  479 

Other  examples,  scarcely  less  striking,  are  recorded  by  Mr.  Wlicwell,* 
where  imaginary  laws  of  nature  have  continued  to  be  rcceivcMl  as  leal, 
merely  becauae  no  one  person  had  steadily  looked  at  facts  which  almost 
every  one  had  the  opportunity  of  obsei-\ing.  "  A  vague  and  loose 
mode  of  looking  at  facts  very  easily  observable,  left  men  for  a  long 
time  under  the  belief  that  a  body  ten  times  as  heavy  as  another  falls 
ten  times  as  fast ;  that  objects  immersed  in  water  are  always  magnified, 
without  regard  to  the  form  of  the  sui-face;  that  the  magnet  exerts  an 
irresistible  force;  that  crystal  is  always  found  associated  with  ice;  and 
the  like.  These  and  many  other  are  examples  how  blind  and  careless 
man  can  be,  even  in  observation  of  the  plainest  and  commonest  ap- 
pearances ;  and  they  show  us  tliat  the  mere  facidties  of  perception, 
although  constantly  exercised  upon  innumerable  objects,  may  long  fail 
in  leading  to  any  exact  knowledge." 

The  influence  of  a  preconceived  theory  is  well  exemplified  in  the 
superstitions  of  barbarians  respecting  the  virtues  of  medicaments,  and 
of  charms.  The  negroes,  among  whom  coral,  as  of  old  among  oui> 
selves,  is  worn  as  an  amulet,  affirm,  acccording  to  Dr.  Paris, t  that  its 
color  "  is  always  affected  by  the  state  of  health  of  the  wearer,  it  becom- 
ing paler  in  disease."  On  a  matter  open  to  universal  observation,  a 
general  proposition  which  has  not  the  smallest  vestige  of  truth,  is 
received  as  a  result  of  experience;  the  preconceived  opinion  prevent- 
ing all  observation  of  such  instances  as  do  not  accord  with  it. 

§  4.  For  illustration  of  the  first  species  of  non-observation,  that  of 
Instances,  what  has  now  been  stated  may  suffice.  But  there  may  also 
be  non- observation  of  some  material  circumstances,  in  instances  which 
have  not  been  altogether  overlooked — nay,  which  may  be  the  very 
instances  upon  which  the  whole  superstructure  of  a  theory  has  been 
founded.  As,  in  the  cases  hitherto  examined,  a  general  proposition 
was  too  rashly  adopted,  on  the  evidence  of  particulars,  true  indeed,  but 
insufficient  to  support  it ;  so  in  the  cases  to  which  we  now  turn,  the 
particulars  themselves  have  been  imperfectly  observed,  and  the  singu- 
lar propositions  upon  which  the  generalization  is  gi'ounded,  or  some  at 
least  of  those  singular  propositions  are  false. 

Such,  for  instance,  was  one  of  the  mistakes  committed  in  the  cele- 
brated phlogistic  theory ;  a  doctrine  which  accounted  for  combustion 
by  the  extrication  of  a  substance  supjjoscd  to  be  contained  in  all  com- 
bustible matter,  and  to  which  the  name  phlogiston  was  given.  Tlie 
hypothesis  accorded  tolerably  well  with  superficial  appearances  :  the 
ascent  of  flame  naturally  suggests  the  escape  of  a  substance  ;  and  the 
visible  residuum  of  ashes,  in  bulk  and  weight,  generally  falls  extremely 
short  of  the  combustible  material.  The  error  was,  non-observation  of 
an  important  portion  of  the  actual  residue,  namely,  the  gaseous  pro- 
ducts of  combustion.  When  these  were  at  last  noticed  and  brought 
into  account,  it  appeared  to  be  an  luiiversal  law,  that  all  substances 
gain  instead  of  losing  weight  by  undergoing  combustion  ;  and,  after 
the  usual  attempt  to  accommodate  the  old  theory  to  the  new  fiict  by 
means  of  an  arbitrary  hypothesis  (that  phlogiston  had  the  cpiality  of 
positive  levity  instead  of  gravity),  chemists  were  conducted  to  the  true 

*  Wheweli,'.-?  Phil  of  the  Inductive  Sciences,  ij.,  203. 
t  Pharmacologia,  p.  21 


480  FALLACIES. 

explanation,  namely  that  instead  of  a  substance  separated,  there  was 
on  the  contrary  a  substance  absorbed. 

Many  of  the  absurd  practices  which  have  been  deemed  to  possess 
medicinal  efficacy,  have  been  indebted  for  their  reputation  to  non- 
obsei"A'ance  of  some  accompanpng  circumstance  which  was  the  real 
ao-ent  in  the  cures  ascribed  to  them.  Thus,  of  the  sympathetic  powder 
of  Sir  Kenelm  Digby  :  "  Whenever  any  wound  had  been  inflicted, 
this  powder  was  applied  to  the  weapon  that  had  inflicted  it,  which 
was,  moreover,  covered  ■v\'ith  ointment,  and  dressed  two  or  three  times 
a  day.  The  wound  itself,  in  the  meantime,  was  directed  to  be  brought 
to"-ether,  and  carefiilly  bound  up  \\'ith  clean  linen  rags,  but  above  all, 
to  be  let  alone  for  seven  days,  at  the  end  of  which  period  the  bandages 
were  removed,  when  the  wound  was  generally  found  perfectly  united. 
The  tri^unph  of  the  cure  was  decreed  to  the  mysterious  agency  of  the 
sympathetic  powder  which  had  been  so  assiduously  applied  to  tlie 
weapon,  whereas  it  is  hardly  necessary  to  observe  that  the  promptness 
of  the  cure  depended  upon  the  total  exclusion  of  air  from  the  wound, 
and  upon  the  sanative  operations  of  nature  not  baring  received  any 
disturbance  from  the  officious  interference  of  art.  The  result,  beyond 
all  doubt,  furaished  the  first  hint  which  led  surgeons  to  the  improved 
practice  of  healing  wounds  by  what  is  technically  called  the  Jirst  inten- 
tion.'"* "  In  all  records,"  adds  Dr.  Paris,  "  of  extraordinary  cures 
performed  by  mysterious  agents,  there  is  a  great  desire  to  conceal  the 
remedies  and  other  em'ative  means  which  were  simultaneously  admin- 
istered with  them  :  thus  Oribasius  commends  in  high  terms  a  necklace 
of  Peeony  root  for  the  cure  of  epilepsy ;  but  we  le"ani  that  he  always 
took  care  to  accompany  its  use  with  copious  evacuations,  although  he 
assigns  to  them  no  share  of  credit  in  the  cure.  In  later  times  we  have 
a  good  specimen  of  this  species  of  deception,  presented  to  us  in  a  work 
on  Scrofula  by  INIr.  Morley,  written,  as  we  are  infonned,  for  the  sole 
purpose  of  restoring  the  much  injured  character  and  use  of  the  Ver- 
vain ;  in  which  the  author  directs  the  root  of  this  plant  to  be  tied  -vrith 
a  yard  of  white  satin  riband  around  the  neck,  where  it  is  to  remam 
imtil  the  patient  is  cured  ;  but  mark — during  this  inten-al  he  calls  to 
his  aid  the  most  active  medicines  in  the  materia  medica  !"t 

In  other  cases  the  cures  really  produced  by  rest,  regimen,  and 
amusement,  have  been  ascribed  to  the  medicinal,  or  occasionally  to 
the  supernatural,  means  which  were  put  in  requisition.  "  The  cele- 
brated John  Wesley,  while  he  commemorates  the  triumph  of  sulphur 
and  supplication  over  his  bodily  infirmity,  forgets  to  appreciate  the 
resuscitating  influence  of  foirr  months  repose  from  his  apostolic  labors  ; 
and  such  is  the  disposition  of  die  human  mind  to  place  confidence  in 
the  operation  of  mysterious  agents,  that  we  find  him  more  disposed  to 
attribute  his  cure  to  a  brown  paper  plaster  of  e^^  and  brimstone,  than 
to  Dr.  Fothergill's  salutaiy  prescription  of  country  air,  rest,  asses'  milk, 
and  horse  exercise. "f 

In  the  following  example,  the  circumstance  overlooked  was  of  a 
somewhat  diSerent  character.  "  Wlien  the  yellow  fever  raged  in 
America,  the  practitioners  trusted  exclusively  to  the  copious  use  of 
mercm-y ;  at  first  this  plan  was  deemed  so  universally  efficacious,  that, 
in  the  enthusiasm  of  the  moment,  it  was  triumphantly  proclaimed  that 

*  Pharmacologia,  pp.  23-4.  f  Ibid.,  p.  28.  t  Ibid.,  p.  C2. 


FALLACIES    OF    OBSERVATION.  481 

deatli  never  took  place  after  the  mercury  had  evinced  its  effect  upon 
the  system  :  all  this  was  very  true,  but  it  funiished  no  proof  of  t!ie 
efficaoy  of  that  metal,  since  the  disease  in  its  aggravated  form  was  so 
rapid  in  its  career,  that  it  swept  away  its  victims  long  before  the  sys- 
tem could  be  brought  under  mercurial  intluence,  while  in  its  milder 
shape  it  2>assed  off  etpuilly  well  without  any  assistance  from  art."* 

In  these  examples  the  circumstance  overlooked  was  cognizable  by 
the  senses.  In  other  cases,  it  is  one  the  knowledge  of  which  could 
only  be  an'ived  at  by  reasoning;  but  the  fallacy  may  still  be  classed 
untler  the  head  to  which,  for  want  of  a  more  appropriate  name,  we 
have  given  the  appellation  Fallacies  of  Non-observation.  It  is  not  the 
natui'e  of  the  faculties  which  ought  to  have  been  employed,  but  the  non- 
employment  of  them,  which  constitutes  this  natural  Order  of  Fallacies. 
"Wherever  the  error  is  negative,  not  positive ;  wherever  it  consists 
specially  in  overlooking,  in  being  ignorant  or  unmindful  of  some  fact 
which,  if  known  and  attended  to,  would  have  made  a  diilbrence  in  the 
conclusion  arrived  at ;  the  error  is  properly  placed  in  the  Class  which 
we  are  considering.  lu  this  Class,  there  is  not,  as  in  all  other  falla- 
cies there  is,  a  positive  mis-estimate  of  evidence  actually  had.  The 
conclusion  would  be  just,  if  the  portion  which  is  seen  of  the  case  were 
the  whole  of  it ;  but  there  is  another  portion  overlooked,  which  vi- 
tiates the  result. 

For  instance,  there  is  a  remarkable  doctrine  which  has  occasionally 
found  a  vent  in  the  public  speeches  of  unwise  legislators,  but  which 
only  in  one  instance  that  I  am  aware  of  has  received  the  sanction  of  a 
philosopher,  namely  M.  Victor  Cousin,  who,  in  his  preface  to  the  Gorgias 
of  Plato,  contending  that  punishment  must  have  some  other  and  higher 
justification  than  the  prevention  of  crime,  makes  use  of  this  argument 
— that  if  punishment  were  only  for  the  sake  of  example,  it  would  be 
indifferent  whether  we  punished  the  innocent  or  the  guilty,  since  the 
punishment,  considered  as  an  example,  is  equally  efficacious  in  either 
case.  Now  we  must,  in  order  to  go  along  with  M.  Cousin,  suppose, 
that  the  person  who  feels  himself  under  temptation,  observing  some- 
body punished,  concludes  himself  to  be  in  danger  of  being  punished 
likewise,  and  is  terrified  accordingly.  But  it  is  forgotten  that  if  the 
person  punished  is  supposed  to  be  innocent,  or  even  if  there  be  any 
doubt  of  his  guilt,  the  spectator  will  reflect  that  his  own  danger,  what- 
ever it  may  be,  is  not  contingent  upon  his  guiltiness,  but  threatens  him 
equally  if  he  remains  innocent,  and  how  therefore  is  he  deterred  from 
guilt  liy  the  apprehension  of  such  pimishmcnt  1  M.  Cousin  supposes 
that  men  will  be  dissuaded  from  guilt  by  whatever  renders  the  condi- 
tion of  the  guilty  more  perilous,  forgetting  that  the  condition  of  the 
innocent  (also  one  of  the  elements  in  the  calculation)  is,  in  the  case 
supposed,  made  perilous  in  precisely  an  equal  degree.  This  is  a  fal- 
lacy of  overlooking;  or  of  non-observation,  within  the  intent  of  our 
classification. 

Fallacies  of  this  description  are  the  great  stumbling-block  to  just 
views  in  political  economy.  The  economical  workings  of  society  allbrd 
innumerable  cases  in  which  the  effects  of  a  cause  consist  of  two  sets 
of  phenomena :  the  one  immediate,  concentrated,  obvious  to  vulgar 
eyes,  and  passing,  in  common  apprehension,  for  the  whole  effect ;  the 

♦  Pharmacologia,  pp.  61-C2. 

3P 


482  FALLACIES. 

Other  widely  cllffused,  or  lying  deeper  under  the  surface,  and  which  is 
exactly  contrary  to  the  former.  Take,  for  instance,  the  vulgar  notion, 
so  plausible  at  the  first  glance,  of  the  encouragement  given  to  industry 
hy  lavish  expenditure.  A,  who  spends  his  whole  income,  and  even 
his  capital,  in  expensive  living,  is  supposed  to  give  gi'eat  employment  to 
labor.  B,  who  lives  upon  a  small  portion,  and  invests  the  remainder  in 
the  funds,  is  thought  to  give  little  or  no  employment.  For  everybody 
sees  the  gains  which  are  made  by  A's  tradesmen,  servants,  and  others, 
while  his  money  is  spending.  B's  savings,  on  the  contrary,  pass  into  the 
hands  of  the  person  whose  stock  he  purchased,  who  with  it  pays  a  debt 
he  owed  to  some  banker,  who  lends  it  again  to  some  merchant  or  manu- 
facturer ;  and  the  capital,  being  laid  out  in  hiring  spinners  and  weavers, 
or  carriers  and  the  crews  of  merchant  vessels,  not  only  gives  immediate 
employment  to  as  much  industry  at  once  as  A  employs  during  the  whole 
of  his  career,  but  coming  back  with  increase  by  the  sale  of  the  goods 
which  have  been  manufactured  or  imported,  form  a  fund  for  the  em- 
ployment of  the  same  and  perhaps  a  greater  quantity  of  labor  in  per- 
petuity. But  the  careless  observer  does  not  see,  and  therefore  does 
not  consider,  what  becomes  of  B's  money ;  he  does  see  what  is  done 
with  A's  :  he  observes  the  amount  of  industry  which  A's  profusion 
feeds ;  he  observes  not  the  far  greater  quantity  which  it  prevents  from 
being  fed :  and  thence  the  prejvidice,  universal  to  the  time  of  Adam 
Smith,  and  even  yet  only  exploded  among  persons  more  than  com- 
monly instructed,  that  prodigality  encourages  industry,  and  parsimony 
is  a  discouragement  to  it. 

The  common  argument  against  free-trade  is  a  fallacy  of  the  same 
nature.  The  purchaser  of  British  silk  encourages  British  industry  ; 
the  purchaser  of  Lyons  silk  encourages  only  French ;  the  former  con- 
duct is  patriotism,  the  latter  ought  to  be  interdicted  by  law.  The 
circumstance  is  overlooked,  that  the  purchaser  of  any  foreign  com- 
modity of  necessity  causes,  directly  or  indirectly,  the  export  of  an 
equivalent  value  of  some  English  article  (beyond  what  would  other- 
wise be  exported),  either  to  the  same,  foreign  country  or  to  some 
other  :  which  fact,  although  from  the  complication  of  the  circumstances 
it  cannot  always  be  verified  by  specific  observation,  no  observation  can 
possibly  be  brought  to  contradict,  while  the  evidence  of  reasoning  upon 
which  it  rests  is  absolutely  irrefragable.  The  fallacy  is,  therefore,  the 
same  as  in  the  preceding  case,  that  of  seeing  a  part  only  of  the  phe- 
nomena, and  imagining  that  part  to  be  the  whole ;  and  may  be  ranked 
among  Fallacies  of  Non-observation. 

§  5.  To  complete  the  examination  of  the  second  of  our  five  classes, 
we  have  now  to  speak  of  Mal-observation ;  in  which  the  eiTor  does 
not  lie  in  the  fact  that  something  is  unseen,  but  that  something  seen  is 
seen  wrong. 

Perception  being  infallible  evidence  of  whatever  is  really  perceived, 
the  error  now  under  consideration  can  be  committed  no  otherwise 
than  by  mistaking  for  perception  what  is  in  fact  inference.  We  have 
formerly  shown  how  intimately  the  two  are  blended  in  almost  every- 
thing which  is  called  observation,  and  still  more  in  every  Description.* 
What  is  actually  on  any  occasion  perceived  by  our  senses  being  so 

*  Supra,  p.  383. 


FALLACIES  OF  OBSERVATION.  483 

minute  in  amount,  and  generally  so  unimpoilant  a  portion  of  the  state 
of  facts  which  we  wish  to  ascertain  or  to  communicate,  it  would  be 
absurd  to  say  that  either  in  Our  observations,  or  in  conveying  their 
result  to  others,  we  ought  not  to  mingle  inference  with  fact ;  all  thut 
can  be  said  is,  that  when  wo  do  so  we  ought  to  be  aware  of  what  we 
aie  doing,  and  to  know  what  part  of  the  assertion  rests  upon  conscious- 
ness, and  is  therefore  indisputable,  what  part  upon  inference,  and  is 
therefore  questionable. 

One  of  the  most  celebrated  examj)lcs  of  an  univei-sal  error  produced 
by  mistaking  an  inference  tor  the  direct  e%-idence  of  the  senses,  was 
the  resistance  made,  on  the  ground  of  conunon  sense,  to  the  Copernican 
system.  People  fancied  they  at/ /r  the  sun  rise  and  set,  the  stars  revolve 
m  circles  round  the  pole.  We  now  know  that  they  saw  no  such  thing: 
what  they  really  saw  were  a  set  of  appearances,  equally  reconcila- 
ble with  the  theory  they  held  and  with  a  totally  diHerent  one.  It 
seems  strange  that  such  an  instance  as  this,  of  the  testimony  of  the 
senses  pleaded  with  the  most  entire  conviction  in  favor  of  something 
which  was  a  mere  inference  of  the  judgment,  and,  as  it  turned  out, 
a  false  inference,  should  not  have  (opened  the  eyes  of  the  bigots 
of  common  sense,  and  inspired  them  with  a  more  modest  distrust 
of  the  competency  of  mere  ignorance  to  judge  the  conclusions  of 
science. 

In  proportion  to  any  person's  deficiency  of  knowledge  and  mental 
cultivation,  is  generally  his  inability  to  discriminate  between  his  infer- 
ences and  the  perceptions  on  which  they  were  grounded.  INIany  a 
marvelous  tale,  many  a  scandalous  anecdote,  owes  its  origin  to  this 
incapacity.  The  narrator  relates,  not  what  he  saw  or  heard,  but  the 
impression  which  he  derived  from  what  he  saw  or  heard,  and  of  which 
perhaps  the  greater  part  consisted  of  inference,  though  the  whole  is 
related  not  as  inference,  but  as  matter-of-fact.  The  difficulty  of  in- 
ducing witnesses  to  restrain  within  any  moderate  limits  the  intermix- 
ture of  their  inferences  with  the  naiTative  of  their  perceptions,  is  well 
known  to  experienced  cross-examiners  ;  and  still  more  is  this  the  case 
when  ignorant  persons  attempt  to  describe  any  natural  phenomenon. 
"The  simplest  narrative,"  says  Dugald  Sttnvart,*  "of  the  most  illiterate 
obscner  involves  more  or  less  of  hypothesis ;  nay,  in  general,  it  will 
be  found  that,  in  proportion  to  his  ignmance,  the  gieater  is  the  number 
of  conjectural  principles  involved  in  his  statements.  A  village  pothe- 
cary  (and,  if  possible,  in  a  still  greater  degree,  an  experienced  nurse) 
is  seldom  able  to  describe  the  plainest  case,  without  employing  a  phra- 
seology of  which  every  word  is  a  theory  ;  whereas  a  simph;  and  gen- 
uine specification  of  the  phenomena  which  mark  a  particular  disease, 
a  specification  unsophisticated  l>y  fancy,  or  by  preconceivtul  opinions, 
may  be  regarded  as  unequivocal  evidence  of  a  mind  trained  by  long 
and  successful  study  to  the  most  difficult  of  all  arts,  that  of  the  fuilhfui 
interpretation  of  nature.''t 

*  Elements  of  the  Philosophy  of  the  Mind,  vol.  ii.,  ch.  4,  sect.  5. 

tThe  following  anecdote,  related  by  Dr.  Paris  (Pharmacologia,  pp.  7G-7),  is  an  amusing 
instance  of  an  inference  mistaken  for  a  direct  perception.  "Shortly  after  Sir  Humphry 
Davy  had  succeeded  in  decomposing  the  fi.xcd  alkalies,  a  portion  of  potassium"  (a  sub- 
stance so  light  as  to  swim  upon  water)  "  was  placed  in  the  hand  of  one  of  our  most  dis- 
tinguished chemists,  with  a  query  as  to  its  nature.  The  philosopher  observing  its  aspect 
and  splendor  did  not  hesitate  in  pronouncing  it  to  be  metallic,  and  uniting  at  once  the  idea 
of  weight  with  that  of  metal,  the  evidence  of  his  senses  was  even  insulficient  to  dissever 


484  FALLACIES. 

The  universality  of  tlie  confusion  between  perceptions  and  the  infer- 
ences drawn  from  them,  and  the  rarity  of  the  power  to  discriminate 
the  one  from  the  other,  ceases  to  surprise  us  when  we  consider  that  in 
the  far  gieater  number  of  instances  the  actual  perceptions  of  our  senses 
are  of  no  importance  or  interest  to  us  except  as  marks  fi-om  which  we 
infer  something  beyond  them.  It  is  not  the  color  and  superficial  exten- 
sion perceived  by  the  eye  that  are  important  to  us,  but  the  object,  of 
which  those  visible  appearances  testify  the  presence  ;  and  v/here  the 
sensation  itself  is  indifferent,  as  it  generally  is,  we  have  no  motive  to 
attend  particularly  to  it,  but  acquire  a  habit  of  passing  it  over  without 
distinct  consciousness,  and  going  on  at  once  to  the  inference.  So  that 
to  know  what  the  sensation  actually  was,  is  a  study  in  itself,  to  which 
the  painter,  for  example,  has  to  train  himself  by  special  and  long  con- 
tinued discipline  and  application.  In  things  further  removed  fi-om  the 
dominion  of  the  outward  senses,  no  one  who  has  not  great  experience 
in  psychological  analysis  is  competent  to  break  this  intense  association : 
and  when  such  analytic  habits  do  not  exist  in  the  requisite  degree,  it  is 
hardly  possible  to  mention  any  of  the  habitual  judgments  of  mankind 
on  subjects  of  a  high  degree  of  abstraction,  from  the  being  of  God  and 
the  immortality  of  the  soul  dovni  to  the  multiplication  table,  which  are 
not,  or  have  not  been,  considered  as  matter  of  direct  intuition.  In 
saying  this  I  do  not  seek  to  prejudge  the  question  of  transcendental 
metaphysics,  how  far  a  certain  number  of  these  habitual  judgments  are 
really  intuitive,  or  otherwise.  I  only  point  out  the  strength  of  the 
tendency  to  ascribe  an  intuitive  character  to  judgments  which  are  mere 
inferences,  and  often  false  ones.  No  one  can  doubt  that  many  a  de- 
luded visionary  has  actually  believed  that  he  was  directly  inspired  from 
heaven,  and  that  the  Almighty  had  conversed  with  him  face  to  face ; 
which  yet  was  only,  on  his  part,  a  conclusion  drawn  from  appearances 
to  his  senses  or  feelings  in  his  internal  consciousness  which  were  alto- 
gether an  insufficient  foundation  for  any  such  belief.  The  caution, 
thei"efore,  which  is  needful  against  this  class  of  errors,  could  not  with 
any  propriety  have  been  foregone  ;  though  to  determine  whether,  on 
any  of  the  great  questions  of  metaphysics,  such  errors  are  actually 
committed,  belongs  not  to  this  place,  but,  as  I  have  so  often  said,  to  a 
different  science. 

ideas  so  inseparably  associated  in  his  mind,  and,  balancing  the  specimen  on  his  fingers,  he 
exclaimed, '  it  is  certainly  metallic,  and  very  po7idcrous.'  "  He  mistook  his  judgment  of  the 
ponderosity  of  the  substance  for  a  smsation  of  it. 


FALLACIES  OF  GENERALIZATION.  485 

CHAPTER  V. 

FALLACIES  OF  GENERALIZATION. 

§  1.  The  class  of  Fallacies  of  which  we  aro  now  to  speak,  is  the 
most  extensive  of  all ;  einbracin;T  a  greater  number  and  variety  of 
unfuunclcd  inferences  than  any  of  the  other  classes,  and  which  it  is  even 
more  difficult  to  reduce  to  sub-classes  or  species.  If  the  attempt  made 
in  tlie  precedin<T  Books  to  define  the  principles  of  well-grounded  gener- 
alization has  been  successful,  all  generalizations  not  conformable  to 
tliose  principles  might,  in  a  certain  sense,  be  brought  under  the  present 
class  :  when  however  the  rules  ai-e  known  and  kept  in  view,  but  a 
casual  lapse  committed  in  the  application  of  them,  this  is  a  blunder, 
not  a  fallacy.  To  entitle  an  error  of  generalization  to  the  latter  ej)ithet, 
it  must  be  committed  on  principle ;  there  must  lie  in  it  some  erroneous 
general  conception  of  the  inductive  process ;  the  legitimate  mode  of 
tlrawing  conclusions  from  observation  and  experiment  must  be  funda- 
mentally misconceived. 

Without  attempting  anything  so  chimerical  as  an  exhaustive  classifi- 
cation of  all  the  misconceptions  which  can  exist  on  the  subject,  let  us 
content  ourselves  with  noting,  among  the  cautions  which  might  be 
suggested,  a  few  of  the  most  useful  and  needful. 

§  2.  In  the  first  place,  there  are  certain  kinds  of  generalization  which, 
if  the  principles  already  laid  down  be  coiTOCt,  must  be  groundless  : 
experience  cannot  afford  the  necessary  conditions  for  establishing  tliem 
by  a  correct  induction.  Such,  for  instance,  are  all  inferences  from  the 
order  of  nature  existing  on  the  earth,  or  in  the  solar  system,  to  that 
which  may  exist  in  remote  parts  of  the  universe;  where  the  phenom- 
ena, for  aught  we  know,  may  be  entirely  different,  or  may  succeed  one 
another  according  to  different  laws,  or  even  according  to  no  fixed  law 
at  aU.  Such,  again,  in  matters  dependent  on  causation,  are  all  universal 
negatives,  all  propositions  that  assert  impossibility.  The  non-existence 
of  any  given  phenomenon,  however  uniformly  experience  may  as  yet 
have  testified  to  the  fact,  proves  at  most  that  no  cause,  adeijuate  to  its 
production,  has  yet  manifested  itself;  but  that  no  such  causes  exist  in 
nature  can  only  be  inferred  if  we  commit  the  absurdity  of  supposing 
that  we  know  all  the  forces  in  nature.  The  supposition  would  at  le.-ist 
be  premature  while  our  acquaintance  with  some  even  of  those  which 
we  do  know  Ls  so  extremely  recent.  And  however  much  our  knowl- 
edge of  nature  may  hereafter  be  ext(!nd(ul,  it  is  not  easy  to  see  how 
that  knowledge  could  ever  be  complete,  or  how,  if  it  were,  we  could 
ever  be  assured  of  its  being  so. 

The  only  laws  of  nature  which  afford  sufficient  wanant  for  atlribtit- 
ing  impossibility,  are  first,  those  of  number  and  extension,  which  are 
paramount  to  the  laws  of  the  succession  of  jdienomena,  and  not  ex- 
posed to  the  agency  of  counteracting  causes  ;  and  secondly,  the  univer- 
sal law  of  causality  itself  That  no  viunation  in  any  effect  or  consorpicnt 
will  take  place  while  the  whole  of  the  antecedents  remain  tlie  same, 
may  be  afhrmed  with  full  assurance.  But,  that  the  addition  of  some 
new  antecedent  might  not  entirely  alter  and  subvert  the  accustomed 


486  FALLACIES. 

consequent,  or  that  antecedents  competent  to  do  this  do  not  exist  in 
nature,  we  are  in  no  case  empowered  positively  to  conclude. 

§  3.  It  is  next  to  be  remarked  that  all  generalizations  which  profess, 
like  the  theories  of  Thales,  Democritus,  and  others  of  the  early  Greek 
philosophers,  to  resolve  all  things  into  some  one  element,  or,  like  many 
hiodei-n  theories,  to  resolve  phenomena  radically  different  into  the 
same,  are  necessarily  false.  By  radically  difterent  phenomena  I  mean 
impressions  on  our  senses  which  differ  in  quality,  and  not  merely  in 
degree.  On  this  subject  what  appeared  necessary  was  said  in  the 
chapter  on  the  Limits  to  the  Explanation  of  Laws  of  Nature;  but  as 
the  fallacy  is  even  in  our  own  times  a  common  one,  I  shall  touch  upon 
it  somewhat  further  in  this  place. 

When  we  say  that  the  force  which  holds  the  planets  in  their  orbits 
is  resolved  into  gravity,  or  that  the  force  which  make  substances  com- 
bine chemically  is  resolved  into  electricity,  we  assert  in  the  one  case 
what  is,  and  in  the  other  case  what  might,  and  probably  will  ultimately 
be  a  legitimate  result  of  induction.  In  both  these  cases,  motion  is 
resolved  into  motion.  The  assertion  is,  that  a  case  of  motion,  which 
was  supposed  to  be  special,  and  to  follow  a  distinct  law  of  its  own, 
conforms  to  and  is  included  in  the  general  law  which  regulates  another 
class  of  motions.  But,  fi-om  these  and  similar  generalizations,  counte- 
nance and  currency  has  been  given  to  attempts  to  resolve  not  motion 
into  motion,  but  heat  into  motion,  light  into  motion,  sensation  itself  into 
motion  (as  in  Hartley's  doctrine  of  vibi-ations) ;  states  of  consciousness 
into  states  of  the  nervous  system,  as  in  the  ruder  forms  of  the  materi- 
alist philosophy;  vital  phenomena  into  mechanical  or  chemical  pro- 
cesses, as  in  some  schools  of  physiology. 

Now  I  am  far  from  pretending  that  it  may  not  be  capable  of  proof, 
or  that  it  would  not  be  a  very  important  addition  to  our  knowledge  if 
proved,  that  certain  motions  in  the  particles  of  bodies  are  among  the 
conditions  of  the -production  of  heat  or  light;  that  certain  assignable 
physical  modifications  of  the  nerves  may  be  among  the  conditions  not 
only  of  our  sensations  or  emotions,  but  even  of  our  thoughts;  that  cer- 
tain mechanical  and  chemical  conditions  may,  in  the  order  of  nature,  be 
sufficient  to  detennine  to  action  the  physiological  laws  of  life.  All  I 
insist  upon,  in  common  with  every  sober  thinker  since  modem  science 
has  been  definitively  constituted,  is,  that  it  shall  not  be  supposed  that  by 
proving  these  things  one  step  would  be  made  towards  a  real  explanation 
of  heat,  light,  or  sensation;  or  that  the  generic  peculiarity  of  those 
phenomena  can  be  in  the  least  degree  evaded  by  any  such  discoveries, 
however  well  established.  Let  it  be  shown,  for  instance,  that  the 
most  complex  series  of  physical  causes  and  effects  succeed  one  another 
in  the  eye  and  in  the  brain  to  produce  a  sensation  of  color;  rays  falling 
upon  the  eye,  refracted,  converging,  crossing  one  another,  making  an 
inverted  image  on  the  retina,  and  after  this  a  motion — let  it  be  a 
vibration  or  a  rush  of  nervous  fluid,  or  whatever  else  you  are  pleased  to 
suppose,  along  the  optic  nerve — a  propagation  of  this  motion  to  the 
brain  itself,  and  as  many  more  different  motions  as  you  choose;  still, 
at  the  end  of  these  motions,  there  is  something  which  is  not  a  motion, 
there  is  a  feeling  or  sensation  of  color.  "VVliatever  number  of  motions 
we  may  be  able  to  intei-polate,  and  whether  they  be  real  or  imaginary, 
we  shall  still  find,  at  the  end  of  the  series,  a  motion  antecedent  and  a  color 


FALLACIES    OF    GENERALIZATION.  187 

consciiueiit.  The  nioilc  in  which  any  one  of  the  motions  piodiurs  the 
next,  nii^ht  })ossil)ly  be  susceptible  of  explanation  by  some  general 
law  ot"  motion  previou^^ly  known;  but  the  mode  in  which  the  last  mo- 
tion produces  the  sensation  ol"  color,  cannot  be  explained  by  any  law 
of  motion;  it  is  the  law  of  color;  which  is,  and  nnist  always  remain  a 
peculiar  thing.  Where  our  consciousness  recognizes  between  two 
phenomena  an  inherent  distinction;  where  we  are  sensible  of  a  dift'er- 
ence  which  is  not  merely  of  degree,  and  feel  that  no  adding  one  of  the 
phenomena  to  itself  would  jiroduce  the  other;  any  theory  which 
attempts  to  bring  either  under  the  laws  of  the  other  must  be  false; 
though  a  theory  which  merely  treats  the  one  as  a  cause  or  condition  of 
the  other,  may  possibly  be  true. 

§  4.  Among  the  remaining  forais  of  erroneous  generalization,  sev- 
eral of  those  most  wtnthy  of  and  most  requiring  notice  have  fallen  under 
our  examination  in  former  places,  where,  in  investigating  the  rules  of 
correct  induction,  we  have  had  occasion  to  advert  to  the  distinction 
between  it  and  some  common  mode  of  the  incorrect.  In  this  number 
is  what  I  have  formerly  called. the  natural  Induction  of  unincjuiring 
minds,  the  Induction  of  the  ancients,  which  proceeds  iter  cnumcratio- 
ncm  simplkcm:  "This,  that,  and  the  other  A  are  B,  I  cannot  think  of 
any  A  which  is  not  E,  therefore  every  A  is  B."  As  a  final  condem- 
nation of  this  rude  and  slovenly  mode  of  generalization,  I  will  (]uote 
Bacon's  emphatic  deimnciation  of  it ;  the  most  important  jiart,  as  I  have 
more  than  once  ventured  to  assert,  of  tho  permanent  service  rendered 
by  him  to  philosophy.  "Inductio  quae  procedit  per  enumerationem 
simplicem,  res  puerilis  est,  et  pi'ccario  concludit,"  (concludes  only  by 
yuur  leave,  or  provisionally,)  "  et  periculo  exponitur  ab  instantiii  con- 
tradictoria,  et  plerumque  secundum  pauciora  quam  par  est,  et  ex  his 
tantummudo  qu(e  2)rcesto  sunt  Y>ioi\\inc'va\..  At  Inductio  qute  ad  inven- 
tionem  et  demonstrationem  Scicntiarum  et  Artium  erit  utilis,  Naturam 
separare  debet,  per  rejectiones  et  exclusiones  debitas;  ac  deinde  post 
negativas  tot  quot  sufticiunt,  super  aflinnativas  concludere." 

I  have  aheady  said  that  the  uKjde  of  Simple  Enumeration  is  still  tho 
common  and  received  method  of  Inducti(»n  in  whatever  relates  to  man 
and  society.  Of  this  a  very  few  instances,  more  by  way  of  nu-mento 
than  of  instruction,  may  suttice.  What,  for  example,  is  to  be  thought 
of  all  the  "  common-sense"  maxims  for  which  the  following  may  serve 
as  the  universal  formula  :  "  Whatsoever  has  never  been,  will  never 
be."  As  for  example  ;  negroes  have  never  been  as  civilized  as  whites 
sometimes  are,  therefore  it  is  imp«)ssibl(!  they  should  be  so.  Women, 
as  a  class,  have  not  hitherto  e()ualed  men  as  a  class  in  intellectual 
energy  and  comprehensiveness,  then-fore  they  are  nece.ssarily  inferior. 
Society  cannot  prosper  without  this  or  the  other  institution  ;  e.  g.,  in 
Aristotle's  time,  without  slavery  ;  in  later  times,  witlumt  an  established 
priesthood,  without  artificial  distinctions  of  ranks,  &c.  One  working 
man  in  a  thousand,  educated,  while  the  nine  hundred  and  ninety-nine 
remain  uneducated,  has  usually  aimed  at  raisiiii4  himself  out  of  his 
class,  thercjfore  education  makes  jieople  <lissalisiied  with  tlieit  (Condi- 
tion in  life.  Booki.sh  men,  taken  from  speculative  pursuits  and  set  to 
work  on  something  they  know  nothing  ab(»ut,  have  generally  been 
found  or  thought  to  do  it  ill ;  therefore  j)hilosnphers  are  unfit  for  busi- 
ness,   &c.,   &c.      All    those    are   inductions   by  simple   enumeration. 


488  FALLACIES. 

Reasons  having  some  reference  to  the  canons  of  scientific  investigation 
may  have  been  given  or  attempted  to  be  given  for  several  of  these 
propositions ;  but  to  the  multitude  of  those  who  parrot  them,  the 
enumeratio  siviflcx,  ex  his  tantumtnodo  qnce,  prcesto  stint  fronuncians^ 
is  the  sole  evidence.  Their  fallacy  consists  in  this,  that  they  are  induc- 
tions without  elimination  ;  there  has  been  no  real  comparison  of  in- 
stances, nor  even  ascertainment  of  the  material  circumstances  in  any 
given  instance.  There  is  also  the  further  en'or,  of  forgetting  that  such 
generalizations,  even  if  well  established,  cannot  be  ultimate  truths,  but 
must  be  the  results  of  other  laws  much  more  elementary  ;  and  there- 
fore could  at  most  be  admitted  as  empirical  laws,  holding  good  within 
the  limits  of  space  and  time  by  which  the  particular  observations-  that 
suggested  the  generalization  were  bounded. 

This  error  of  placing  mere  empirical  laws,  and  laws  in  which  there 
is  no  direct  evidence  of  causation,  on  the  same  footing  of  certainly  as 
laws  of  cause  an  effect,  and  error  which  is  at  the  root  of  perhaps  the 
gi'eater  number  of  bad  inductions,  is  exemplified  only  in  its  grossest 
form  in  the  kind  of  generalizations  to  which  we  have  now  referred. 
These,  indeed,  do  not  possess  even  the  degree  of  evidence  which  per- 
tains to  a  well-ascertained  empirical  law ;  but  admit  of  refutation  on 
the  empirical  ground  itself,  without  ascending  to  causal  laws.  A  little 
reflection,  indeed,  will  show  that  mere  negations  can  only  form  the 
ground  of  the  lowest  and  least  valuable  kind  of  empirical  law.  A 
phenomenon  has  never  been  noticed ;  this  only  proves  that  the  condi- 
tions of  that  phenomenon  have  not  yet  occurred  in  human  experience, 
but  does  not  prove  that  they  may  not  occur  to-moiTow.  There  is  a 
higher  kind  of  empirical  law  than  this,  namely,  when  a  phenomenon 
which  is  observed  presents  within  the  limits  of  observation  a  series  of 
gradations,  in  which  a  regularity,  or  something  like  a  mathematical 
law,  is  perceptible :  from  which,  therefore,  something  may  be  ration- 
•  ally  presumed  as  to  those  terms  of  the  series  which  are  beyond  the 
limits  of  observation.  But  in  negation  there  are  no  gradations,  and  no 
series  :  the  generalizations,  therefore,  which  deny  the  possibility  of  any 
given  condition  of  Man  and  Society  merely  because  it  has  never  yet 
been  witnessed,  cannot  possess  this  higher  degree  of  validity  even  as 
empirical  laws.  What  is  more,  the  minuter  examination  which  that 
higher  order  of  empirical  laws  presupposes,  being  applied  to  the  sub- 
ject matter  of  these,  not  only  does  not  confirm  but  actually  i-efutes 
them.  For  in  reality  the  past  history  of  Man  and  Society,  instead  of 
exhibiting  them  as  immovable,  unchangeable,  incapable  of  ever  pre- 
senting new  phenomena,  shows  theni  on  the  contrary  to  be,  in  many 
most  important  particulars,  not  only  changeable,  but  actually  undergo- 
ing a  progressive  change.  The  empirical  law,  therefore,  best  expres- 
sive, in  most  cases,  of  the  genuine  result  of  observation,  would  be,  not 
that  such  and  such  a  phenomenon  will  continue  unchanged,  but  that  it 
will  continue  to  change  in  some  particular  manner. 

Accordingly,  while  almost  all  generalizations  relating  to  Man  and 
Society,  antecedent  to  the  last  fifty  years,  have  eiTed  in  the  gross  way 
which  we  have  attempted  to  characterize,  namely,  by  implicitly  as- 
suming that  human  nature  and  society  will  for  ever  revolve  in  the 
same  orbit,  and  exhibit  essentially  the  same  phenomena  ;  which  is  also 
the  vulgar  eiTor  of  practicalism  and  common  sense  in  our  own  day, 
especially  in  Great  Britain ;   the  more  thinking  minds  of  the  present 


FALLACIES   OF  GENERALIZATION.  489 

age,  having  applied  a  more  minute  analysis  to  the  past  rcconls  oi'  uur 
race,  have  lor  the  most  part  adopted  the  contrary  opinion,  that  the 
human  species  is  in  a  state  of  necessary  progression,  and  that  from  tho 
tenns  of  the  series  which  are  past  we  may  infer  with  certainty  llmsd 
which  are  yet  to  come.  Of  this  doctrine,  considered  as  a  philoso])lii(  al 
tenet,  we  shall  have  occasion  to  speak  fully  in  the  concluding  IJook. 
If  not,  in  all  its  forms,  free  from  error,  it  is  at  least  always  free  from 
the  gross  and  stupid  error  which  we  previously  oxem|»lilied.  But,  in  all 
except  the  most  eminently  philosophical  minds,  it  is  infected  with  pre- 
cisely the  same  kind  of  fallacy  as  that  is.  For  wo  must  remember  that 
even  this  other  and  better  generalization,  the  progressive  change  in  the 
condition  of  the  human  spi-cit-s,  is,  alter  all,  but  an  empirical  law  :  to 
which,  moreover,  it  is  nut  diilicult  to  point  out  exceedingly  large  excep- 
tions ;  and  even  if  these  could  be  got  rid  of,  either  by  disputing  the  facts 
or  by  explaining  and  limiting  the  theory,  the  general  objectif)n  remains 
valid  against  the  supposed  law,  as  applicable  to  any  other  than  what,  in 
our  third  Book,  were  tenned  Adjacent  Cases,  For  not  only  is  it  no  ulti- 
mate, but  not  even  a  causal  law.  Changes  do  indeed  take  place  in 
human  affairs,  but  every  one  of  those  changes  depends  upon  determi- 
nate causes ;  the  "  progressibility  of  the  species"  is  not  a  cause,  but  a 
summary  expression  for  the  general  result  of  all  the  causes.  So  soon 
aa,  by  a  quite  different  sort  of  induction,  it  shall  be  ascertained  what 
causes  have  produced  these  successive  changes  from  the  beginning  of 
history  in  so  far  as  they  have  really  taken  place,  and  by  what  causes  of  a 
contrary  tendency  they  have  been  occasionally  checked  or  entirely  coun- 
teracted, we  shall  then  be  prepared  to  predict  the  future  with  reason- 
able foresight :  we  shall  be  in  possession  of  the  real  /aw  of  the  future; 
and  shall  be  able  to  declare  upon  what  circumstances  the  continuance 
of  the  same  onward  movement  will  eventually  depend.  But  this  it  is 
the  enor  of  many  of  the  more  advanqcd  thinkers,  in  the  present  age, 
to  overlook  ;  and  to  imagine  that  the  empirical  law  collected  from  a 
mere  comparison  of  the  condition  of  our  species  at  different  past  times, 
is  a  real  law,  is  the  law  of  its  changes,  not  only  past  but  also  to  come. 
The  truth  is,  that  the  causes  upon  which  the  phenomena  of  the  moral 
world  depend,  are  in  every  age,  and  almost  in  every  country,  com- 
bined in  some  different  proportion;  so  that  it  is  scarcely  to  be  expect- 
ed that  the  general  result  of  them  all  sIkjuUI  conform  very  closely,  in 
its  details  at  least,  to  any  uniforndy  progressive  series.  And  all 
generalizations  which  afhrm  that  mankind  have  a  tendency  to  grow 
better  or  worse,  ncher  or  poorer,  more  cultivated  or  more  barbarous, 
that  population  increases  faster  than  subsistence,  or  subsistence  than 
population,  that  inequality  of  fortunes  has  a  tendency  to  increase  or  to 
break  down,  and  the  like,  propositions  of  considerable  value  jis  empiri- 
cal laws  within  certain  (but  gc^nerally  rather  narrow)  limits,  are.  in 
reality  true  or  false  according  to  times  and  circumstances. 

What  wo  have  saJd  of  empirical  generalizations  from  times  past  to 
times  still  to  come,  holds  ecpially  tnie  of  similar  generalizations  from 
present  times  to  times  past ;  wlu;n  men  whoso  acf|uainlance  with  moral 
and  social  facts  is  confined  to  their  own  age;,  take  tlie  men  and  the 
things  of  that  age  for  the  typo  of  men  and  things  in  general,  and  apply 
without  scruple  to  the  interpretation  of  the  events  of  history,  the  em- 
pirical laws  which  represent  sufficiently  for  daily  guidance  the  com- 
mon phenomena  of  human  nature  at  that  time  and  in  tiiat  particular 
3Q 


490  FALLACIES. 

State  of  society.  If  examples  are  wanted,  almost  every  historical  work, 
until  a  very  recent  period,  abounded  in  them.  The  same  may  be  said 
of  those  who  generalize  empirically  from  the  people  of  their  owti 
country  to  the  people  of  other  countries,  as  if  human  beings  felt, 
judged,  and  acted,  everywhere  in  the  same  manner. 

§  5.  In  the  foregoing  instances,  the  distinction  is  confounded  between 
empirical  laws,  which  express  merely  the  customary  order  of  the  suc- 
cession of  effects,  and  the  laws  of  causation  on  which  the  effects  depend. 
There  may,  however,  be  incorrect  generalization  when  this  mistake 
is  not  committed ;  when  the  investigation  takes  its  proper  direction, 
that  of  causes,  and  the  result  erroneously  obtained  purports  to  be  a 
really  causal  law. 

The  most  vulgar  form  of  this  fallacy  is  that  which  is  commonly  called 
post  hoc,  ergo  propter  hoc,  or  cum  hoc,  ergo  propter  hoc.  As  when  it  is 
infeiTed  that  England  owes  her  industrial  preeminence  to  her  restric- 
tions on  commerce :  as  when  the  old  school  of  financiers,  and  I  am 
sorry  to  add,  Coleridge,  maintained  that  the  national  debt  was  one  of 
the  causes  of  the  national  prosperity  :  as  when  the  excellence  of  the 
Church,  of  the  Houses  of  Lords  and  Commons,  of  the  procedure  of 
the  law  courts,  &c.,  are  inferred  from  the  mere  fact  that  the  country 
has  prospered  under  them.  In  these  and  similar  cases,  if  it  can  be 
rendered  probable  by  other  evidence  that  the  supposed  causes  have 
some  tendency  to  produce  the  effect  ascribed  to  them,  the  fact  of  its 
having  been  produced,  though  only  in  one  instance,  is  of  some  value 
as  a  verification  by  specific  experience  :  but  in  itself  it  goes  scarcely 
any  way  at  all  towards  establishing  such  a  tendency,  since,  admitting 
the  effect,  a  hundred  other  antecedents  could  show  an  equally  strong 
title  oi  that  kind  to  be  considered  as  the  cause. 

In  these  examples  we  see  bad  generalization  a  posteriori,  or  empir- 
icism properly  so  called  :  causation  infeiTed  from  casual  conjunction, 
without  either  due  elimination,  or  any  presumption  arising  from  known 
properties  of  the  supposed  agent.  But  bad  generalization  a  j^riori  is 
fully  as  common ;  which  is  properly  called  false  theory ;  conclusions 
drawn,  by  way  of  deduction,  from  properties  of  some  one  agent  which 
is  known  or  supposed  to  be  present,  all  other  coexisting  agents  being 
overlooked.  As  the  former  is  the  error  of  sheer  ignorance,  so  the 
latter  is  especially  that  of  instructed  minds ;  and  is  mainly  committed 
in  attempting  to  explain  complicated  phenomena  by  a  simpler  theory 
than  their  nature  admits  of  As  when  one  school  of  physicians  sought 
for  the  universal  principle  of  all  disease  in  "  lentor  and  morbid  viscid- 
ity of  the  blood,"  and  imputing  most  bodily  derangements  to  mechan- 
ical obstructions,  thought  to  cure  them  by  mechanical  remedies  ;*  while 
another,  the  chemical  school,  "  acknowledged  no  source  of  disease  but 
the  presence  of  some  hostile  acid  or  alkali,  or  some  deranged  con- 

*  "  Thus  Fourcroy,"  says  Dr.  Paris,  "explained  the  operation  of  mercury  by  its  specific 
gravity,  and  the  advocates  of  this  doctrine  favored  the  general  introduction  of  the  prepara- 
tions of  iron,  especially  in  schirrus  of  the  spleen  or  liver,  upon  the  same  hypothetical  prin- 
ciple ;  for,  say  they,  whatever  is  most  forcible  in  removing  the  obstruction  must  be  the 
most  proper  instrument  of  cure  ;  such  is  steel,  which,  besides  the  attenuating  power  with 
which  it  is  furnished,  has  still  a  greater  force  in  this  case  from  the  gravity  of  its  particles, 
which,  being  seven  times  specifically  heavier  than  any  vegetable,  acts  in  proportion  with 
a  stronger  impulse,  and  therefore  is  a  more  powerful  deobstruent.  This  may  be  taken  as  a 
epecinien  of  the  style  in  which  these  mechanical  physicians  reasoned  and  practised." 
t'harmacologia,  pp.  38-9. 


FALLACIES    OF    GENERALIZATION.  491 

dition  in  the  chemical  composition  of  the  fluid  or  sohd  parts,"  and 
conceived,  therefore,  that  "  all  remedies  must  act  hy  producing  <lu>m- 
ical  changes  in  the  body.  We  find  Tournefort  busily  engaged  in  test- 
ing every  vegetable  juice,  in  order  to  discover  in  it  some  traces  of  an 
acid  or  alkaline  ingredient,  which  might  confer  upon  it  medicinal  ac- 
tivity. The  fatal  errors  into  which  such  an  hypotlu'sis  was  liable  to 
betray  the  practitioner,  receive  an  awful  illustration  in  the  history  of 
the  memorable  fever  that  raged  at  Leydenin  the  year  1699,  and  which 
consigned  two-thirds  of  the  pojiulation  of  that  city  to  an  untimely 
gi-ave ;  an  event  which  in  a  great  measure  depended  uj)on  the  Pro- 
fessor Sylvius  de  la  Boe,  who  having  just  embraced  the  chemical  doc- 
ti'ines  of  ^'an  Helmont,  assigned  tlie  origin  of  the  distemj)er  to  a  pre- 
vailing acid,  and  declared  that  its  cure  could  alone  be  eH'ected  by  the 
copious  administration  of  absorbent  and  testaceous  medicines."*  John 
Brown,  the  author  of  the  famous  Brunonian  Theory,  *'  generalized  dis- 
eases, and  brought  all  within  the  compass  of  two  grand  clas.ses,  those 
of  increased  and  diminished  excitement;"  and  maintained  "  that  every 
agent  which  could  operate  on  the  human  body  was  a  stimulant,  having 
an  identity  of  action,  and  dificring  only  in  the  degree  of  its  force  ;  so 
that  according  to  his  views  the  lancet  and  the  brandy  bottle  were  but 
the  opposite  extremes  of  one  and  the  same  class."! 

These  aberrations  in  medical  theory  have  their  exact  parallels  in 
politics.  All  the  doctrines  which  ascribe  absolute  goudn(;ss  to  partic- 
ular forms  of  govemment,  particular  social  arrangements,  and  even  to 
particular  modes  of  education,  without  reference  to  the  state  of  civiliza- 
tion and  the  various  distinguishing  characters  of  the  society  for  which 
they  are  intended,  are  open  to  the  same  objection — that  of  assuming 
one  class  of  influencing  circumstances  to  be  the  paramount  rulers  of 
phenomena  which  depend  in  an  equal  or  greater  degree  upon  many 
others.  But  on  these  considerations  it  is  the  less  necessary  that  wo 
should  now  dwell,  as  they  will  occupy  our  attention  very  largely  in 
the  concluding  Book. 

§  6.  The  last  of  the  modes  of  ciToneons  generalization  to  which  I 
shall  advert,  is  that  to  which  wo  may  give  the  name  of  False  Analogies. 
This  Fallacv  stands  distinguished  from  those  already  treated  of  by  the 
peculiarity,  that  it  does  not  even  simulate  a  complete  and  conclusive 
induction,  but  consists  in  the  misapplication  of  an  argument  which  is 
at  best  only  admissible  as  an  inconclusive  presumption,  where  real 
proof  is  unattainable. 

An  argument  from  analogy,  is  an  inference  that  what  is  tnie  in  a  cer- 
tain case  is  true  in  a  case  known  to  bo  somewhat  similar,  but  not  known 
to  be  exactly  parallel,  that  is,  to  be  similar  in  all  the  material  circum- 
stances. An  ol)joct  has  the  property  B:  another  object  is  not  known  to 
have  that  propeit}',  but  resembles  tlu^  first  in  a  property  A,  not  known  to 
be  connected  with  B;  and  the  conclusion  to  which  the  analogy  points, 
is  that  this  object  has  the  property  B  also.  As,  fi)r  example,  that  the 
planets  are  inhabited  because  the  earth  is.  The  planets  resemble  tho 
earth  in  describing  elliptical  orbits  round  the  sun,  in  V)eing  attracted 
by  it  and  by  one  another,  in  being  spherical,  revolving  u])on  their  axes, 
&c. ;  but  it  is  not  knoAvn  that  any  of  these  properties,  or  all  of  tliem 

»  Pharmacohsia,  pp.  39,  10.  f  id'd.,  p.  43. 


492  FALLACIES. 

together,  are  the  conditions  upon  which  the  possession  of  inhabitants 
is  dependent,  or  are  even  marks  of  those  conditions.  Nevertheless, 
so  long  as  we  do  not  know  what  the  conditions  are,  they  may  be  con- 
nected by  some  law  of  nature  with  those  common  properties ;  and  to 
the  extent  of  that  possibility  the  planets  are  more  likely  to  be  inhabited, 
than  if  they  did  not  resemble  the  eai'th  at  all.  This  non-assignable 
and  generally  small  increase  of  probability,  beyond  what  would  other- 
wise exist,  is  all  the  evidence  which  a  conclusion  can  derive  from 
analogy.  For  if  we  have  any  the  slightest  reason  to  suppose  any  real 
connexion  between  the  two  properties  A  and  B,  the  argument  is  no 
longer  one  of  analogy.  If  it  had  been  ascertained  (I  purposely  put 
an  absurd  supposition)  that  there  was  any  connexion,  by  causation, 
between  the  fact  of  revolving  round  an  axis  and  the  existence  of  ani- 
mated beings,  or  if  there  were  any  reasonable  ground  for  even  suspect- 
ing such  a  connexion,  a  probability  would  arise  of  the  existence  of 
inhabitants  in  the  planets,  which  might  be  of  any  degree  of  strength, 
up  to  a  complete  induction  ;  but  we  should  then  infer  the  fact  from  the 
ascertained  or  presumed  law  of  causation,  and  not  from  the  analogy  of 
the  earth. 

The  name  analogy,  however,  is  sometimes  employed  by  extension, 
to  denote  those  arguments  of  an  inductive  character,  but  not  amount- 
ing to  a  real  induction,  which  are  employed  to  strengthen  the  argument 
drawn  from  a  simple  resemblance.  Though  A,  the  property  common 
to  the  two  cases,  cannot  be  shown  to  be  the  cause  or  effect  of  B,  the 
analogical  reasoner  will  endeavor,  if  he  can,  to  show  that  there  is  some 
less  close  degree  of  connexion  between  them ;  that  A  is  one  of  a  set 
of  conditions  from  which,  when  all  united,  B  would  result ;  or  is  an 
occasional  effect  of  some  cause  which  has  been  known  also  to  produce 
B;  and  the  like.  Any  of  which  things,  if  shown,  would  render  the 
existence  of  B  by  so  much  more  probable,  than  if  there  had  not  been 
even  that  amount  of  known  connexion  between  B  and  A. 

Now  an  error,  or  fallacy,  of  analogy  may  occur  in  two  ways.  Some- 
times it  consists  in  employing  an  argument  of  either  of  the  above  kinds 
with  correctness  indeed,  but  oveiTating  its  probative  force.  This  very 
common  aberration  is  sometimes  supposed  to  be  particularly  incident 
to  persons  distinguished  for  their  imagination ;  but  in  reality  it  is  the 
characteristic  intellectual  vice  of  those  whose  imaginations  are  ban-en, 
either  fi-om  want  of  exercise,  natural  defect,  or  the  narrowness  of  their 
range  of  ideas.  To  such  minds,  objects  present  themselves  clothed  in 
but  few  properties ;  and  as,  therefore,  few  analogies  between  one  ob- 
ject and  another  occur  to  them,  they  almost  invariably  overrate  the 
degi'ee  of  importance  of  those  few  :  while  one  whose  fancy  takes  a 
wider  range,  perceives  and  remembers  so  many  analogies  tending  to 
conflicting  conclusions,  that  he  is  not  so  likely  to  lay  undue  stress  upon 
any  of  them.  We  always  find  that  those  are  the  gi'eatest  slaves  to 
metaphoiical  language  who  have  but  one  set  of  metaphors. 

But  this  is  only  one  of  the  modes  of  eiTor  in  the  employment  of 
arguments  of  analogy.  There  is  another,  more  properly  deserving  the 
name  of  fallacy;  namely,  when  resemblance  in  one  point  is  inferred 
from  resemblance  in  another  point,  although  there  is  not  only  no 
evidence  to  connect  the  two  circumstances  by  way  of  causation,  but 
the  evidence  tends  positively  to  disconnect  them.  This  is  properly  tho 
Fallacy  of  False  Analogies. 


FALLACIES    OF    GENERALIZATION.  493 

As  a  first  instance,  wc  may  cite  that  favorite  argument  in  defence 
of  absolute  power,  drawn  from  tl)o  analogy  of  paternal  government  in 
a  family,  which  govcnnnent  is  not,  and  by  universal  admission  ought 
not  to  be,  controlled  hij  (tliDugh  it  sometimes  ought  to  be  controlled 
for)  the  children,  I'aternal  govermnent,  in  a  family,  works  well; 
therefore,  says  the  argument,  despotic  government  in  a  state  will  work 
well :  implying  that  the  beneficial  working  of  parental  goveniment 
depends,  in  the  family,  upon  the  only  point  which  it  has  in  common 
with  political  despotism,  namely,  irresjionsibility.  Whereas  it  does  not 
depend  upon  that,  but  upon  two  other  attributes  <jf  j)arental  govern- 
ment, the  attection  of  the  parent  for  the  children,  and  the  superiority  of 
the  parent  in  wisdom  and  experience  ;  neither  of  which  properties  can 
be  reckoned  upon,  or  are  at  all  likely  to  exist,  between  a  political 
desjDot  and  his  subjects ;  and  when  either  of  these  circumstances  fails, 
even  in  the  family,  and  the  influence  of  the  irresponsibility  is  allowed 
to  work  uncoiTected,  the  result  is  anything  but  good  government. 
This,  therefore,  is  a  false  analogy. 

Another  example  is  the  not  uncommon  dictum,  that  bodies  politic 
have  youth,  maturity,  old  age,  and  death,  like  bodies  natural :  that 
after  a  certain  duration  of  prosperity,  they  tend  spontaneously  to  decay. 
This  also  is  a  false  analogy,  because  the  decay  of  the  vital  powers  in 
an  animated  body  can  be  distinctly  traced  to  the  natural  progress  of 
those  very  changes  of  structure  which,  in  their  earlier  stages,  constitute 
its  growth  to  maturity;  while  in  the  body  politic  the  progress  of  those 
changes  cannot,  generally  speaking,  have  any  effect  but  the  still  further 
continuance  of  growth  :  it  is  the  stoppage  of  that  progress,  and  the 
commencement  of  reti-ogression,  that  alone  would  constitute  decay. 
Bodies  politic  die,  but  it  is  of  disease,  or  violent  death :  they  have  no 
old  age. 

The  following  sentence  from  Hooker's  Ecclesiastical  Polity  is  an 
instance  of  a  false  analogy  from  physical  bodies  to  what  are  called 
bodies  politic.  "As  there  could  be  in  natural  bodies  no  motion  of  any- 
thing unless  there  were  some  which  moveth  all  things,  and  contlnueth 
immovable ;  even  so  in  politic  societies  there  must  be  some  unpunish- 
able, or  else  no  man  shall  suffer  punishment."  There  is  a  double 
fallacy  here,  for  not  only  the  analogy,  but  the  premise  Irom  which  it  is 
drawn,  is  untenable.  The  notion  that  there  must  be  something  im- 
movable which  moves  all  others,  is  the  old  scholastic  error  of  a  inimum 
mobile. 

Some  of  the  false  analogies  upon  which  systems  of  physics  were 
confidently  grounded  in  the  time  of  the  Greek  philosophers,  are  such 
as  we  now  call  fanciful ;  not  that  the  resemblances  arc  not  often  real, 
but  that  it  is  long  since  any  one  has  been  inclined  to  draw  from  them 
the  inferences  which  were  then  drawn.  Such,  for  instance,  are  the 
curious  speculations  of  the  Pythagoreans  on  the  subject  of  numbers. 
Finding  that  the  distances  of  tlie  planets  bore  or  seemed  to  bear  to  one 
another  a  proportion  not  varying  much  from  that  of  the  divisions  of  the 
monochord,  they  inferred  from  it  the  existence  of  an  inaudiblo  music, 
that  of  the  spheres  ;  as  if  the  music  of  a  harp  had  di-pended  solely  on 
the  numerical  proportions,  and  not  on  the  material,  nor  even  on  the  ex- 
istence of  any  material,  any  stnngs  at  all.  It  has  been  similarly  ima- 
gined that  certain  combinati(jns  of  numbers,  whicli  were  found  to  pre- 
vail in  some  natural  phenomena,  must  run  through  the  whole  of  nature  : 


494  FALLACIES. 

as  that  there  must  be  four  elements,  because  there  are  four  possible 
combinations  of  hot  and  cold,  wet  and  dry  :  that  there  must  be  seven 
planets,  because  there  were  seven  metals,  and  even  because  there  were 
seven  days  of  the  week.  Kepler  himself  thought  that  there  could  be 
only  six  planets  because  there  were  only  five  regular  solids.  With  these 
we  may  class  the  reasonings,  so  common  in  the  speculations  of  the 
ancients,  founded  upon  a  supposed  perfection  in  nature  ;  meaning  by 
nature  the  customary  order  of  events  as  they  take  place  of  themselves 
without  human  interference.  This  also  is  a  rude  guess  at  an  analogy 
supposed  to  pervade  all  phenomena,  however  dissimilar.  Since  what 
was  thought  to  be  perfection  appeared  to  obtain  in  some  phenomena, 
it  was  inferred  to  obtain  in  all.  "  We  always  suppose  that  which  is 
better  to  take  place  in  nature,  if  it  be  possible,"  says  Aristotle  :  and 
the  vaguest  and  most  heterogeneous  qualities  being  confounded  to- 
gether under  the  notion  of  being  better,  there  was  no  limit  to  the  wild- 
ness  of  the  inferences.  Thus,  because  the  heavenly  bodies  were  "  per- 
fect," they  must  move  in  circles,  and  uniformly.  For  "  they"  (the 
Pythagoreans)  "would  not  allow,"  says  Geminus,*  "  of  any  such  disor- 
der among  divine  and  eternal  things,  as  that  they  should  sometimes 
move  quicker  and  sometimes  slower,  and  sometimes  stand  still ;  for  no 
one  would  tolerate  such  anomaly  in  the  movements  even  of  a  man 
who  was  decent  and  orderly.  The  occasions  of  life,  however,  are 
often  reasons  for  men  going  quicker  or  slower,  but  in  the  incoiTupt- 
ible  nature  of  the  stars,  it  is  not  possible  that  any  cause  can  be  alleged 
of  quickness  or  slowness."  It  is  seeking  an  argument  of  analogy  very 
far  to  suppose  that  the  stars  must  observe  the  rules  of  decorum  in  gait 
and  can'iage,  prescribed  for  themselves  by  the  long-bearded  philos- 
ophers satirized  by  Lucian. 

As  late  as  the  Copernican  controversy  it  was  ui-ged  as  an  argument 
in  favor  of  the  true  theory  of  the  solar  system,  that  "  it  placed  the  fire, 
the  noblest  element,  in  the  centre  of  the  universe."!  This  was  a  rem- 
nant of  the  notion  that  the  order  of  nature  must  be  perfect,  and  that 
perfection  consisted  in  conformity  to  rules  of  precedency  in  dignity, 
either  real  or  conventional.  Again,  reverting  to  numbers :  certain 
numbers  were  2^<^''fict,  therefore  those  numbers  must  obtain  in  the 
great  phenomena  of  nature.  Six  was  a  perfect  number,  that  is,  equal 
to  the  sum  of  all  its  factors  ;  an  additional  reason  why  there  must  be 
exactly  six  planets.  The  Pythagoreans,  on  the  other  hand,  attributed 
perfection  to  the  number  ten  ;  but  agreed  in  thinking  that  the  perfect 
number  must  be  somehow  realized  in  the  heavens;  and  knowing  only 
of  nine  heavenly  bodies  to  make  up  the  enumeration,  they  asserted 
"  that  there  was  an  anticlithon  or  counter-earth,  on  the  other  side  of  the 
sun,  invisible  to  us."|  Even  Huygens  was  persuaded  that  when  the 
number  of  the  heavenly  bodies  had  reached  twelve,  it  could  not  admit 
of  any  further  increase.  Creative  power  could  not  go  beyond  that 
sacred  number. 

Some  curious  instances  of  false  analogy  are  to  be  found  in  the  argu- 
ments of  the  Stoics  to  prove  the  equality  of  all  crimes,  and  the  equal 
wretchedness  of  all  who  had  not  realized  their  idea  of  perfect  virtue. 
Cicero,  towards  the  end  of  his  Fourth  Book  De  FiniUcs,  states  some 


*  I  quote  from  Mr.  Whewell's  Hist,  of  the  Ind.  Sc,  I  165. 
t  Ibid.,  i.,  365.  t  Ibid.,  70. 


FALLACIES    OF    GE.VERAHZATIOIV.  495 

of  these  as  follows.  "  Ut,  iiKjuit,  in  fidibus  plurimis,  si  nulla  oaruni  ita 
contenta  nmneris  sit,  ut  concentum  servare  possit,  omnes  ueque  incon- 
tentie  sint ;  sic  peccata,  quia  discrepant,  a^quc  discrepant :  })aria  sunt 
i2:itur."  To  which  Cicero  himself  aptly  answers,  "  aatpic  contintrit  om- 
nibus fidibus,  ut  incontentue  sint  ;  illu(l  non  continuo,  ut  a!quc  incon- 
t^nt;e."  The  Stoic  resumes  :  "  Ut  cnim,  inquit,  p;iibernator  teque 
peccat,  si  palearum  navcm  evertit,  et  si  auri ;  item  terpie  peccat  qui 
parentem,  et  qui  servum,  injuria  verberat ;"  assuming,  that  because 
the  magnitude  of  the  interest  at  stake  makes  no  difference  in  the  mere 
defect  of  skill,  it  can  make  none  in  the  moral  defect  :  a  false  analogy. 
Again,  "  Q,uis  ignorat,  si  plures  ex  alto  emergere  velint,  propius  fore  eos 
quidem  ad  lespirandum,  qui  ad  summam  jam  aquam  a]ipr<ipinquant, 
sed  nihilo  magis  respirare  posse,  quam  eos,  qui  sunt  in  profundo  ? 
Nihil  ergo  adjuvat  proccdere,  et  progredi  in  virtute,  (juomiims  miserri- 
mus  sit,  antequam  ad  cam  peiA^cnerit,  quoniam  in  acjua  nihil  adjuvat : 
et  quoniam  catuli,  qui  jam  despecturi  sunt,  ca;ci  a^que,  et  ii  qui  modo 
nati  ;  Platonem  quoque  necesse  est,  quoniam  nondum  videbat  sapien- 
tiara,  aeque  caecum  animo,  ac  Phalarim  fuisse."  Cicero,  in  his  own 
person,  combats  these  false  analogies  by  other  analogies  tending  to 
an  opposite  conclusion.  "  Ista  similia  non  sunt,  Cato  :  .  .  .  .  Ilia  sunt 
similia  ;  hebes  acies  est  cuipiam  oculorum  :  corpore  alius  langucscit  : 
hi  curatione  adhibita  levautur  in  dies  :  alter  valet  plus  quotidie  :  alter 
videt.  Hi  similes  sunt  omnibus,  qui  virtuti  student ;  levautur  vitiis, 
levantur  eiToribus." 

§  7.  In  these  and  all  other  arguments  drawn  from  remote  analogies, 
and  from  metaphors,  Avhicli  are  cases  of  analogy,  it  is  apparent  (espe- 
cially when  we  consider  the  extreme  facility  of  raising  up  contrary  anal- 
ogies and  conflicting  metaphors),  that  so  f;vr  from  the  metaphor  or 
analogy  proving  anything,  the  applicability  of  the  metaphor  is  the  very 
thing  to  be  made  out.  It  has  to  be  shown  that  in  the  two  cases  asserted 
to  be  analogous,  the  same  law  is  really  operating ;  that  between  the 
known  resemblance  and  the  inferred  one  there  is  some  connexion  by 
means  of  causation.  Cicero  and  Cato  might  have  bandied  oj)posite 
analogies  forever:  it  rested  with  each  of  them  to  prove  by  just  induc- 
tion, or  at  least  to  render  probable,  that  the  case  resembled  the  one  set 
of  analogous  cases  and  not  the  other,  in  the  circumstances  upon  which 
the  disputed  question  really  hinged.  Metaphors,  for  the  most  part, 
therefore,  assume  the  proposition  which  they  are  brought  to  prove  : 
their  use  is,  to  aid  the  apprehension  of  it;  to  make  clearly  and  vividly 
comprehended  what  it  is  that  the  person  who  employs  the  meta])hor  is 
proposing  to  make  out;  and  sometimes  also,  by  what  media  he  proposes 
to  do  so.  For  an  apt  metaphor,  though  it  cannot  prove,  often  suggests 
the  proof. 

For  instance,  when  Mr.  Carlyle,  rebuking  the  Byronic  vein,  says 
that  "  strength  does  not  manifest  itself  in  spa.sms,  but  in  stout  bearing 
of  burdens ;"  the  metaphor  proves  nothing,  it  is  no  argument,  only  an 
allusion  to  an  argument;  in  no  other  way  however  could  so  much  of 
argument  be  so  completely  suggested  in  .so  few  words.  In  fact,  this 
admirable  expre.ssion  suggests  a  whole  train  of  reasoning,  which  it 
would  take  many  sentences  to  write  out  at  length.  As  thus  :  Motions 
which  are  violent  but  brief,  which  lead  to  no  end,  and  are  not  under 
the  control  of  the  will,  are,  in  the  physical  body,  more  ijicident  to  a 


496  FALLACIES. 

weak  than  to  a  strong  constitution.  If  this  be  owing  to  a  cause  which 
equally  operates  in  what  relates  to  the  mind,  the  same  conclusion  will 
hold  there  likewise.  J3ut  such  is  really  the  fact.  For  the  body's 
liability  to  these  sudden  and  uncontrollable  motions  arises  from  irrita- 
bility, that  is,  unusual  susceptibility  of  being  moved  out  of  its  ordinary 
course  by  transient  influences  :  which  may  equally  be  said  of  the  mind. 
And  this  susceptibility,  whether  of  mind  or  body,  must  arise  from  a 
weakness  of  the  forces  which  maintain  and  carry  on  the  ordinary  ac- 
tion of  the  system.  All  this  is  conveyed  in  Mr.  Carlyle's  short  sen- 
tence. And  since  the  causes  are  alike  in  the  body  and  in  the  mind,  the 
analogy  is  a  just  one,  and  the  maxim  holds  of  the  one  as  much  as  of 
the  other. 

Thus  we  see  that  the  metaphor,  although  no  proof  but  a  statement 
of  the  thing  to  be  proved,  states  it  in  terms  which,  by  suggesting  a 
parallel  case,  put  the  mind  upon  the  track  of  the  real  proof  The 
hearer  says,  "  Strength  does  not  manifest  itself  in  spasms — very  true  ; 
and  for  what  reason  V  Then  in  discovering  the  reason,  he  finds  it  pre- 
cisely as  applicable  to  the  mind  as  it  is  to  the  body.  This  mode,  there- 
fore, of  conveying  an  argument,  independently  of  its  rhetorical  advan- 
tages, has  a  logical  value;  since  it  not  only  suggests  the  grounds  of 
the  conclusion,  but  points  out  another  case  in  which  those  gi'ounds 
have  been  found,  or  at  least  deemed  to  be,  sufficient. 

On  the  other  hand,  when  Bacon,  who  is  equally  conspicuous  in  the 
use  and  abuse  of  figurative  illustration,  says  that  the  stream  of  time 
has  brought  down  to  us  only  the  least  valuable  part  of  the  writings  of 
the  ancients,  as  a  river  can-ies  fi"oth  and  straws  floating  on  its  surface, 
while  more  weighty  objects  sink  to  the  bottom;  this,  even  if  the  asser- 
tion illustrated  by  it  were  true,  would  be  no  good  illustration,  there 
being  no  parity  of  cause.  The  levity  by  which  substances  float  on  a 
stream,  and  the  levity  which  is  synonymous  with  worthlessness,  have 
nothing  in  common  except  the  name ;  and  (to  show  how  little  value 
there  is  in  the  metaphor)  we  need  only  change  the  word  into  htioyancy, 
to  turn  the  semblance  of  argument  involved  in  Bacon's  illustration 
directly  against  himself 

A  metaphor,  then,  is  not  to  be  considered  as  an  argument,  but  as 
an  assertion  that  an  argument  exists ;  that  a  parity  subsists  between 
the  case  from  which  the  metaphor  is  drawn  and  that  to  which  it  is 
applied.  This  parity  may  exist  though  the  two  cases  be  apparently 
very  remote  from  one  another:  the  only  resemblance  existing  between 
them  may  be  a  resemblance  of  relations,  an  analog}^  in  Ferguson's  and 
Archbishop  Whately's  sense.  As  in  the  instance  quoted  from  Mr. 
Carlyle :  there  is  no  resemblance  between  convulsions  of  the  body  and 
fits  of  passion  in  the  mind,  considered  in  themselves ;  the  resemblance 
is  between  the  relation  which  convulsions  of  the  body  bear  to  its  ordi- 
nary motions,  and  that  which  fits  of  passion  in  the  mind  bear  to  its 
steadier  feelings.  Thus,  where  the  real  difference  between  the  two 
cases  is  the  widest ;  where  the  metaphor  seems  the  most  far-fetched, 
the  analogy  the  most  remote  ;  dnd  where,  consequently,  a  limited  and 
literal  understanding  would  be  most  apt  to  shut  itself  up  \vithin  its 
intrenchment  of  prose,  and  refuse  admittance  to  the  metaphor,  under 
an  idea  that  cases  so  very  unlike  can  throw  no  light  upon  each  other ; 
it  is  often  in  those  very  cases  that  the  argument  which  the  metaphor 
involves  and  suggests  is  the  most  conclusive. 


FALLACIES    OF    GENKRALIZATION,  497 

§  8.  To  terminate  the  subject  of  Fallacies  of  Generalization,  it  re- 
mains to  be  said,  that  the  most  fertile  source  of  thorn  is  bad  classifica- 
tion ;  bringing  together  in  one  group,  and  under  one  namc^  things 
which  have  no  common  properties,  or  none  but  such  as  are  too  unim- 
portant to  allow  general  proj)ositions  of  any  considerable  value  to  be 
made  respecting  the  class.  The  misleading  cdect  is  greatest,  when  a 
word  wliich  in  common  use  expresses  some  definite  fact,  is  extended 
by  slight  links  of  connexion  to  cases  in  which  that  fact  does  not  exist, 
but  some  other  or  others  only  slightly  resembling  it.  Thus  Jiacon,* 
in  speaking  of  the  Idola  or  Fallacies  arising  from  notions  tctnere  ct 
incequalitcr  «  rebus  abstractcc,  exemplifies  them  by  the  notion  of  Humi- 
dum  or  Wet,  so  familiar  in  the  physics  of  anti(juity  and  of  the  middle 
ages.  "  Invenietur  vcrbum  istud,  Humidum,  nihil  aliud  quam  nota 
confusa  diversarum  actionum,  qute  nullam  constantiam  aut  reductionem 
patiuntur.  Significat  enim,  et  quod  circa  aliud  corpus  facile  se  cir- 
cumfundit;  et  quod  in  se  est  indeterminabilc,  nee  consistere  potest; 
et  quod  facile  cedit  undique ;  ct  quod  facile  se  dividit  et  dispergit ;  et 
quod  facile  se  unit  et  colligit ;  et  quod  facile  fluit,  et  in  motu  ponitur; 
et  quod  alteri  corpori  facile  adhasret,  idque  madefacit;  et  quod  facile 
rcducitur  in  liquidum,  sivc  colliquatur,  cum  antea  consisteret.  Itaque 
quum  ad  hujus  nominis  pritdicationcm  et  impositionem  ventum  sit; 
si  alia  accipias,  flamma  humida  est ;  si  alia  accipias,  aer  humidus  non 
est;  si  alia,  pulvis  minutus  humidus  est;  si  alia,  vitrum  humidum  est: 
ut  facile  appareat,  istam  norionem  ex  aqua  tantum,  et  communibus  et 
vulgaribus  liquoribus,  absque  ulla  debita  verificatione,  temere  abstrac- 
tam  esse." 

Bacon  himself  is  not  exempt  from  a  similar  accusation  when  inquir- 
ing into  the  nature  of  heat ;  where  he  occasionally  proceeds  like  one 
who,  seeking  for  the  cause  of  hardness,  after  examining  that  quality  in 
iron,  flint,  and  diamond,  should  expect  to  find  that  it  is  sometliing 
which  can  b»  traced  also  in  hard  water,  a  hard  knot,  and  a  hard 
heart. 

The  word  Kcvrjaig  in  the  Greek  philosophy,  and  the  words  Genera- 
tion and  Corruption  both  then  and  long  afterwards,  denoted  such  a 
multitude  of  heterogeneous  phenomena,  that  any  attempt  at  philo- 
sophizing in  which  those  words  were  used  was  almost  as  necessarily 
abortive  as  if  the  word  /uird  had  been  taken  to  denote  a  class  including 
all  the  things  mentioned  above.  KivTjOC^,  for  instance,  wliich  properly 
signified  motion,  was  taken  to  denote  not  only  all  emotion  but  even  all 
change  :  dXAoiojotg  being  recognized  as  one  of  the  modes  of  Kivrjoi^. 
The  effect  was,  to  connect  with  every  form  of  aXXoiojai^  or  change, 
ideas  drawn  from  motion  in  the  proper  and  literal  sense,  and  wliich 
had  no  real  connexion  with  any  other  kind  o(  Kivrjoig  than  that.  Aris- 
totle and  Plato  labored  under  a  contiimal  embarrassment  from  this 
misuse  of  terms.  J3ut  if  we  proceed  further  in  this  direction  we  shall 
encroach  upon  the  Fallacy  of  Ambiguity,  which  belongs  to  a  different 
class,  the  last  in  order  of  our  classification,  Fallacies  of  Confuaion. 

•  Nov.  Org.,  Aph.  CO. 


3R 


498  FALLACIES. 


CHAPTER  VI. 

FALLACIES  OF  RATIOCINATION. 


§  1.  We  have  now,  in  our  progress  through  the  classes  of 'Fallacies, 
amved  at  those  to  which,  in  the  common  books  of  logic,  the  appellation 
is  in  general  exclusively  appropriated ;  those  which  have  their  seat  in 
the  ratiocinative  or  deductive  part  of  the  investigation  of  truth.  On 
these  fallacies  it  is  the  less  necessary  for  us  to  insist  at  any  length,  as 
they  have  been  so  admirably  treated  in  a  work  familiar  to  almost  all, 
in  this  country  at  least,  who  feel  any  interest  in  these  speculations, 
Archbishop  Whately's  Logic.  Against  the  more  obvious  forms  of  this 
class  of  fallacies,  the  rules  of  the  syllogism  are  a  complete  protection. 
Not  (as  we  have  so  often  said)  that  the  ratiocination  cannot  be  good 
unless  it  be  in  the  form  of  a  syllogism ;  but  that,  by  showing  it  in  that 
form,  we  are  sure  to  discover  if  it  be  bad,  or  at  least  if  it  contain  any 
fallacy  of  this  class. 

§  2.  Among  Fallacies  of  Ratiocination  we  ought,  perhaps,  to  include 
the  errors  committed  in  processes  which  have  the  appearance  only,  not 
the  reality,  of  an  inference  from  premisses  ;  the  fallacies  connected  with 
the  conversion  and  aequipollency  of  propositions.  I  believe  errors  of 
this  description  to  be  far  more  frequently  committed  than  is  generally 
supposed,  or  than  their  extreme  obviousness  might  seem  to  admit  of. 
For  example,  the  simple  conversion  of  an  universal  affirmative  propo- 
sition, All  A  are  B  therefore  all  B  are  A,  I  take  to  be  a  very  common 
form  of  error :  though  committed,  like  many  other  fallacies,  oftener  in 
the  silence  of  thought  than  in  express  words,  for  it  can  scarcely  be 
cleai-ly  enunciated  without  being  detected.  And  so  with  another  form 
of  fallacy,  not  substantially  different  from  the  preceding  ;  the  eiToneous 
conversion  of  an  hypothetical  proposition.  The  proper  converse  of  an 
hypothetical  proposition  is  this  :  If  the  consequent  be  false,  the  ante- 
cedent is  false  ;  but  this,  If  the  consequent  be  true,  the  antecedent  is 
true,  by  no  means  holds  good,  but  is  an  error  corresjjonding  to  the 
simple  conversion  of  an  universal  affirmative.  Yet  hardly  anything  is 
more  common  than  for  people,  in  their  private  thoughts,  to  draw  this 
inference.  As  when  the  conclusion  is  accepted,  which  it  so  often  is, 
for  proof  of  the  premisses.  That  the  premisses  cannot  be  true  if  the 
conclusion  is  false,  is  the  unexceptionable  foundation  of  the  legitimate 
mode  of  reasoning  called  a  reductio  ad  ahsurdtim..  But  men  continu- 
ally think  and  express  themselves  as  if  they  also  believed  that  the 
premisses  cannot  be  false  if  the  conclusion  is  true.  The  truth,  or  sup- 
posed truth,  of  the  inferences  which  follow  from  a  doctrine,  often  ena- 
bles it  to  find  acceptance  in  spite  of  gross  absurdities  in  it.  How  many 
systems  of  philosophy,  which  had  scarcely  any  intrinsic  recommenda- 
tion, have  been  received  by  thoughtful  men  because  they  were  sup- 
posed to  lend  additional  support  to  religion,  morality,  some  favorite 
view  of  politics,  or  some  other  cherished  persuasion  ?  not  merely  be- 
cause their  wishes  were  thereby  enlisted  on  its  side,  but  because  its 
leading  to  what  they  deemed  sound  conclusions  appeared  to  them  a 
strong  presumption  in  favor  of  its  truth  :  though  the  presumption,  when 
viewed  in  its  true  light,  amounted  only  to  the  absence  of  that  particular 


FALLACIES    OF    RATIOCIXATION.  499 

kind  of  evidence  of  falsehood,  which  would  have  resulted  from  its  lead- 
ing by  correct  inference  to  somethintr  already  recoL-nized  as  false. 

Again,  the  very  frequent  error  in  conduct,  of  mistaking  reverse  of 
wrong  for  right,  is  the  practical  form  of  a  logical  error  with  respec!  to 
the  Opposition  of  Propositions.  It  is  committed  for  want  of  the  habit 
of  distinguishing  the  contrar;/  of  a  proposition  from  the  contradictory 
of  it,  and  of  attending  to  the  logical  canon,  that  contrary  propositions, 
though  they  camiot  both  be  true,  may  both  be  false.  If  the  eiTor 
were  to  express  itself  in  words  it  would  run  distinctly  counter  to  this 
canon.  It  generally,  however,  does  not  so  c-xpress  itself,  and  to  com- 
pel it  to  do  so  is  the  most  effectual  method  of  detecting  and  exposing  it. 

§  3.  Among  Fallacies  of  Ratiocination  are  to  be  ranked,  in  the  first 
place,  all  the  cases  of  vicious  syllogism  laid  down  in  the  books.  These 
generally  resolve  themselves  into  having  m»re  than  three  terms  to  the 
syllogism,  either  avowedly,  or  in  the  covert  mode  of  an  undistributed 
middle  term  or  an  illicit  process  of  one  of  the  two  extrc>mes.  It  is 
not,  indeed,  very  easy  fully  to  convict  an  argiftnent  of  falling  under 
any  one  of  these  vicious  cases  in  particular ;  for  the  reason  already 
quoted  from  Archbishop  Whately,  that  the  prcmiss(!S  are  seldom  for- 
mally set  out:  if  they  were,  the  fallacy  would  impose  upon  nobody; 
and  while  they  are  not,  it  is  almost  always  to  a  certain  degree  oi)tional 
in  what  manner  the  suppressed  link  shall  be  filled  up.  The  rules  of 
the  syllogism  are  rules  for  compelling  a  person  to  be  aware  of  the 
whole  of  what  he  must  undertake  to  defend  if  he  persists  in  maintain- 
ing his  conclusion.  He  has  it  almost  always  in  his  power  to  make  his 
syllogism  good  by  introducing  a  false  premiss  ;  and  hence  it  is  scarcely 
ever  possible  decidedly  to  affirm  that  any  argument  involves  a  bad 
syllogism  :  but  this  detracts  nothing  from  the  value  of  the  syllogistic 
rules,  since  it  is  by  them  that  a  reasoner  is  compelled  distinctly  to  make 
his  election  what  premisses  he  is  prepared  to  maintain.  The  eletlion 
made,  there  is  generally  so  little  difficulty  in  seeing  whether  the  con- 
clusion follows  from  tl>e  premisses  set  out,  that  we  might  without  much 
logical  impropriety  have  merged  this  fourth  class  of  fallacies  in  the 
fifth,  or  Fallacies  of  Confusion. 

4 

§  4.  Perhaps,  however,  the  commonest,  and  certainly  the  most  dan- 
gerous fallacies  of  this  class,  are  those  which  do  not  lie  in  a  single 
syllogism,  but  slip  in  between  one  syllogism  and  another  in  a  chain  of 
argument,  and  are  committed  by  chani^ini^  the  premisses.  A  proposi- 
tion is  proved,  or  an  acknowledged  truth  laid  down,  in  the  first  part  of 
an  argumentation,  and  in  the  second  a  further  argument  is  founded  not 
upon  the  same  proposition,  but  upon  some  other,  resembling  it  suffi- 
ciently to  be  mistaken  for  it.  Instances  of  this  fallacy  will  be  found 
in  almost  all  the  argumentative  discourses  of  unprecise  thinkers ;  and 
we  need  only  here  advert  to  one  of  the  obscurer  forms  of  it,  recognized 
by  the  schoolmen  as  the  fallacy  h  dicta  secundum  quid  ad  dictum  sim- 
pliciter.  This  is  committed  wlien,  in  the  premisses,  a  proj)osition  is 
asserted  with  a  qualification,  and  the  qualification  lost  sight  of  in  the 
conclusion ;  or  oftener,  when  a  limitation  or  condition,  though  not  as- 
serted, is  necessary  to  the  truth  of  tin;  proposition,  but  is  forgotten 
when  that  proposition  comes  to  be  employed  a.s  a  premiss.  Many  of 
the  bad  arguments  in  vogue  belong  to  this  class  of  error.  The  premiss 


500  FALLACIES. 

is  some  admitted  truth,  some  common  maxim,  the  reasons  or  evidence 
for  which  have  been  forgotten,  or  are  not  thought  of  at  the  time,  but 
if  they  had  been  thought  of  would  have  shown  the  necessity  of  so 
limiting  the  premiss,  that  it  would  no  longer  have  supported  the  con- 
clusion drawn  fiom  it. 

Of  this  nature  is  the  fallacy  in  what  is  called,  by  Adam  Smith  and 
others,  the  Mercantile  Theory  in  Political  Economy.  That  theory  sets 
out  from  the  common  maxim,  that  whatever  brings  in  money  enriches; 
or  that  every  one  is  rich  in  proportion  to  the  quantity  of  money  he 
obtains.  From  this  it  is  concluded  that  the  value  of  any  branch  of 
trade,  or  of  the  trade  of  the  country  altogether,  consists  in  the  balance 
of  money  it  brings  in ;  that  any  trade  which  carries  more  money  out 
of  the  country  than  it  draws  ftito  it  is  a  losing  trade ;  that  therefore 
money  should  be  attracted  into  the  country,  and  kept  there,  by  pro- 
hibitions and  bounties  ;  and  a  train  of  similar  corollaries.  All  for  want 
of  reflecting  that  if  the  riches  of  an  individual  are  in  proportion  to  the 
quantity  of  money  he  can  command,  it  is  because  that  is  the  measure 
of  his  power  of  purchasing  money's  worth;  and  is  therefore  subject 
to  the  proviso  that  he  is  not  debarred  from  employing  his  money  in 
such  purchases.  The  premiss,  therefore,  is  only  true  secundum  quid  ; 
but  the  theory  assumes  it  to  be  true  absolutely,  and  infers  that  increase 
of  money  is  increase  of  riches,  even  when  produced  by  means  subver- 
sive of  the  condition  under  which  alone  money  is  riches. 

A  second  instance  is,  the  argument  by  which  it  used  to  be  contended, 
before  the  commutation  of  tithe,  that  titlies  fell  upon  the  landlord,  and 
were  a  deduction  from  rent ;  because  the  rent  of  tithe-free  land  was 
always  higher  than  that  of  land  of  the  same  quality  and  the  same  ad- 
vantages of  situation,  subject  to  tithe.  Whether  it  be  true  that  a  tithe 
falls  on  rent  or  no,  a  treatise  on  Logic  is  not  the  place  to  examine : 
but  it  is  certain  that  this  is  no  proof  of  it.  Whether  the  proposition 
be  true  or  false,  tithe-free  land  imist,  by  the  necessity  of  the  case,  pay 
a  higher  rent.  For  if  tithes  do  not  fall  on  rent,  it  must  be  because 
they  fall  on  the  consumer ;  because  they  raise  the  price  of  com.  But 
if  corn  be  raised  in  price,  the  farmer  of  tithe-free  as  well  as  tlie  farmer 
of  tithed  land  gets  the  benefit.  To  the  latter  the  rise  is  but  a  com- 
^  pensation  for  the  tithe  he  pays  ;  to  the  first,  who  pays  none,  it  is  clear 
gain,  and  therefore  enables  him,  and  if  there  be  freedom  of  competi- 
tion forces  him,  to  pay  so  much  the  moi'e  rent  to  his  landlord.  This 
is  the  refutation  of  the  fallacy.  The  question  remains,  to  what  class 
of  fallacies  it  belongs.  The  premiss  is,  that  the  oWTier  of  tithed  land 
receives  less  rent  than  the  ovraer  of  tithe-free  land ;  the  conclusion  is, 
that  therefore  he  receives  less  than  he  himself  would  receive  if  tithe 
were  abolished.  But  the  premiss  is  only  true  conditionally  ;  the  o-\vner 
of  tithed  land  receives  less  than  what  the  owner  of  tithe-free  land  is 
enabled  to  receive  when  other  lands  are  tithed;  while  the  conclusion 
is  applied  to  a  state  of  circumstances  in  which  that  condition  fails,  and 
in  which,  by  consequence,  the  premiss  would  not  be  true.  The  fallacy, 
therefore,  is  a  dicto  secundum  quid  ad  dictum  simj>liciter. 

A  third  example  is  the  opposition  sometimes  made  to  legitimate  in- 
terferences of  government  in  the  economical  affairs  of  society,  grounded 
upon  a  misapplication  of  the  maxim,  that  an  individual  is  a  better 
judge  than  the  government  of  what  is  for  his  own  pecuniary  interest. 
This  objection  was  urged  to  Mr.  Wakefield's  system  of  colonization, 


FALLACIES    OF    RATIOCINATION.  501 

one  of  the  greatest  practical  improvements  in  public  affairs  which  have 
been  made  in  our  time.  Mr.  Wakt^field'vS  principle,  as  most  ]ie(tplc 
are  now  aware,  is  the  artificial  concentration  of  the  settlers,  by  fixing 
such  a  price  upon  unoccupied  land  as  may  preserve  the  most  desirable 
proportion  between  the  <juanlity  of  land  in  culture,  and  the  laboring 
population.  Against  this  it  was  argued,  tliat  if  individuals  found  it  for 
their  advantage  to  occupy  extensive -tracts  of  land,  they,  being  better 
judges  of  their  own  interest  than  the  legislature  (which  can  only  pro- 
ceed on  general  rules),  ought  not  to  be  restrained  from  doing  so.  But 
in  this  argument  it  was  forgotten  that  the  fact  of  a  man's  taking  a  largo 
tract  of  land  is  evidence  only  that  it  is  his  interest  to  take  as  much  as 
other  people,  but  not  that  it  might  not  be  for  his  interest  to  content 
himself  with  less,  if  he  could  be  assured  that  other  people  would  do 
so  too ;  an  assurance  which  nothing  but  a  government  regulation  can 
give.  If  all  other  people  took  much,  and  he  only  a  little,  he  would 
reap  none  of  the  advantages  derived  from  the  concentration  of  the 
population  and  the  consequent  possibility  of  procuring  labor  for  hire, 
but  would  have  placed  himself,  without  equivalent,  in  a  situation  of 
voluntary  inferiority.  Tlie  proposition,  therefore,  that  the  quantity  of 
land  which  people  will  take  when  left  to  themselves  is  that  which  it 
is  most  for  their  interest  to  take,  is  true  only  secundum  quid:  it  is  only 
their  interest  while  they  have  no  guarantee  for  the  conduct  of  ono 
another.  But  the  argument  disregards  the  limitation,  and  takes  tho 
proposition  for  true  simpliciter. 

One  of  the  conditions  oftenest  dropped,  when  what  would  otherwise 
be  a  true  proposition  is  employed  as  a  premiss  for  proving  others,  is 
the  condition  of  time.  It  is  a  principle  of  political  economy  that  prices, 
profits,  wages,  &c.  "  always  find  their  level ;"  but  this  is  often  inter- 
preted as  if  it  meant  that  they  are  always,  or  generally,  at  their  level ; 
while  the  truth  is,  as  Coleridge  epigrammatically  expresses  it,  that 
they  are  always ^wfZ/w^  their  level,  "  which  might  be  taken  as  a  para- 
phrase or  ironical  definition  of  a  storm." 

Under  the  same  head  of  fallacy  (a  dicto  secundum  quid  ad  dictum, 
simpliciter)  might  be  placed  all  the  errors  which  are  vulgarly  called 
misapplications  of  abstract  truths  :  that  is,  where  a  principle,  true  (as 
the  common  expression  is)  iti  the  abstract,  that  is,  all  modifying  causes 
being  supposed  absent,  is  reasoned  upon  as  if  it  were  true  absolutely, 
and  no  modifying  circumstances  could  ever  by  possibility  exist.  This 
very  common  form  of  error  it  is  not  recjuisite  that  we  should  exemplify 
here,  as  it  will  be  particularly  treated  of  hereafter  in  its  application  to 
the  subjects  on  which  it  is  most  frequent  and  most  fatal,  those  of  poli- 
tics and  society. 


502  FALLACIES. 


CHAPTER  VII. 

FALLACIES  OF  CONFUSION. 


§  1.  Under  this  fifth  and  last  class  we  find  it  convenient  to  arrange 
all  those  fallacies,  in  which  the  source  of  error  is  not  so  mnch  a  false 
estimate  of  the  probative  force  of  known  evidence,  as  an  indistinct,  in- 
definite, and  fluctuating  conception  of  what  the  evidence  is. 

At  the  head  of  these  stands  that  multitudinous  body  of  fallacious 
reasonings  in  which  the  source  of  error  is  the  ambiguity  of  terms :  when 
something  which  is  true  if  a  word  be  used  in  a  particular  sense,  is  rea- 
soned upon  as  if  it  were  true  in  another  sense.  In  such  a  case  there 
is  not  a  mal-estimation  of  evidence,  because  there  is  not  properly  any 
evidence  to  the  point  at  all ;  there  is  evidence,  but  to  a  different  point, 
which,  from  a  confused  apprehension  of  the  meaning  of  the  terms  used, 
is  supposed  to  be  the  same.  This  en-or  will  naturally  be  oftener  com- 
mitted in  our  ratiocinations  than  in  our  direct  inductions,  because  in 
the  former  we  are  deciphering  our  own  or  other  people's  notes,  while 
in  the  latter  we  have  the  things  themselves  present,  either  to  our  senses 
or  to  our  memory.  Except,  indeed,  when  the  induction  is  not  from 
individual  cases  to  a  generality,  but  from  generalities  to  a  still  higher 
generalization ;  in  that  case  the  fallacy  of  ambiguity  may  affect  the  in- 
ductive process  as  well  as  the  ratiocinative.  It  occurs  in  ratiocination 
in  two  ways :  when  the  middle  term  is  ambiguous,  or  when  one  of  the 
terms  of  the  syllogism  is  taken  in  one  sense  in  the  premisses,  and  in 
another  sense  in  the  conclusion. 

Some  good  exemplifications  of  this  fallacy  are  given  by  Archbishop 
Whately.  "  One  case,"  says  he,  "  which  may  be  regar'led  as  coming 
imder  the  head  of  Ambiguous  Middle,  is  what  is  called  Fallacia 
Figura:  Dictionis,  the  fallacy  built  on  the  grammatical  structure  of 
language,  from  men's  usually  taking  for  granted  that  paronyinous 
words  {i.  e.  those  belonging  to  each  other,  as  the  substantive,  adjec- 
tive, verb,  &c.,  of  the  same  root)  have  a  precisely  correspondent 
meaning,  which  is  by  no  means  universally  the  case.  Such  a  fallacy 
could  not  indeed  be  even  exhibited  in  strict  logical  foim,  which  would 
preclude  even  the  attempt  at  it,  since  it  has  two  middle  terms  in  sound 
as  well  as  sense  ;  but  nothing  is  more  common  in  2:)ractice  than  to  vary 
continually  the  terms  employed,  with  a  view  to  grammatical  conve- 
nience ;  nor  is  there  anything  unfair  in  such  a  practice,  as  long  as  the 
meaning  is  preserved  unaltered ;  e.  g.  '  murder  should  be  punished 
with  death;  this  man  is  a  murderer,  therefore  he  deserves  to  die,'  &c. 
Here  we  proceed  on  the  assumption  (in  this  case  just)  that  to  commit 
murder,  and  to  be  a  murderer,  to  deserve  death,  and  to  be  one  who 
ought  to  die,  are,  respectively,  equivalent  expressions ;  and  it  would 
frequently  prove  a  heavy  inconvenience  to  be  debarred  this  kind  of 
liberty;  but  the  abuse  of  it  gives  rise  to  the  Fallacy  in  question  :  e.g. 
projectors  are  unfit  to  be  trusted  ;  this  man  has  formed  a.  project,  there- 
fore he  is  unfit  to  be  trusted  :  here  the  sophist  proceeds  on  the 
hypothesis  that  he  who  forms  2l  project  must  be  a  projector:  whereas 
the  bad  sense  that  commonly  attaches  to  the  latter  word,  is  not  at  all 
implied  in  the  former.     This  fallacy  may  often  be  considered  as  lying 


FALLACIES    OF    CONFUSIO\.  503 

not  in  the  miiLUc,  bvit  in  one  of  the  terms  of  the  conclusion  ;  so  that 
the  conchision  (hawn  sliall  not  be,  in  reality,  at  all  warranted  by  tho 
premisses,  thoutjh  it  will  appear  to  be  so,  by  means  of  the  grammatical 
affinity  of  the  words ;  e.  g.  to  bo  acquainted  with  the  guilty  is  a  jyrc- 
sumption  of  guilt ;  this  man  is  so  acijuainted,  therefore  wc  may  presume 
that  he  is  guilty:  this  argument  proceeds  on  the  supposition  of  an 
exact  coiTespondence  between  presume  and  jiresumjttio/i,  which,  how- 
ever, does  not  really  exist ;  for  '  presumption'  is  commonly  used  to 
express  a  kind  of  slight  suspicion;  whereas  'to  presume'  amounts  to 
absolute  belief.  There  are  innumerable  instances  of  a  non-corres- 
pondence in  paronymous  words,  similar  to  that  above  instanced ;  as 
between  art  and  artful,  design  and  designing,  faith  -and  faithful,  &;c., 
and  the  more  slight  the  variation  of  meaning,  the  more  likely  is  the 
fallacy  to  be  successful ;  for  when  the  words  have  become  so  widely 
removed  in  sense  as  '  pity'  and  '  pitiful,'  every  one  would  j)erceivo 
such  a  fallacy,  nor  could  it  be  employed  but  in  jest.* 

"  The  present  Fallacy,"  continues  the  Archbishop,  "  is  nearly  allied 
to,  or  rather,  perhaps,  may  be  regarded  as  a  branch  of,  that  founded 
on  etymology ;  viz.,  when  a  term  is  used,  at  one  time  in  its  customary, 
and  at  another  in  its  etymological  sense.  Perhaps  no  example  of 
this  can  be  found  that  is  more  extensively  and  mischievously  employed 
than  in  the  case  of  the  word  representative :  assuming  that  its  right 
meaning  must  correspond  exactly  with  the  strict  and  original  sense  of 
the  verb  '  represent,'  thesophist  persuades  the  multitude,  that  a  member 
of  the  House  of  Commons  is  bound  to  be  guided  in  all  points  by  the 
opinion  of  his  constituents ;  and,  in  short,  to  be  merely  their  spokes- 
man: whereas  law  and  custom,  which  in  this  case  may  be  considered 
a.s  fixing  the  meaning  of  the  term,  require  no  such  thing,  but  enjcjin  the 
representative  to  act  according  to  the  best  of  his  own  judgment,  and  on 
his  own  responsibility." 

The  following  are  instances,  of  great  practical  importance,  in  which 
arguments  are  habitually  founded  upon  a  verbal  ambiguity. 

The  mercantile  pul)lic  are  frequently  led  into  this  fallacy  by  the 
phrase  "scarcity  of  money."  In  the  language  of  commerce  "money" 
has  two  meanings :  cvrrcncy,  or  the  circulating  medium  ;  and  capital 
seeking  imrestyncnt,  especially  investment  on  loan.  In  this  last  sense 
the  word  is  used  when  the  "money  market"  is  spoken  of,  and  when 
the  "  value  of  money"  is  said  to  be  high  or  low,  the  rate  of  interest 
being  meant.  The  consequence  of  this  ambiguity  is,  that  as  soon  as 
scarcity  of  money  in  the  latter  of  these  senses  begins  to  be  felt,  as 
soon  as  there  is  difficulty  of  obtaining  loans,  and  the  rate  of  interest  is 
high,  it  is  concluded  that  this  must  arise  from  causes  acting  upon  tho 
quantity  of  money  in  the  other  and  more  popular  sense  ;  that  the 
circulating  medium  must  have  diminished  in  quantity,  or  ought  to  bo 
increased.  I  am  aware  that,  independently  of  the  double  meaning  of 
the  term,  there  are  in  the  facts  themselves  some  peculiarities,  giving  an 
appaient  support  to  this  error ;  but  the  ambiguity  of  the  language 

*  An  example  of  this  fallacy  is  the  popular  error  that  ttrong  drink  must  be  a  cause  of 
strength.  There  is  here  fallacy  within  fallacy  ;  for  granting  that  the  wortls  -'strong"  and 
"strength"  were  not  (as  they  arc)  applied  in  a  totally  diflbrcnt  sense  to  fennenied  liquor* 
and  to  the  human  hody,  there  would  still  be  involved  the  error  of  supposing  that  an  effect 
must  be  like  its  cause ;  that  the  conditions  of  a  phenomenon  are  likely  to  resemble  the 
phenomenon  itself;  which  we  have  already  treated  of  as  an  h  priori  fallacy  of  tho  faat 
rank. 


504  FALLACIES. 

Stands  upon  the  very  threshold  of  the  subject,  and  intercepts  all  at- 
tempts to  throw  light  upon  it. 

Another  ambiguous  expression  which  continually  meets  us  in  the 
political  controversies  of  the  present  time,  especially  in  those  which 
relate  to  organic  changes,  is  the  phrase  "influence  of  property;" 
which  is  sometimes  used  for  the  influence  of  respect  for  superior  in- 
telligence, or  gratitude  for  the  kind  offices  which  persons  of  large 
property  have  it  so  much  in  their  power  to  bestow ;  at  other  times  for 
the  hifluence  of  fear;  fear  of  the  worse  sort  of  power,  which  large 
property  also  gives  to  its  possessor,  the  power  of  doing  mischief  to 
dependents.  To  confound  these  two,  is  the  standing  fallacy  of  ambi- 
guity brought  against  those  who  seek  to  purify  our  electoral  system 
from  corruption  and  intimidation.  "  The  influence  of  property  is 
beneficial:"  granted,  if  the  former  species  of  influence  and  that  alone 
be  meant;  but  conclusions  are  thence  drawn  in  condemnation  of 
expedients  which  (like  secret  voting,  for  example)  would  deprive 
property  of  some  of  its  influences,  though  only  of  the  latter  and  bad 
kind.  Persuasive  influence,  acting  through  the  conscience  of  the 
voter,  and  carrying  his  heart  and  mind  with  it,  is  beneficial — there- 
fore we  are  to  infer  that  coercive  influence,  which  compels  him  to 
forget  that  he  is  a  moral  agent,  or  to  act  in  opposition  to  his  moral 
convictions,  ought  not  to  be  placed  under  restraint. 

Another  word  which  is  often  turned  into  an  instrument  of  the  fallacy 
of  ambiguity  is  Theory.  In  its  most  proper  acceptation,  theory  means 
the  completed  result  of  philosophical  induction  from  experience.  In 
that  sense,  there  are  erroneous  as  well  as  true  theories,  for  induction 
may  be  incorrectly  performed,  but  theory  of  some  sort  is  the  necessary 
result  of  knowing  anything  of  a  subject,  and  having  put  one's  knowl- 
edge into  the  form  of  general  propositions  for  the  guidance  of  practice. 
In  another  and  more  vulgar  sense,  theory  means  any  mere  fiction  of 
the  imagination,  endeavoring  to  conceive  how  a  thing  may  possibly 
have  been  produced,  instead  of  examining  how  it  was  produced.  In 
this  sense  only  are  theory,  and  theorists,  unsafe  guides  ;  but  because 
of  this,  ridicule  or  discredit  is  attempted  to  be  attached  to  theory  in  its 
proper  sense,  that  is,  to  legitimate  generalization,  tlie  end  and  aim  of 
all  philosophy;  and  a  conclusion  is  represented  as  worthless,  just 
because  that  has  been  done,  which  if  done  coiTectly  constitutes  the 
highest  worth  that  a  principle  for  the  guidance  of  practice  can  possess, 
namely,  to  comprehend  in  a  few  words  the  real  law  on  which  a  phe- 
nomenon depends,  or  some  property  or  relation  which  is  universally 
true  of  it. 

"  The  Church"  is  sometimes  understood  to  mean  the  clergy  alone, 
sometimes  the  whole  body  of  believers,  or  at  least  of  communicants. 
The  declamations  respecting  the  inviolability  of  church  property  are 
indebted  for  the  gi-eater  part  of  their  apparent  force  to  this  ambiguity. 
The  clergy,  being  called  the  church,  are  supposed  to  be  the  real  ownei^s 
of  what  is  called  church  property;  whereas  they  are  in  tl'uth  only  tlie 
managing  member's  of  a  much  larger  body  of  pro})rietors,  and  enjoy 
on  their  own  part  a  mere  usufruct,  not  extending  beyond  a  life  interest. 

The  following  is  a  favorite  argument  of  Plato.  No  one  desires  evil, 
knowing  it  to  be  so  :  to  do  wrong  is  evil ;  therefore  no  one  desires  to 
do  vn-ong  knovdng  that  which  he  desires,  but  only  in  consequence  of 
ignorance.     In  this  syllogism  the  ambiguous  word  is  the  middle  term, 


FALLACIES    OF    CONFUSION.  505 

Ev-il,  the  double  meaning  of  which  is  too  obvious  to  need  explanation: 
yet  on  this  foundation  Plato  constructs  his  principal  ethical  doctrine, 
in  which  he  was  followed  by  most  of  the  philosophical  sects  among 
the  later  Greeks;  that  virtue  is  a  branch  of  intelligence,  and  is  to  be 
produced,  therefore,  mainly  by  intellectual  cultivation.  All  the  intjuiries 
into  the  summum  bonum  in  the  philosoj)hical  schools  were  infected  with 
the  same  fallacy ;  the  ambiguous  word  being,  as  before,  Evil,  or  its 
contrary  con-elative.  Good,  which  sometimes  meant  what  is  good  for 
oneself,  at  other  times  what  is  good  for  other  people.  That  nothing 
which  is  a  cause  of  evil  on  the  whole  to  other  people,  can  be  really 
good  for  the  agent  himself,  is  indeed  a  possible  tenet,  and  always  a 
favorite  one  with  moralists,  although  in  the  present  age  the  question 
has  rather  been,  not  whether  the  proposition  is  true,  but  how  society 
and  education  can  be  so  ordered  as  to  make  it  true.  At  all  events,  it 
is  not  proved  merely  by  the  fact  that  a  thing  beneficial  to  the  world, 
and  a  thing  beneficial  to  a  person  himself,  are  both  in  common  parlance 
called  good.     That  is  no  valid  argument,  but  a  fallacy  of  ambiguity. 

Of  such  stuff,  however,  were  the  ethical  speculations  of  the  ancients 
principally  composed,  especially  in  the  declining  period  of  the  Greek 
philosophic  mind.  The  following  is  a  stoical  argument  taken  from 
Cicero  De  F'uubus,  book  the  third  :  "  Quod  est  bonum,  omne  laudabile 
est.  Quod  autem  laudabile  est,  omne  honestum  est.  Eonum  igitur 
quod  est,  honestum  est."  Here  the  ambiguous  word  is  laudabile, 
which  in  the  minor  premiss  means  anything  which  mankind  are  accus- 
tomed, on  good  gi'ounds,  to  admire  or  value;  as  beauty,  for  instance, 
or  good  fortune  :  but  in  the  major,  it  denotes  exclusively  moral  qualities. 
In  much  the  same  manner  the  Stoics  were  led  to  all  their  absurdest 
paradoxes ;  as  that  the  virtuous  man  is  alone  free,  alone  beautiful, 
alone  a  king,  &c.  Whoever  has  virtue  has  Good  (because  it  has  been 
previously  determined  not  to  call  anything  else  good) ;  but  again.  Good 
necessarily  includes  freedom,  beauty,  and  even  royalty,  all  of  these 
being  good  things ;  therefore  whoever  has  virtue  has  all  these. 

The  following  is  an  argument  of  Descartes  to  prove,  in  his  d  priori 
manner,  the  being  of  God.  The  conception,  says  he,  of  an  infinite 
Being  proves  the  real  existence  of  such  a  being.  For  if  there  is  not 
really  any  such  being,  /  must  have  made  the  conception  ;  but  if  I 
could  make  it,  I  can  also  unmake  it ;  which  evidently  is  not  true ; 
therefin-e,  there  must  be  externally  to  myself,  an  archetype,  from  which 
the  conception  was  derived.  The  ambiguity  in  this  case  is  in  the  pro- 
noun /,  by  which,  in  one  place,  is  to  be  understood  my  will,  in  anotlier 
the  laws  of  my  nature.  If  the  conception,  existing  as  it  does  in  my 
mind,  had  no  original  without,  the  conclusion  would  uncjuestionably 
follow  that  /  made  it :  that  is,  the  laws  of  my  natuie  must  have  spon- 
taneously evolved  it ;  but  that  my  ivill  made  it,  would  not  follow. 
Now  when  Descartes  afterwards  adils  that  I  cannot  unmake  the  con- 
ception, he  means  that  I  cainiot  get  rid  of  it  by  an  act  of  my  will : 
which  is  true,  but  is  not  the  proposition  required.  That  what  some 
of  the  laws  of  my  nature  have  produced,  other  laws,  or  those  same 
laws  in  other  circumstances,  might  not  subsequently  efface,  he  would 
have  found  it  difficult  to  establish. 

Analogous  to  thia  art;  some  of  the  ambiguities  in  the  freo-will  con- 
troversy ;  which,  as  they  will  come  under  special  consideration  in  the 
concluding  Book,  I  only  mention  mcmorice  causd.  In  that  discussion, 
3S 


506  FALLACIES. 

too,  the  word  I  is  often  shifted  from  one  moaning  to  another,  at  one 
time  standing  for  my  vohtions,  at  another  time  for  the  actions  which  ai-e 
the  consequences  of  them,  or  the  mental  dispositions  from  which  they 
proceed.  The  latter  ambiguity  is  exemplified  in  an  argument  of  Cole- 
rid"-e  (in  his  Aids  to  Reflection),  in  support  of  the  freedom  of  the  will. 
It  is  not  true,  he  says,  that  man  is  governed  by  motives ;  "  the  man 
makes  the  motive,  not  the  motive  the  man;"  the  proof  being  that 
"  what  is  a  strong  motive  to  one  man  is  no  motive  at  all  to  another." 
The  premiss  is  true,  but  only  amounts  to  this,  that  different  persona 
have  different  degrees  of  susceptibility  to  the  same  motive ;  as  they 
have  also  to  the  same  intoxicating  liquid,  which  however  does  not  prove 
that  they  are  free  fo  be  drunk  or  not  drunk,  whatever  quantity  they  may 
drink.  What  is  proved  is,  that  certain  mental  conditions  in  the  man 
himself,  must  cooperate,  in  the  production  of  the  act,  with  the  external 
inducement :  but  those  mental  conditions  also  are  the  effect  of  causes  ; 
and  there  is  nothing  in  the  argument  to  prove  that  they  can  arise  with- 
out a  cause — that  a  spontaneous  determination  of  the  man's  will,  with- 
out any  cause  at  all,  ever  takes  place,  as  the  free-will  doctrine  supposes. 

The  double  use,  in  the  free-will  controversy,  of  the  word  Necessity, 
which  sometimes  stands  only  for  Certainty,  at  other  times  for  Compul- 
sion ;  sometimes  for  what  cannot  be  prevented,  at  other  times  only  for 
what  we  have  reason  to  be  assured  7vill  not ;  has  been  pointed  out 
by  Archbishop  Whately,  and  we  shall  have  occasion  hereafter  to  pur- 
sue it  to  some  of  its  ulterior  consequences. 

A  most  important  ambiguity,  both  in  common  and  in  metaphysical 
language,  is  thus  pointed  out  by  Archbishop  Whately  in  the  Appendix 
to  his  Logic :  "  Same  (as  well  as  One,  Identical,  and  other  words  de- 
rived from  them)  is  used  frequently  in  a  sense  very  different  from  its 
primary  one,  as  applicable  to  a  single  object ;  being  employed  to  de- 
note great  similarity.  When  several  objects  are  undistinguishably 
alike,  one  single  description  will  apply  equally  to  any  of  them  :  and 
thence  they  are  said  to  be  all  of  one  and  the  same  nature,  appearance, 
&c.  As,  e.g.,  when  we  say,  '  this  house  is  built  of  the  saine  stone  with 
such  another,'  we  only  mean  that  the  stones  are  undistinguishable  in 
their  qualities  ;  not  that  the  one  building  was  pulled  down,  and  the 
other  constructed  with  the  materials.  Whereas  sa?nencss,  in  the  pri- 
mary sense,  does  not  even  necessarily  imply  similarity ;  for  if  we  say 
of  any  man  that  he  is  greatly  altered  since  such  a  time,  we  understand, 
and  indeed  imply  by  the  very  expression,  that  he  is  one  iierson,  though 
different  in  several  qualities.  It  is  worth  observing  also,  that  Same,  in 
the  secondary  sense,  admits,  according  to  popular  usage,  of  degrees : 
we  speak  of  two  things  being  nearly  the  same,  but  not  entirely  :  per- 
sonal identity  does  not  admit  of  degrees.  Nothing,  perhaps,  has  con- 
tributed more  to  the  error  of  Realism  than  inattention  to  this  ambiguity. 
When  several  persons  are  said  to  have  one  and  the  same  opinion, 
thought,  or  idea,  men,  overlooking  the  true,  simple  statement  of  the 
case,  which  is,  that  they  are  all  thinking  alike,\odk  for  something  more 
abstruse  and  mystical,  and  imagine  there  must  be  some  Otic  Thing,  in 
the  primai-y  sense,  though  not  an  individual,  which  is  present  at  once 
in  the  mind  of  each  of  these  persons ;  and  thence  readily  sprung  Plato's 
theory  of  Ideas,  each  of  which  was,  according  to  him,  one  real,  eternal 
object,  existing  entire  and  complete  in  each  of  the  individual  objects 
that  are  known  by  one  name." 


FALLACIES  OF  CONFUSION.  507 

It  is,  indeed,  not  a  matter  of  inference  but  of  authentic  history,  tliat 
Plato's  doctrine  of  Ideas,  and  the  Anstotelian  doctrine  (essentially  the 
same  as  the  Platonic)  of  substantial  forms  and  second  substances,  frrew 
up  in  the  precise  way  here  pointed  out ;  from  the  supposed  necessity 
of  findinc:,  in  thinc^s  vvliich  wore  said  to  have  the  same,  nature,  or  the 
satne  qualities,  somethinrr  which  was  the  same  in  the  very  sense  in  which 
a  man  is  the  same  as  himself  All  the  idle  speculations  respectinir  to 
6v,  TO  ev,  TO  o^oiov,  and  similar  abstractions,  so  common  in  the  ancient 
and  in  some  modern  schools  of  philosophy,  sprung  from  the  same 
source.  The  Aristotelian  logicians  had,  however,  seen  one  case  of  the 
ambiguity,  and  provided  against  it,  with  their  peculiar  ft^licity  in  the 
invention  of  technical  language,  when  they  distingnished  things  which 
diflered  both  specie  and  numero  from  those  which  dirtero<l  numero 
tantum,  that  is,  which  were  exactly  alike  (in  some  particular  resjKict  at 
least)  but  were  distinct  individuals.  An  extension  of  this  distinction 
to  the  two  meanings  of  the  word  Same,  namely,  things  which  are  the 
same  specie  tantum,  and  a  thing  which  is  the  same  numero  as  well  as 
specie,  would  have  prevented  the  confusion  which  has  been  a  source  of 
so  much  darkness  and  such  an  abundance  of  positive  error  in  the  higher 
philosophy. 

One  of  the  most  singular  examples  of  the  lengths  to  which  a  philos- 
opher of  eminence  may  be  led  away  by  an  ambiguity  of  language,  is 
afforded  by  this  very  case.  1  refer  to  the  famous  argument  by  which 
Bishop  Berkeley  flattered  himself  that  he  had  for  ever  put  an  end  to 
"  skepticism,  atheism,  and  irreligion."  It  is  briefly  as  follows.  1 
thought  of  a  thing  yesterday ;  I  ceased  to  think  of  it ;  I  think  of  it  again 
to-day.  I  had,  therefore,  in  my  mind  yesterday  an  idea  of  the  object ; 
I  have  also  an  idea  of  it  to-day :  this  idea  is  evidently  not  another,  but 
the  very  same  idea.  Yet  an  intervening  time  elapsed  in  which  I  had 
it  not.  Where  was  the  idea  during  this  interval  1  It  must  have  been 
somewhere;  it  did  not  cease  to  exist;  otherwise  the  idea  1  had  yester- 
day could  not  be  the  sa?ne  idea;  no  more  than  a  man  I  see  alive  to-day 
can  be  the  same  whom  I  saw  yesterday,  if  the  man  has  died  in  the 
meanwhile.  Now  an  idea  cannot  be  conceived  to  exist  anywhere 
except  in  a  mind  ;  and  hence  here  must  exist  an  Universal  Mind,  in 
which  all  ideas  have  their  permanent  residence,  during  the  intervals  of 
their  conscious  presence  in  our  own  minds. 

That  Berkeley  here  confounded  sameness  numero  with  sameness 
specie,  that  is,  with  exact  resemblance,  and  assumed  the  former  when 
there  was  only  the  latter,  hardly  needs  be  more  particularly  pointed 
out.  He  could  never  have  brf)ached  this  strange  tlieory  if  he  had 
understood,  that  when  we  say  we  have  the  same  thought  to-day  which 
we  had  yesterday,  we  do  not  mean  the  same  individual  thought,  but  a 
thought  exactly  similar:  as  wo  say  that  we  have  the  same  illness  which 
we  had  last  year,  meaning  only  the  same  sort  of  illness. 

In  one  remarkable  instance  the  scientific  world  was  divided  into  two 
furiously  hostile  parties  by  an  ambiguity  of  langtiage  affecting  a  branch 
of  science  which,  more  completely  than  most  others,  enjoys  the  advan- 
tage of  a  precise  and  well-defined  terminology.  I  nsfi^r  to  the  famous 
dispute  respecting  the  vis  viva,  the  history  (tf  which  is  given  at  large  in 
Professor  Playfair's  Dissertation.  The  question  was  whuthi^r  tho. /"orce 
of  a  moving  body  was  proportional  (its  mass  being  given)  to  its  velocity 
simply,  or  to  the  square  of  its  velocity  :  and  the  ambiguity  was  in  the 


508  FALLACIES. 

word  Force.  "  One  of  the  effects,"  says  Playfaiz',  "  produced  by  a 
moving  body  is  proportional  to  the  square  of  the  velocity,  w^hile  another 
is  proportional  to  tlie  velocity  simply  :"  fi-om  w^hence  clearer  thinkers 
were  subsequently  led  to  establish  a  double  measure  of  the  efficiency 
of  a  moving  power,  one  being  called  vis  viva,  and  the  other  momentum. 
About  the  facts,  both  parties  were  from  the  first  agreed :  the  only  ques- 
tion was,  with  which  of  the  two  effects  the  term  force  should  be,  or 
could  most  conveniently  be,  associated.  But  the  disputants  were  by 
no  means  aware  that  this  was  all ;  they  thought  that  force  was  one  thing, 
the  production  of  effects  another  :  and  the  question,  by  which  set  of 
effects  the  force  which  produced  both  the  one  and  the  other  should  be 
measured,  was  supposed  to  be  a  question  not  of  terminology  but  of  fact. 

The  ambiguity  of  the  word  Infinite  is  the  real  fallacy  in  the  amusing 
logical  puzzle  of  Achilles  and  the  Tortoise,  a  puzzle  which  has  been 
too  hard  for  the  ingenuity  or  patience  of  many  philosophers,  and  among 
others  of  Dr.  Thomas  Brown,  who  considered  the  sophism  as  insoluble; 
as  a  sound  argument,  though  leading  to  a  palpable  falsehood:  not  seeing 
that  such  an  admission  would  be  a  reductio  ad  absurdum  of  the  reason- 
ing faculty  itself  The  fallacy,  as  Hobbes  hinted,  lies  in  the  tacit  as- 
sumption that  whatever  is  infinitely  divisible  is  infinite  ;  but  the  follow- 
ing solution  (to  the  invention  of  which  I  have  no  claim)  is  more  precise 
and  satisfactory. 

The  argument  is,  let  Achilles  run  ten  times  as  fast  as  the  tortoise, 
yet  if  the  tortoise  has  the  start,  Achilles  will  never  overtake  him.  For 
suppose  them  to  be  at  first  separated  by  an  interval  of  a  thousand  feet : 
when  Achilles  has  run  these  thousand  feet,  the  tortoise  will  have  got 
on  a  hundred ;  when  Achilles  has  run  those  hundred,  the  tortoise  will 
have  run  ten,  and  so  on  for  ever ;  therefore  Achilles  may  run  for  ever 
without  overtaking  the  tortoise. 

Now,  the  "  for  ever"  in  the  conclusion,  means,  for  any  length  of  time 
that  can  be  supposed  ;  but  in  the  premisses  "  ever"  does  not  mean  any 
length  of  time  :  it  means  any  number  of  subdivisions  of  time.  It  means 
that  we  may  divide  a  thousand  feet  by  ten,  and  that  quotient  again  by 
ten,  and  so  on  as  often  as  we  please ;  that  there  never  needs  be  an  end 
to  the  subdivisions  of  the  distance,  nor  consequently  to  those  of  the 
time  in  which  it  is  performed.  But  an  unlimited  number  of  subdivi- 
sions may  be  made  of  that  which  is  itself  limited.  The  argument 
proves  no  other  infinity  of  duration  than  may  be  embraced  within  five 
minutes.  As  long  as  the  five  minutes  are  not  expired,  what  remains 
of  them  may  be  divided  by  ten,  and  again  by  ten,  as  often  as  we  like, 
which  is  perfectly  compatible  with  their  being  only  five  minutes  alto- 
gether. It  proves,  in  short,  that  to  pass  through  this  finite  space  re- 
quires a  time  which  is  infinitely  divisible,  but  not  an  infinite  time ;  the 
confounding  of  which  distinction  Hobbes  had  already  seen  to  be  the 
gist  of  the  fallacy. 

The  following  ambiguities  of  the  word  right  (in  addition  to  the  ob- 
vious and  familiar  one  of  a  right  and  the  adjective  right)  are  abstracted 
from  a  forgotten  paper  of  my  own,  in  a  periodical  work : — 

"Speaking  morally,  you  are  said  to  have  a  right  to  do  a  thing,  if  all 
persons  are  morally  bound  not  to  hinder  you  from  doing  it.  But,  m 
another  sense,  to  have  a  right  to  do  a  thing,  is  the  opposite  of  having 
no  right  to  do  it,  viz.,  of  being  under  a  moral  obligation  to  forbeai- 
from  doing  it.     In  this  sense,  to  say  that  you  have  a  right  to  do  a 


FALLACIES   OF    CONFUSION.  509 

thing,  means  that  you  may  do  it  without  any  breach  of  duty  on  your 
part ;  that  other  persons  not  only  ought  not  to  hinder  you,  but  have  no 
cause  to  think  the  woree  of  you  for  doing  it.  This  is  a  perfectly  dis- 
tinct proposition  from  the  jireceding.  The  right,  which  you  hav«'  by 
virtue  of  a  duty  incumbent  upon  other  persons,  is  obviously  (piitc  a  differ- 
ent thing  from  a  riglit  consisting  in  the  absence  of  any  duty  incumbent 
upon  yourself  Yet  the  two  things  are  perjictually  confounded.  Thus 
a  man  will  say  he  has  a  right  to  publish  his  opinions  ;  which  may  be 
true  in  this  sense,  that  it  would  be  a  breach  of  duty  in  any  other  per- 
son to  interfere  and  prevent  the  publication  :  but  he  assumes  there- 
upon, that  in  publishing  his  opinions,  he  himself  violates  no  duty; 
which  may  either  be  true  or  false,  depending,  as  it  does,  upon  his 
having  taken  due  pains  to  satisfy  himself,  first,  that  the  opinions  are 
true,  and  next,  that  their  publication  in  this  manner,  and  at  this  par- 
ticular juncture,  will  probably  be  beneficial  to  the  interests  of  truth  on 
the  whole. 

"  The  second  ambiguity  is  that  of  confounding  a  right  of  any  kind, 
with  a  right  to  enforce  that  right  by  resisting  or  punishing  a  violation 
of  it.  Men  will  say,  for  example,  that  they  have  a  right  to  a  good 
government,  which  is  undeniably  true,  it  being  the  moral  duty  of  their 
governors  to  govern  them  well.  But  in  granting  this,  you  are  sup- 
posed to  have  admitted  their  right  or  liberty  to  turn  out  their  govern- 
ors, and  perhaps  to  punish  them,  for  having  failed  in  the  performance 
of  this  duty;  which,  far  from  being  the  same  thing,  is  by  no  means 
universally  true,  but  depends  upon  an  immense  number  of  varying  cir- 
cumstances, and  is  altogether  one  of  the  knottiest  questions  in  practical 
ethics."  This  example  is  (like  others  which  have  been  cited)  a  case 
of  fallacy  within  fallacy ;  it  involves  not  only  the  second  of  the  two 
ambiguities  pointed  out,  but  the  first  likewise. 

One  not  unusual  form  of  the  Fallacy  of  Ambiguous  Terms,  is  known 
technically  as  the  Fallacy  of  Composition  and  Division:  when  the 
same  term  is  collective  in  the  premisses,  distributive  in  the  conclusion, 
or  vice  versd:  or  when  the  middle  term  is  collective  in  one  premiss, 
distributive  in  the  other.  As  if  one  were  to  say  (I  quote  from  Arch- 
bishop Whately)  "All  the  angles  of  a  triangle  are  equal  to  two  right 
angles:  ABC  is  an  angle  of  a  triangle;  therefore  ABC  is  ctpial  to 

two  right  angles There  is  no  fallacy,"  continues  the  Archbishop, 

"  more  common,  or  more  likely  to  deceive,  than  the  one  now  before 
us.  The  form  in  which  it  is  most  usually  employed  is  to  establish 
some  truth,  separately,  concerning  each  single  member  of  a  certain 
chiss,  and  thence  to  infer  the  same  of  the  whole  collectively V  As  in 
the  argument  one  often  hears,  sometimes  from  persons  worthy  of  better 
things,  to  prove  that  the  world  could  do  without  great  men.  If  Co- 
lumbus (it  is  said)  had  never  lived,  America  would  still  have  been  dis- 
covered, at  most  only  a  few  years  later  ;  if  Newton  had  never  lived, 
some  other  person  would  have  discovered  the  law  of  gravitation  ;  and 
so  ff)rth.  Most  true;  these  things  would  have  been  done,  but  in  all 
probability  nf>t  until  some  one  had  again  been  found  with  the  (pialities 
of  a  Columbus  or  a  Newton.  Because  any  one  great  man  might  have 
had  his  place  supplied  by  the  help  of  others,  the  argument  concludes 
that  all  great  m(!n  could  have  been  dispensed  wth.  The  term  "great 
men"  is  distributive  in  the  premisses  and  collective  in  the  conclusion. 

"Such  also,"  says  Archbishop  Whately,  "is  the  fallacy  which  prob- 


510  FALLACIES. 

ably  operates  on  most  adventurers  in  lotteries;  e.g.,  'the  gaining  of  a 
high  prize  is  no  uncommon  occurrence ;  and  what  is  no  uncommon 
occurrence  may  reasonably  be  expected  ;  tlierefore  the  gaining  of  a 
high  prize  may  reasonably  be  expected  :'  the  conclusion  when  applied 
to  the  individual  (as  in  practice  it  is)  must  be  understood  in  the  sense 
of  '  reasonably  expected  hy  a  certain  individual;^  therefore  for  the 
major  premiss  to  be  true,  the  middle  term  must  be  understood  to  mean, 
'no  uncommon  occurrence  to  some  one  particular  ^Qx^on-^  whereas 
for  the  minor  (which  has  been  placed  first)  to  be  true,  you  must 
understand  it  of  'no  uncommon  occuiTence  to  some  one  or  otlier ;^ 
thus  you  will  have  the  Fallacy  of  Composition." 

"  This  is  a  Fallacy  with  which  men  are  extremely  apt  to  deceive 
ilieviselves ;  for  when  a  multitude  of  particulars  are  presented  to  the 
mind,  many  are  too  weak  or  too  indolent  to  take  a  comprehensive  view 
of  them ;  but  confine  their  attention  to  each  single  point,  by  turns ;  and 
then  decide,  infer,  and  act  accordingly :  e.  g.,  the  imprudent  spend- 
thrift, finding  that  he  is  able  to  afford  this,  or  that,  or  the  other  expense, 
forgets  that  all  of  them  together  will  ruin  him."  The  debauchee  de- 
stroys his  health  by  successive  acts  of  intemperance,  because  no  one  of 
those  acts  would  be  of  itself  sufficient  to  do  him  any  serious  harm.  A  sick 
person  reasons  with  himself,  "  one,  and  another,  and  another,  of  ray 
symptoms,  do  not  prove  that  I  have  a  fatal  disease ;"  and  practically 
concludes  that  all  taken  together  do  not  prove  it. 

§  2.  We  have  now  sufficiently  exemplified  one  of  the  principal 
Genera  in  this  Order  of  Fallacies ;  where,  the  source  of  error  being 
the  ambiguity  of  terms,  the  premisses  are  verbally  what  is  required  to 
support  the  conclusion,  but  not  really  so.  In  the  second  great  Fallacy 
of  Confusion  they  are  neither  verbally  nor  really  sufficient,  though, 
from  their  multiplicity  and  confused  arrangement,  and  still  oftener 
from  defect  of  memory,  they  are  not  seen  to  be  what  they  are-.  The 
fallacy  I  mean  is  that  of  Petitio  Principii,  or  begging  the  question; 
including  that  more  complex  and  not  uncommon  variety  of  it,  which 
is  termed  Reasoning  in  a  Circle. 

Petitio  Principii,  as  defined  by  Archbishop  Whately,  is  the  fallacy 
"  in  which  the  premiss  either  appears  manifestly  to  be  the  same  as  the 
conclusion,  or  is  actually  proved  from  the  conclusion,  or  is  such  as 
would  naturally  and  properly  so  be  proved."  By  the  last  clause  I 
presume  is  meant,  that  it  is  not  susceptible  of  any  other  proof;  for 
otherwise,  there  would  be  no  fallacy.  To  deduce  from  a  proposition, 
propositions  from  which  it  would  itself  more  naturally  be  deduced,  is 
often  an  allowable  deviation  fi'om  the  usual  didactic  ordei' ;  or  at  most, 
what,  by  an  adaptation  of  a  phrase  familiar  to  mathematicians,  may  be 
called  a  logical  inelegance. 

The  employment  of  a  proposition  to  prove  that  upon  which  it  is 
itself  dependent  for  proof,  by  no  means  implies  the  degree  of  mental 
imbecihty  which  might  at  first  be  supposed.  The  difficulty  of  com- 
prehending how  this  fallacy  could  possibly  be  committed,  disappears 
when  we  reflect  that  all  persons,  even  philosophers,  hold  a  great  num- 
ber of  opinions  without  exactly  recollecting  how  they  came  by  them. 
Believing  that  they  have  at  some  foiTner  time  veiified  them  by  sufficient 
evidence,  but  having  forgotten  what  the  evidence  was,  they  may  easily 
be  betrayed  into  deducing  from  them  the  very  propositions  which  are 


FALLACIES    OF    CONFUSION.  511 

alone  capable  of  serving  as  premisses  for  their  establishment.  An 
example  is  jj^ven  by  Archbishop  Whately  :  "  As  if  one  should  attempt 
to  prove  the  being  of  a  Giul  i'nmx  the  authority  of  Holy  Writ;"  which 
might  easily  happen  to  one  with  whom  both  propositions,  as  funda- 
mental tenets  of  his  religion,  stand  upon  the  same  ground  of  familiar 
and  traditional  belief. 

Arguing  in  a  circle,  however,  is  a  stronger  case  of  the  fallacy,  and 
implies  more  than  the  mere  passive  reception  of  a  premiss  by  one  who 
does  not  remember  how  it  is  to  be  proved.  It  implies  an  actual 
attempt  to  prove  two  propositions  reciprocally  from  one  another;  and 
is  seldom  resorted  to,  at  least  in  express  terms,  by  any  person  in  his 
own  speculations,  but  is  committed  by  those  who,  being  haixl  pressed 
by  an  adversary,  are  forced  into  giving  reasons  for  an  opinion  of  which, 
when  they  began  to  argue,  they  had  not  sufficiently  considered  the 
grounds.  As  in  the  following  example  from  Archbishop  Whately : 
"  Some  mechanicians  attempt  to  prove  (what  they  ought  to  lay  down 
as  a  probable  liut  doubtful  hypothesis*)  that  every  particle  of  matter 
gravitates  equally:  'why!'  'because  those  bodies  which  contain  more 
particles  ever  gravitate  more  strongly,  i.  e.  are  heavier:'  'but  (it  may 
be  urged),  those  which  are  heaviest  are  not  always  more  bulky;'  'no, 
but  they  contain  more  pai'ticles,  though  more  closely  condensed  :' 
'  how  do  you  know  that  V  'because  they  are  heavier  :'  '  how  docs  that 
prove  itl'  'because  all  particles  of  matter  gravitating  equally,  that 
mass  which  is  specifically  the  heavier  must  needs  have  tlie  more  of 
them  in  the  same  space.'  "  It  appears  to  me  that  the  fallacious 
reasoner,  in  his  private  thoughts,  would  not  be  likely  to  proceed  beyond 
the  first  step.t  He  would  acquiesce  in  the  sufficiency  of  the  reason 
first  given,  "  bodies  which  contain  more  particles  are  heavier."  It  is 
when  he  finds  this  questioned,  and  is  called  upon  to  prove  it,  without 
knowing  how,  that  he  tries  to  establish  his  premiss  by  supposing 
proved  what  he  is  attempting  to  prove  by  it.  The  most  effectual  way, 
in  fact,  of  exposuig  a  Petitio  Principii,  when  circumstances  allow  of 
it,  is  by  challenging  the  reasoner  to  prove  his  premisses ;  which  if  he 
attempts  to  do,  he  is  necessarily  driven  into  arguing  in  a  circle. 

It  is  not  uncommon,  however,  for  thinkers,  and  those  not  of  the  low- 
est description,  to  be  led,  even  in  their  own  thoughts,  not  indeed  into 
formally  proving  each  of  two  propf)sitions  fxom  the  other,  but  into  ad- 
mitting propositions  which  can  only  be  so  proved.  In  the  preceding 
example  the  two  together  form  a  complete  and  consistent,  though  hy- 
pothetical, explanation  of  the  facts  concerned.  And  the  tendency  to 
mistake  mutual  coherency  for  truth ;  to  trust  one's  safety  to  a  strong 
chain  although  it  has  no  point  of  sujjport ;  is  at  the  bottom  of  much 
which,  when  reduced  to  the  strict  forms  of  argumentation,  can  exhibit 
itself  no  otherwise  than  as  reasoning  in  a  circle.  All  experience  bears 
testimony  to  the  enthralling  effect  of  neat  concatenation  in  a  system  of 

*  No  longfir  even  a  probable  liypothesis,  but  (since  the  establishment  of  the  atomic 
lheor>')  opposed  to  all  prol)ability  ;  it  t)eing  now  certain  tliat  the  integrant  particles  of  dif- 
ferent substances  gravitiite  unequally.  It  is  true  that  these  particles,  though  real  minima 
for  the  purposes  of  chemical  combination,  may  not  be  the  ultimate  particles  of  the  sub- 
stance ;  and  this  doubt  alone  renders  the  hyyolhesis  admissible,  even  as  an  hypothesis. 

t  I  have  found,  however,  an  argument  of  this  exact  typo  in  a  BridgewaUr  Treaiine  :— 
"  Ice  and  sijver,  under  the  same  volume,  contain  very  unequal  portions  of  matter,  the  sil- 
ver being  ten  times  as  heavy  as  the  ice.  The  vacuities  in  the  ice,  therefore,  must  be  very 
much  greater  than  those  in  the  silver." 


512  FALLACIES. 

doctrines,  and  the  difficulty  with  which  men  admit  the  persuasion  that 
anything  which  holds  so  well  together  can  possibly  fall. 

Since  every  case  where  a  conclusion  which  can  only  be  proved  from 
certain  premisses  is  used  for  the  proof  of  those  premisses,  is  a  case  of 
petitio  jJrincipii,  that  fallacy  includes  a  very  great  proportion  of  all  in- 
coiTect  reasoning.  It  is  necessary,  for  completing  our  view  of  the 
fallacy,  to  exemplify  some  of  the  disguises  under  which  it  is  accustomed 
to  mask  itself,  and  to  escape  exposure. 

A  proposition  would  not  be  admitted  by  any  person  in  his  senses  as 
a  corollary  from  itself,  unless  it  were  expressed  in  language  which 
made  it  seem  different.  One  of  the  commonest  modes  of  so  expressing 
it,  is  to  present  the  proposition  itself,  in  abstract  terms,  as  a  proof  of 
the  same  proposition  expressed  in  concrete  language.  This  is  a  very 
frequent  mode  not  only  of  pretended  proof,  but  of  pretended  explana- 
tion ;  and  is  parodied  by  Moliere  vdien  he  makes  one  of  his  absurd 
physicians  say,  "I'opium  endormit  parcequ'il  a  une  vertu  soporifique," 
or,  in  the  amusing  doggerel  quoted  by  Mr.  Whewell — 

Mihi  demandatur 

A  (loctissimo  doctore, 
Quare  opium  facit  dormire  ; 

Et  ego  respondeo, 

Quia  est  in  eo 

Virtus  dormitiva, 
Cujus  natura  est  sensus  assopire. 

The  words  Nature  and  Essence  are  grand  instruments  of  this  mode 
of  begging  the  question.  As  in  the  well-known  al"gument  of  the  scho- 
lastic theologians,  that  the  mind  thinks  always,  because  the  essence  of 
the  mind  is  to  think.  Locke  had  to  point  out,  that  if  by  essence  is 
here  meant  some  property  which  must  manifest  itself  by  actual  exer- 
cise at  all  times,  the  premiss  is  a  direct  assumption  of  the  conclusion ; 
while  if  it  only  means  that  to  think  is  the  distinctive  property  of  a 
mind,  there  is  no  connexion  between  the  premiss  and  the  conclusion, 
since  it  is  not  necessary  that  a  distinctive  property  should  be  pei-pet- 
ually  in  action. 

The  following  is  one  of  the  modes  in  which  these  abstract  tei-ms, 
Nature  and  Essence,  are  used  as  instruments  of  this  fallacy.  Some 
particular  properties  of  a  thing  are  selected,  more  or  less  arbitrarily, 
to  be  termed  its  nature  or  essence  ;  and  when  this  has  been  done,  these 
properties  are  supposed  to  be  invested  with  a  kind  of  indefeasible- 
ness  ;  to  have  become  paramount  to  all  the  other  properties  of  the 
thing,  and  incapable  of  being  prevailed  over  or  counteracted  by  them. 
As  when  Aristotle,  in  a  passage  which  we  have  already  cited  from  Mr. 
Whewell,  "  decides  that  there  is  no  void  on  such  arguments  as  this : 
in  avoid  there  could  be  no  difference  of  up  and  down;  for  as  in 
nothing  there  are  no  differences,  so  there  are  none  in  a  privation  or 
negation;  but  a  void  is  merely  a  privation  or  negation  of  matter; 
therefore,  in  a  void,  bodies  could  not  move  up  and  down,  which  it  is 
in  their  nature  to  do."*  In  other  words  ;  It  is  the  nature  of  bodies  to 
move  up  and  down,  ergo  any  physical  fact  which  supposes  them  not 
so  to  move,  cannot  be  authentic.  This  mode  of  reasoning,  by  which 
a  bad  generalization  is  made  to  overrule  all  facts  which  contradict  it, 
is  petitio  principii  in  one  of  its  most  palpable  forms. 

*  Wheweix's  History  of  the  Inductive  Scietices,  i,  44. 


FALLACIES    OF    CONFUSION.  513 

None  of  the  modes  of  assuming  what  should  be  proved  are  in  more 
frequent  use  than  what  are  termed  by  Beutham  "  question-begging 
appelhitives  ;"  names  which  beg  the  question  under  the  guise  of  stating 
it.  Tlie  most  potent  of  these  are  such  as  have  a  hiudatory  or  vituj)e- 
rative  character.  For  instance,  in  pohtics,  the  word  Innovation.  Tlie 
dictionary  meaning  of  this  tei'm  being  merely  "  a  change  to  something 
new,"  it  is  difficult  for  the  defenders  even  of  the  most  salutary  im- 
provement to  deny  that  it  is  an  innovation ;  yet  the  word  having  ac- 
quired in  common  usage  a  vituperative  connotation  in  addition  to  its 
dictionary  meaning,  the  admission  is  always  constioied  as  a  large  con- 
cession to  the  disadvantage  of  the  thing  proposed. 

The  following  passage  from  the  argument  in  refutation  of  the  Epi- 
cureans, in  the  second  book  of  Cicero  Dc  Finihus,  affords  a  fine  exam- 
ple of  this  sort  of  fallacy.  "  Et  quidem  illud  ipsum  non  nimium  probo 
(et  tantum  patior)  philosophum  loqui  de  cupiditatibus  finiendis.  An 
potest  cupiditas  finiri  ?  tollonda  est,  atque  exfrahcnda  radicitus.  Quis 
est  enim,  in  quo  sit  cupiditas,  quin  recte  cupidus  dici  possit  1  Ergo  et 
avarus  erit,  sed  finite:  adulter,  vcrum  habcbit  modum:  et  luxuriosus 
eodem  modo.  Qualis  ista  philosophia  est,  qua^  non  interitum  affcrat 
pravitatis,  sed  sit  contenta  mediocritate  vitiorum  ]"  The  (juestion  was 
whether  certain  desires,  when  kept  within  definite  bounds,  are  vices 
or  not ;  and  the  argument  decides  the  point  by  applying  to  them  a 
word  [cupiditas)  which  implies  y\ce.  It  is  shown,  however,  in  the 
remarks  which  follow,  that  Cicero  did  not  intend  this  as  a  serious 
argument,  but  as  a  criticism  on  what  he  deemed  an  inappropriate 
expression.  "  Rem  ipsam  prorsus  probo  :  elegantiam  desidero.  Ap- 
pellet  hoec  dcsideria  naturcB  i  cupiditatis  nomen  servet  alio,"  &c.  But 
many  persons,  both  ancient  and  modem,  have  employed  this,  or  some- 
thing equivalent  to  it,  as  a  real  and  conclusive  argument.  We  may 
remark  that  the  passage  respecting  cupiditas  and  cupidus  is  also  an 
example  of  another  fallacy  already  noticed,  that  of  Paronymous  Terms. 

Many  more  of  the  arguments  of  the  ancient  moralists,  and  especially 
of  the  Stoics,  fall  within  the  definition  of  Petitio  Principii.  In  the  Dc 
Finibus,  for  example,  which  I  continue  to  quote  as  being  probably  the 
best  extant  exemplification  at  once  of  the  doctrines  and  the  methods  of 
the  schools  of  Gi-eek  philosophy  existing  at  that  time ;  what  arc  wo  to 
think  of  the  arguments  of  Cato  in  the  third  book,  derived  from  comnnjn 
notions :  That  if  virtue  were  not  happiness,  it  could  not  be  a  thing  to 
boast  of:  That  if  death  or  pain  were  evils,  it  woidd  be  impossible  not 
to  fear  them,  and  it  covdd  not,  therefore,  be  laudable  to  despise  them, 
&c.  In  one  way  of  viewing  these  arguments,  they  may  be  regarded 
as  appeals  to  the  authority  of  the  general  sentiment  of  mankind,  which 
had  stamped  its  approval  upon  certain  actions  and  characters  by  the 
phrases  referred  to ;  but  that  such  could  have  been  the  meaning  in- 
tended is  very  unlikely,  considering  the  contempt  of  the  ancient  philo- 
sophers for  vulgar  opinion.  In  any  other  sense  they  are  clear  cases  of 
Petitio  Principii,  since  the  word  laudable,  and  tho  idea  of  boasting, 
imply  pi'inciples  of  conduct ;  and  practical  maxims  can  finly  be  proved 
from  speculative  truths,  namely,  from  the  properties  of  the  suljject 
matter,  and  cannot,  therefore,  be  employed  to  prove  those  properties. 
As  well  might  it  be  argued  that  a  government  is  good  beciiust^  we 
ought  to  support  it,  or  that  there  is  a  God  because  it  is  our  duty  to 
pray  to  him. 
3  T 


514  FALLACIES. 

It  is  assumed  by  all  the  disputants  in  the  Ve  Finibus  as  the  founda- 
tion of  the  inquiry  into  the  sumvium  bonum,  that  "  sapiens  semper 
beatus  est."  The  idea  that  wisdom  could  be  consistent  with  unhap- 
piness,  was  always  rejected  as  inadmissible :  the  reason  assigned  by 
one  of  the  interlocutors,  near  the  beginning  of  the  third  book,  being, 
that  if  the  wise  could  be  unhappy,  there  was  not  much  use  in  jiursuing 
wisdom.  But  by  unhappiness  they  did  not  mean  pain  or  suffering  ;  to 
that,  it  was  granted  that  the  wisest  person  was  liable  in  common  with 
others  :  he  was  happy,  because  in  possessing  wisdom  he  had  the  most 
valuable  of  possessions,  the  most  to  be  sought  and  prized  of  all  things, 
and  to  possess  the  most  valuable  thing  was  to  be  the  most  happy.  By 
laying  it  down,  therefore,  at  the  commencement  of  the  inquiry,  that  the 
sage  must  be  happy,  the  disputed  question  respecting  the  summum 
honum  was  in  fact  begged ;  with  the  further  assumption,  that  pain  and 
suffering,  so  far  as  they  can  coexist  with  wisdom,  are  not  unhappiness, 
and  are  no  evil. 

The  following  are  additional  instances  of  Petitio  Principii,  under 
more  or  less  of  disguise. 

Plato,  in  the  Sophistes,  attempts  to  prove  that  things  may  exist  which 
are  incorporeal,  by  the  argument  that  justice  and  wisdom  are  incorpo- 
real, and  justice  and  wisdom  must  be  something.  Here,  if  by  some- 
thing be  meant,  as  Plato  did  in  fact  mean,  a  thing  capable  of  existing 
in  and  by  itself,  and  not  as.  a  quality  of  some  other  thing,  he  begs  the 
question  in  asserting  that  justice  and  wisdom  must  be  something :  if 
he  means  anything  else,  his  conclusion  is  not  proved.  This  fallacy 
might  also  be  classed  under  ambiguous  middleterm  ;  something,  in  the 
one  premiss,  meaning  some  substance,  in  the  other,  merely  some  object 
of  thought,  whether  substance  or  attribute. 

It  was  formerly  an  argument  employed  in  proof  of  what  is  now  no 
longer  a  popular  doctrine,  the  infinite  divisibility  of  matter,  that  every 
portion  of  matter,  however  small,  must  at  least  have  an  upper  and  an 
under  sm-face.  Those  who  used  this  argument  did  not  see  that  it 
assumed  the  very  point  in  dispute,  the  impossibility  of  aniving  at  a 
minimum  of  thickness;  for  if  there  be  a  minimum,  its  upper  and  under 
surface  will  of  course  be  one :  it  will  be  itself  a  surface  and  no  more. 
The  argument  owes  its  very  considerable  plausibility  to  this,  that  the 
premiss  does  actually  seem  more  obvious  than  the  conclusion,  although 
really  identica,!  with  it.  As  expressed  in  the  premiss,  the  proposition 
appeals  directly  and  in  concrete  language  to  the  incapacity  of  the 
human  imagination  for  conceiving  a  minimum.  Viewed  in  this  light, 
it  becomes  a  case  of  the  u  j^^iori  fallacy  or  natural  prejudice,  that 
whatever  cannot  be  conceived  cannot  exist.  Every  Fallacy  of  Confu- 
sion (it  is  almost  unnecessary  to  repeat)  will,  if  cleared  up,  become  a 
fallacy  of  some  other  sort ;  and  it  will  be  found  of  deductive  or  ratio- 
cinative  fallacies  generally,  that  when  they  mislead  there  is  mostly,  as 
in  this  case,  a  latent  fallacy  of  some  other  description  lurking  under 
them,  by  virtue  of  which  chiefly  it  is  that  the  verbal  juggle  which  is 
the  outside  or  body  of  this  kind  of  fallacy,  passes  undetected. 

Euler's  Algebra,  a  book  otherwise  of  gi-eat  merit,  but  full,  to  over- 
flowing, of  logical  errors  in  respect  to  the  foundation  of  the  science, 
contains  the  follovdng  argument  to  prove  that  minus  multiplied  by  minus 
^weaplus,  a  doctrine  the  opprobrium  of  all  mathematicians  who  are  not 
philosophers,  and  which  Euler  had  not  a  glimpse  of  the  true  method  of 


FALLACIES    OF    CONFUSION.  516 

proving.  He  says,  jnhius  multlplictl  by  7ninus  cannot  give  minus;  for 
minus  multiplied  by  j>lus  gives  minus,  and  minus  nmltiplicd  by  minus 
cannot  give  the  same  product  as  minus  multi])licd  by  ])lus.  Now  one 
is  obliged  to  ask,  wliy  minus  multiplird  ])y  minus  must  give  any  pro-, 
duct  at  all  I  and  if  it  does,  wliy  its  pioduct  caimot  be  the  same  as  that 
of  minus  multiplied  by  plus?  for  this  would  seem,  at  the  first  glance, 
not  more  absurd  than  that  minus  by  minus  should  give  the  same  as 
plus  by  plus,  the  proposition  whlcli  Euler  prefers  to  it.  The  premiss 
requires  proof,  as  much  as  the  conclusion :  nor  can  it  be  proved,  except 
by  tliat  more  comprehensive  view  of  the  nature  of  multiplication,  and 
of  algebraic  processes  in  general,  which  would  also  supply  a  far  better 
proof  of  the  mysterious  doctrine  which  Euler  is  here  endeavoring  to 
demonstrate. 

A  very  striking  instance  of  reasoning  in  a  circle  is  that  of  some  ethical 
philosophers,  who  first  take  for  their  standard  of  moral  truth  what,  being 
the  general,  they  deem  to  be  the  natural  or  instinctive,  sentiments  and 
perceptions  of  mankind,  and  then  explain  away  the  numerous  instances 
of  divergence  from  their  assumed  standard  by  representing  them  as 
cases  in  which  the  perceptions  are  unhealthy.  Some  particular  mode 
of  conduct  or  feeling  is  affirmed  to  be  unnatural ;  why?  because  it  is 
abhorrent  to  the  universal  and  natural  sentiments  of  mankind.  Find- 
ing no  such  sentiment  in  yourself,  you  question  the  fact;  and  the 
answer  is  (if  your  antagonist  is  polite)  that  you  are  an  exception,  a 
peculiar  case.  But  neither  (say  you)  do  I  find  in  the  people  of  some 
other  country,  or  of  some  former  ago,  any  such  feeling  of  abhorrence ; 
"aye,  but  their  feelings  were  sophisticated  and  unhealthy." 

One  of  the  most  notable  specimens  of  reasoning  in  a  circle  is  the 
doctrine  of  Hobbes,  Rousseau,  and  others,  which  rests  tlie  obligations 
by  which  human  beings  are  bound  as  members  of  society,  upon  a  sup- 
posed social  compact.  I  wave  the  consideration  of  the  fictitious  nature 
of  the  compact  itself;  but  when  a  philosopher  (as  Hobbes  does  through 
the  whole  Leviathan)  elaborately  deduces  the  obligation  of  obeying 
the  sovereign,  not  from  the  necessity  or  utility  of  doing  so,  but  from  a 
promise  supposed  to  have  been  made  by  our  ancestors,  on  renouncing 
savage  life  and  agreeing  to  establisli  a  political  society,  it  is  impossible 
not  to  retoit  by  the  question,  why  are  we  bound  to  keep  a  promise 
made  for  us  by  others  I  or  why  bound  to  keep  a  promise  at  all  ?  No 
satisfactoiy  ground  can  be  assigned  for  the  obligation,  except  the  mis- 
chievous consequences  of  the  absence  of  faith  and  mutual  confidence 
among  mankind.  We  are,  therefore,  brought  round  to  the  interests  of 
society,  as  the  ultimate  ground  of  the  obligation  of  a  promise;  and  yet 
those  interests  are  not  admitted  to  be  a  sufficient  justification  for  the 
existence  of  government  and  law.  Witliout  a  promise  it  is  thought 
that  we  should  not  be  bound  to  that  without  which  tlio  existence  of 
society  would  be  impossible,  namely,  to  yield  a  general  obedience  to 
the  laws  therein  established ;  and  so  necessary  is  the  promise  deemed, 
that  if  none  has  actually  been  made,  some  additional  safety  is  supposed 
to  be  given  to  the  foundations  of  society  by  feigning  one. 

§  3.  Two  principal  subdivisions  of  the  class  of  Fallacies  of  Con- 
fusion having  been  disposed  of;  there  remains  a  third,  in  whioh  the 
confusion  is  not,  as  in  the  Fallacy  of  Ambiguity,  in  misconceiving  the 
import  of  the  premisses,  nor,  as  in  Pctitio  Principii,  in  forgetting  what 


516  FALLACIES. 

the  premisses  are,  but  in  mistaking  the  conclusion  which  is  to  be  proved. 
This  is  the  fallacy  of  Ignoratio  Elcnchi,  in  the  widest  sense  of  the 
phrase  ;  also  called  by  Archbishop  Whately  the  fallacy  of  Irrelevant 
Conclusion.     His  examples  and  remarks  are  highly  worthy  of  citation. 

"  Various  kinds  of  propositions  are,  according  to  the  occasion,  sub- 
stituted for  the  one  of  which  proof  is  required :  sometimes  the  par- 
ticular for  the  univei-sal;  sometimes  a  proposition  with  different  terms; 
and  various  are  the  contrivances  employed  to  effect  and  to  conceal  this 
substitution,  and  to  make  the  conclusion  which  the  sophist  has  dra^vn, 
answer  practically  the  same  purpose  as  the  one  he  ought  to  have 
established.  We  say,  '  practically  the  same  purpose,'  because  it  will 
very  often  happen  that  some  emotion  will  be  excited,  some  sentiment 
impressed  on  the  mind  (by  a  dextrous  employment  of  this  fallacy), 
such  as  shall  bring  men  into  the  disposition  requisite  for  your  purpose  ; 
though  they  may  not  have  assented  to,  or  even  stated  distinctly  in  their 
own  minds,  the  proposition  which  it  was  your  business  to  establish. 
Thus  if  a  sophist  has  to  defend  one  who  has  been  guilty  of  some 
serious  offence,  which  he  \%'ishes  to  extenuate,  though  he  is  unable  dis- 
tinctly to  prove  that  it  is  not  such,  yet  if  he  can  succeed  in  malcingthe 
audience  lavgh  at  some  casual  matter,  he  has  gained  practically  the 
same  point.  So  also  if  any  one  has  pointed  out  the  extenuating  cir- 
cumstances in  some  particular  case  of  offence,  so  as  to  show  that  it 
differs  widely  from  the  generality  of  the  same  class,  the  sophist,  if  he 
find  himself  unable  to  disprove  these  circumstances,  may  do  away  the 
force  of  them,  by  simply  referring  tJie  action  to  that  very  class,  which 
no  one  can  deny  that  it  belongs  to,  and  the  very  name  of  which  will 
excite  a  feeling  of  disgust  sufficient  to  counteract  the  extenuation ; 
e.  g.,  let  it  be  a  case  of  peculation,  and  that  many  mitigating  circum- 
stances have  been  brought  forward  which  cannot  be  denied ;  the 
sophistical  opponent  will  reply,  '  Well,  but  after  all,  the  man  is  a 
rogue,  and  there  is  an  end  of  it ;'  now  in  reality  this  was  (by  hypoth- 
esis) never  the  question ;  and  the  mere  assertion  of  what  was  never 
denied,  ought  not,  in  fairness,  to  be  regarded  as  decisive :  but,  prac- 
tically, the  odiousness  of  the  word,  arising  in  great  measure  from  the 
association  of  those  very  circumstances  which  belong  to  most  of  the 
class,  but  which  we  have  supposed  to  be  absent  in  this  particuJar  in- 
stance, excites  precisely  that  feeling  of  disgust,  which  in  effect  desti'oys 
the  force  of  the  defence.  In  like  manner,  we  may  refer  to  this  head 
all  cases  of  improper  appeal  to  the  passions,  and  everything  else  which 
is  mentioned  by  Aristotle  as  extraneous  to  the  matter  in  hand  (efw 
rov  Trpdyfiarog). 

"  A  good  iuvStance  of  the  employment  and  exposure  of  this  fallacy 
occurs  in  Thucydides,  in  the  speeches  of  Cleon  and  Diodotus  con- 
cerning the  Mitylenaeans  :  the  former  (over  and  above  his  appeal  to 
the  angry  passions  of  his  audience)  urges  the  justice  of  putting  the  re- 
volters  to  death ;  which,  as  the  latter  remarked,  was  nothing  to  the 
purpose,  since  the  Athenians  were  not  sitting  in  jiidgment,  but  in  de- 
liberatiov,  of  which  the  pr-oper  end  is  expedic7tcy. 

"  It  is  evident  that  ignoratio  elcnchi  may  be  employed  as  well  for 
the  apparent  refutation  of  your  opponent's  proposition,  as  for  the  ap- 
parent establishment  of  your  own  ;  for  it  is  substantially  the  same 
thing,  to  prove  what  was  not  denied  or  to  disprove  what  was  not 
asserted :  the  latter  practice  is  not  less  common,  and  it  is  more  ofien- 


FALLACIES    OF    CONFUSION.  517 

sive,  because  it  frequently  amounts  to  a  jiersonal  afTiont,  in  attriliuting 
to  a  person  opinions,  Sec,  wliii-U  ho  prrliaps  holds  in  ahhorniice. 
Thus,  when  in  a  discussion  one  party  vindicates,  on  the  ground  of 
general  expediency,  a  particular  instance  of  resistance  to  govern- 
ment in  a  case  of  intolerable  oppression,  the  op[)oncnt  inay  gravely 
maintain,  that  '  we  ought  not  to  do  evil  that  good  may  come ;'  a 
proposition  which  of  course  had  never  been  denied,  the  point  in  dis- 
pute being,  '  wliether  resistance  iu  this  paiticular  caac  were  doing  evil 
or  not.'  " 

The  works  of  controversial  writers  are  seldom  free  from  this  fallacy. 
They  join  issue  on  the  wrong  point,  or  do  not  join  issue  at  all.  Tho 
attempts,  for  instance,  to  disprove  the  population  doctrines  of  Malthus, 
have  been  mostly  cases  of  igiwratio  ehnchi.  Malthus  has  b«'i'u  sup- 
posed to  be  refuted  if  it  could  be  shown  that  in  some  couutrii-s  or  ages 
population  has  been  nearly  stationary  ;  as  if  he  had  asserted  tliat  popu- 
lation always  increases  in  a  given  ratio,  or  had  not  expressly  declared 
that  it  increases  only  in  so  fju-  as  it  is  not  restrained  by  prudence,  or 
kept  down  by  poverty  and  disease.  Or,  perhaps,  a  great  collection  of 
facts  is  produced  to  prove  that  in  some  one  country  the  people  aro 
better  oft'  with  a  dense  population  than  they  are  in  another  country 
with  a  thin  0!ie  ;  or  that  the  people  have  become  more  numerous  and 
better  off'  at  the  same  time.  As  if  the  assertion  were  that  a  dense  popu- 
lation could  not  possibly  be  well  oft':  as  if  it  were  not  part  of  the  very 
doctrine,  and  essential  to  it,  that  where  there  is  a  more  abundant  cap- 
ital there  may  be  a  greater  population  without  any  increase  of  poverty, 
or  even  with  a  diminution  of  it. 

The  favorite  argument  against  Berkeley's  theory  of  the  non-existence 
of  matter,  and  the  most  popularly  eff'ective,  next  to  a  "  grin"* — an 
argument,  moreover,  which  is  not  confined  to  "  coxcombs,"  nor  to 
men  like  Samuel  Johnson,  of  practical  understanding,  without  any 
particular  turn  for  metaphysical  speculation,  but  is  the  stock  argument 
of  the  Scotch  school  of  metaphysicians,  is  a  palpable  ignuratio  eUnchi. 
The  argument  is  perhaps  as  freciuently  expressed  by  gesture  as  by 
words,  and  one  of  its  commonest  forms  consists  in  knocking  a  stick 
against  the  ground.  This  short  and  easy  confutation  overlooks  the 
fact,  that  in  denying  matter,  Berkeley  did  not  deny  anything  to  which 
our  senses  bear  witness,  and  therefore  cannot  be  answen.'d  by  any 
appeal  to  them.  His  skepticism  related  to  the  supposed  substratum, 
or  hidden  cause  of  the  appearances  perceived  by  our  senses  :  tlie  evi- 
dence of  which,  whatever  may  bo  its  conclusiveness,  is  ceitaiidy  not 
the  evidence  of  sense.  And  it  will  always  remain  a  .signal  proof  of 
the  want  of  metaphysical  profundity  <jf  Reid,  Stewart,  and,  I  am  sorry 
to  add,  of  Brown,  that  they  should  have  persi.sted  iu  asserting  that 
Berkeley,  if  he  believed  his  own  doctrine,  wa-s  bound  to  walk  into  the 
kennel,  or  run  his  head  against  a  post.  As  if  men  who  do  not  recog- 
nize an  occult  cause  of  their  sensations  could  not  j)ossibly  believe  that 
a  fixed  order  subsists  among  the  sensations  themselves.  Such  a  want 
of  comprehension  of  the  distinction  between  a  thing  and  its  sensible 
manifestation,  or,  in  transcendental  language,  between  the  noumenon 
and  the  j)henom(!non,  would  be  impossible  to  even  the  dullest  disciple 
of  Kant  or  Coleridge. 

*  And  coxcombs  vanquish  Berkeley  with  a  grin. — (Pope.) 


518  FALLACIES. 

It  would  be  easy  to  add  a  greaternumber  of  examples  of  this  fallacy, 
as  well  as  of  the  others  which  I  have  attempted  to  characterize.  But 
a  more  copious  exemplification  does  not  seem  to  be  necessaiy  ;  and 
the  intelligent  reader  will  have  little  difficulty  in  adding  to  the  cata- 
logue fi'om  his  own  reading  and  experience.  We  shall  therefore  here 
close  our  exposition  of  the  general  principles  of  logic,  and  proceed 
at  once  to  the  supplemental  inquiry  which  is  necessary  to  complete 
our  design. 


BOOK  VI. 

ON  THE  LOGIC  OF  THE  MORAL  SCIENCES. 


"  Une  propriety  fondamentale  que  jc  dois  fairc  remarquer  d^s  ce  moment  dans  cc  que 
i'ai  appele  la  philosophic  positive,  et  qui  doit  sans  doiite  lui  meriter  plus  que  toute  autre 
rattention  gencrale,  puisqu'elle  est  aujourd'hui  la  plus  iinportante  pour  la  pratique,  c'est 
qu'elle  peut  6tre  considcree  comme  la  seule  base  solide  de  la  reorRanisatioii  sociale  qui  doit 
tenniner  I'etat  de  crise  dans  lequcl  se  trouvent  depuis  si  long-temps  les  nations  Ics  plus 

civilisees Tant  que  les  intelligences  individuelles  n'auront  pas  adherfe  par  un  asscnti- 

ment  unanime  a  un  certain  noinbre  d'ldces  generales  capablesde  former  unc  doctrine  sociale 
commune,  on  ne  peut  se  dissimuler  que  I'ctat  des  nations  restera.de  toute  nccegsitc,essen- 
tiellement  revolutionnaire,  malgre  tous  les  palliatifs  poliliques  qui  pourront  6tre  adoptds,  et 
ne  comportera  reeilement  que  des  institutions  provisoires.  II  est  egalement  certain  que  si 
cette  reunion  des  esprits  dans  une  m^me  communion  de  principes  peut  unc  fois  6tre 
obtenue,  les  institutions  convenables  en  decouleront  necessairement,  sans  donner  lieu  i 
aucune  secousse  grave,  le  plus  grand  desordre  6tant  dejk  dissipe  par  ce  seul  fait." — Comtk, 
Cows  de  Philosophie  Positive,  Ire  le(^n. 


CHAPTER  I. 

INTRODUCTORY  KEM.ARKS. 


§  1.  Principles  of  Evidence  anJ  Theories  of  Method  are  not  to  be 
constructed  d  priori.  The  laws  of  our  rational  faculty,  like  those  of 
every  other  natural  agency,  are  only  learnt  by  seeing  the  agent  at 
work.  The  earHcr  achievements  of  science  were  made  without  the 
conscious  observance  of  any  Scientific  Method  ;  and  we  should  never 
have  known  by  what  process  truth  is  to  be  ascertained,  if  we  had  not 
previously  ascertained  many  truths.  But  it  was  only  the  easier  pro- 
blems which  could  be  thus  resolved  :  natural  sagacity,  when  it  tried  its 
strength  again.st  the  more  difficult  ones,  cither  failed  altogether,  or  if 
it  succeeded  here  and  there  in  obtaining  a  solution,  had  no  sun-  means 
of  convincing  others  that  its  solution  was  correct.  In  scientific  in- 
vestigation, as  in  all  other  works  of  human  skill,  the  way  of  attaining 
the  end  is  seen  as  it  were  instinctively  by  superior  minds  in  some 
comparatively  simple  case,  and  is  then,  by  judicious  generalization, 
adapted  to  the  variety  of  complex  cases.  We  learn  to  do  a  thing  in 
difficult  circumstances,  by  attending  to  the  manner  in  which  we  have 
spontaneously  done  the  same  thing  in  easy  ones. 

This  truth  is  exemplified  by  the  history  of  the  various  branches  of 
knowledge  which  have  successively,  in  the  ascending  order  of  their 
complication,  ass-limed  the  character  of  sciences  ;  and  will  doubtless 
receive  fresh  confirmation  from  those,  of  which  the  final  scientific  con- 
stitution is  y(;t  to  (;ome,  and  which  are  still  abandoned  to  the  uncer- 
tainties of  vague  and  popular  discussion.  Although  several  other  sci- 
ences have  emerged  fiom  this  state  at  a  comparatively  recent  date, 


520  LOGIC    OF    THE    MORAL    SCIENCES. 

none  now  remain  in  it  ■  except  those  which  relate  to  man  himself,  the 
most  complex  and  most  difficult  subject  of  study  on  which  the  human 
mind  can  be  engaged. 

Concerning  the  physical  nature  of  man,  as  an  organized  being — al- 
though there  is  still  much  uncei-tainty  and  much  controversy,  which 
can  only  be  teiTtiinated  by  the  general  acknowledgment  and  employ- 
ment of  stricter  rules  of  induction  than  are  commonly  recognized — 
there  is,  however,  a  considerable  body  of  truths  which  all  who  have 
attended  to  the  subject  consider  to  be  fully  established ;  nor  is  there 
now  any  radical  imperfection  in  the  method  observed  in  this  depart- 
ment of  science  by  its  most  distinguished  modern  teachers.  But  the 
laws  of  Mind,  and,  in  even  a  gi-eater  degree,  those  of  Society,  are  so 
far  from  having  attained  a  similar  state  of  even  partial  recognition, 
that  it  is  still  a  conti'oversy  whether  they  are  capable  of  becoming  sub- 
jects of  science,  in  the  strict  sense  of  the  term;  and  among  those  who 
are  agi-eed  on  this  point  there  reigns  the  most  irreconcilable  diversity 
on  almost  every  other.  Here,  therefore,  if  anywhere,  the  principles 
laid  down  in  the  preceding  Books  may  be  expected  to  be  useful. 

If  on  matters  so  much  the  most  important  with  which  human  intel- 
lect can  occupy  itself,  a  more  general  agreement  is  ever  to  exist  among 
thinkers;  if  what  has  been  pronounced  "the  proper  study  of  mankind" 
is  not  destined  to  remain  the  only  subject  which  Philosophy  cannot 
succeed  in  rescuing  from  Empiricism ;  the  same  processes  through 
which  the  laws  of  simpler  phenomena  have  by  general  acknowledg- 
ment been  placed  beyond  dispute,  must  be  consciously  and  deliberately 
applied  to  those  more  difficult  inquiries.  If  there  are  some  subjects 
on  which  the  results  obtained  have  finally  received  the  unanimous  as- 
sent of  all  who  have  attended  to  the  proof,  and  others  on  which  man- 
kind have  not  yet  been  equally  successful ;  on  which  the  most  sagacious 
minds  have  occupied  themselves  from  tlie  earliest  date,  with  eveiy 
assistance  except  that  of  a  ti'ied  scientific  method,  and  have  never  suc- 
ceeded in  establishing  any  considerable  body  of  truths,  so  as  to  be 
beyond  denial  or  doubt ;  it  is  by  generalizing  the  methods  success- 
folly  followed  in  the  former  inquiries,  and  applying  them  to  the  latter, 
that  we  may  hope  to  remove  this  blot  upon  the  face  of  science.  The  re- 
maining chapters  are  an  attempt  to  facilitate  this  most  desirable  object. 

§  2.  In  attempting  this,  I  am  not  unmindful  how  little  can  be  done 
towards  it  in  a  mere  Treatise  on  Logic,  or  how  vague  and  unsatis- 
factory all  precepts  of  Method  must  necessarily  appear,  when  not  prac- 
tically exemplified  in  the  establishment  of  a  body  of  doctrine.  Doubt- 
less, the  most  effectual  way  of  showing  how  the  sciences  of  Ethics  and 
Politics  may  be  constructed,  would  be  to  construct  them  :  a  task  which, 
it  needs  scarcely  be  said,  I  am  not  about  to  undertake.  But  even  if 
there  were  no  other  examples,  the  memorable  one  of  Bacon  would  be 
sufficient  to  demonstrate,  that  it  is  sometimes  both  possible  and  usefol 
to  point  out  the  way,  though  without  being  oneself  prepared  to  adven- 
ture far  into  it.  And  if  more  were  to  be  attempted,  this  at  least  is  not 
a  proper  place  for  the  attempt. 

In  substance,  whatever  can  be  done  in  a  work  like  this,  for  the  Logic 
of  the  Moral  Sciences,  has  been  or  ought  to  have  been  accomplished 
in  the  five  preceding  Books  ;  to  which  the  present  can  be  only  a  kind 
of  supplement  or  appendix,  since  the  methods  of  investigation  applica- 


MBF.RTY  AND  NKCESSITV,  531 

ble  to  moral  and  social  scit'iiro  must  have  been  described  by  implica- 
tion, if  1  have  succeeded  in  enumerating  and  cluiracteri/intr  tliosc^  of 
science  in  general.  It  otdy  remains  to  examine  which  of  those 
methods  are  more  especially  suited  to  the  various  branches  of  mf)ral 
inquiry ;  under  what  peculiar  facilities  or  diHiculties  they  are  there 
employed ;  how  far  the  unsatisfactory  state  of  those  incpiiries  is  owing 
to  a  wrong  choice  of  methods,  how  far  to  want  of  skill  in  tlu^  aj)plica- 
tion  of  right  ones ;  and  what  degree  of  ultimate  succt'ss  may  he  at- 
tained or  hoped  for,  by  a  better  choice  or  m()re  cart^ful  emj)loyment  of 
logical  processes  appropriate  to  the  case.  In  other  woids,  whetlier 
moral  sciences  exist,  or  can  exist ;  to  what  degi-ee  of  perfection  they 
are  susceptible  of  being  carried  ;  and  by  what  selection  or  adaptation 
of  the  methods  brought  to  view  in  the  previous  part  of  this  work,  that 
degree  of  perfection  is  attainable. 

At  the  threshold  of  this  inquiry  we  are  met  by  an  objection,  which, 
if  not  removed,  would  be  fatal  to  the  attempt  to  treat  human  conduct 
as  a  subject  of  science.  Are  the  actions  of  man,  hke  all  other  natural 
events,  subject  to  invariable  laws  1  Does  that  constancy  of  causation, 
which  is  the  foundation  of  every  scientific  theory  of  successive;  phe- 
nomena, really  obtain  among  them  ?  This  is  often  denied  ;  and 
for  the  sake  of  systematic  completeness,  if  not  from  any  very  urgent 
practical  necessity,  the  question  .should  receive  a  deliberate  answer  in 
this  place.     We  shall  devote  to  the  subject  a  chapter  apart. 


CHAPTER  11. 

OF  LIBERTY  AND  NECESSITY. 


§  1.  The  question,  whether  the  law  of  causality  applies  in  the  same 
strict  sense  to  human  actions  as  to  other  phenomena,  is  the  celebrated 
controversy  concerning  the  freedom  of  the  will ;  which,  from  at  least  as 
far  back  as  the  time  of  Pelagius,  has  divided  both  the  philosophical 
and  the  religious  world.  The  affirmative  oj)inion  is  commonly  called 
the  doctrine  of  Necessity,  as  asserting  human  volitions  and  actions  to 
be  necessary  and  inevitable.  The  negative  maintains  that  the  will  is 
not  determined,  like  other  phenomena,  by  antecedents,  but  determines 
itself;  that  our  volitions  are  not,  properly  speaking,  the  effects  of 
causes,  or  at  least  have  no  causes  which  they  uniformly  and  implicitly 
obey. 

I  have  already  made  it  sufficiently  appear  that  the  former  of  theso 
opinions  is  that  which  I  (M)nsider  the  truti  one;  but  the  jnisleading 
terms  in  which  it  is  often  csxpressed,  and  the  indistinct  manner  in  which 
it  is  usually  apprehended,  have  both  obstructed  its  reception,  and  per- 
verted its  influence  when  received.  The  metaphysical  theory  of  free 
will,  as  held  by  philosophers  (for  the  practical  feeling  (»f  it,  common  in 
a  greater  or  h-'ss  degree  to  all  mankind,  is  in  no  way  inconsistent  with 
the  contrary  theory),  was  invented  becaust;  the  supposed  alternaliv«M)f 
admitting  human  actions  to  be  ncre.tsari/,  was  deem(;d  inconsistent  with 
every  one's  instinctive  consciousness,  aa  well  as  humiliating  to  the  pride 
3V 


522  LOGIC    OF    THE    MORAL   SCIENCES. 

and  even  degrading  to  the  moral  nature  of  man.  Nor  do  I  deny  that 
the  docti-ine,  as  somethnes  held,  is  open  to  these  imputations ;  for  the 
misapprehension  in  which  1  shall  be  able  to  show  that  they  originate, 
unfortunately  is  not  confined  to  the  opponents  of  the  doctrine,  but  par- 
ticipated in  by  many,  perhaps  we  might  say  by  most  of  its  supporters. 

§  2.  Correctly  conceived,  the  doctrine  called  Philosophical  Neces- 
sity is  simply  this :  that,  given  the  motives  which  are  present  to  an 
individual's  mind,  and  given  likewise  the  character  and  disposition  of 
the  individual,  the  manner  in  which  he  will  act  may  be  uneningly 
infeiTed ;  that  if  we  knew  the  person  thoroughly,  and  knew  all  the 
inducements  which  are  acting  upon  him,  we  could  foretell  his  conduct 
with  as  much  certainty  as  we  can  predict  any  physical  event.  This 
proposition  I  take  to  be  a  mere  interjjretation  of  universal  experience, 
a  statement  in  words  of  what  every  one  is  internally  convinced  of  No 
one  who  believed  that  he  knew  thoroughly  the  circumstances  of  any 
case,  and  the  characters  of  ijie  different  persons  concerned,  would  hes- 
itate to  foretell  how  all  of  them  would  act.  Whatever  degi-ee  of  doubt 
he  may  in  fact  feel,  arises  from  the  uncertainty  whether  he  really  knows 
the  circumstances,  or  the  character  of  some  one  or  other  of  the  persons, 
with  the  degree  of  accuracy  required ;  but  by  no  means  from  thinking 
that  if  he  did  know  these  things,  there  could  be  any  uncertainty  what 
the  conduct  would  be.  Nor  does  this  full  assurance  conflict  in  the 
smallest  degi'ee  with  what  is  called  our  feeling  of  freedom.  We  do 
not  feel  ourselves  the  less  free,  because  those  to  whom  we  are  intimately 
known  are  well  assured  how  we  shall  will  to  act  in  a  particular  case. 
We  often,  on  the  contrary,  regard  the  doubt  what  our  conduct  will  be, 
as  a  mark  of  ignorance  of  our  character,  and  sometimes  even  resent 
it  as  an  imputation.  It  has  never  been  admitted  by  the  religious  phi- 
losophers who  advocated  the  free-will  doctrine,  that  we  must  feel  not 
free  because  God  foreknows  our  actions.  We  may  be  fi-ee,  and  yet 
another  may  have  reason  to  be  perfectly  certain  what  use  we  shall 
make  of  our  freedom.  It  is  not,  therefore,  the  doctrine  that  our  voli- 
tions and  actions  are  invariable  consequents  of  our  antecedent  states 
of  mind,  that  is  either  contradicted  by  our  consciousness,  or  felt  to  be 
degrading. 

But  the  doctrine  of  causation,  when  considered  as  obtaining  between 
our  volitions  and  their  antecedents,  is  almost  universally  conceived  as 
involving  more  than  this.  Many  do  not  believe,  and  very  few  prac- 
tically feel,  that  there  is  nothing  in  causation  but  invariable,  certain, 
and  unconditional  sequence.  There  are  few  to  whom  mere  constancy 
of  succession  appears  a  sufficiently  stringent  bond  of  union  for  so  pe- 
culiar a  relation  as  that  of  cause  and  effect.  Even  if  the  reason  repu- 
diates, imagination  retains,  the  feeling  of  some  more  intimate  connex- 
ion, of  some  peculiar  tie,  or  mysterious  constraint  exercised  by  the 
antecedent  over  the  consequent.  Now  this  it  is  which,  considered  as 
applying  to  the  human  will,  conflicts  with  our  consciousness,  and  re- 
volts our  feelings.  We  are  certain  that,  in  the  case  of  our  volitions, 
there  is  not  this  mysterious  constraint.  We  know  that  we  are  not 
compelled,  as  by  a  magical  spell,  to  obey  any  particular  motive.  We 
feel,  that  if  we  wished  to  prove  that  we  have  the  power  of  resisting 
the  motive  we  could  do  so,  (that  wish  being,  it  needs  scarcely  be  ob- 
served, ^  new  antecedent ;)  and  it  would  be'humiliating  to  our  pride 


LIBERTY    AND    NECESSITY.  523 

and  paralyzing  to  our  desire  i)f  excellence  if  wo  thought  otherwise. 
But  neither  is  any  such  mysterious  compulsion  now  supposed,  by  the 
best  philosophical  authorities,  to  be  exercised  by  anij  cause  over  its 
eft'ect.  Tliose  who  tliirik  lliat  causes  draw  their  etlects  alter  them  by  a 
mystical  tie,  are  right  in  believing  tliat  the  relation  between  volitions 
and  their  antecedents  is  of  another  nature.  But  they  should  go 
further,  and  admit  that  this  is  also  true  of  all  other  elVects  and  their  an- 
tecedents. If  such  a  lie  is  considered  to  be  involved  in  the  word  ne- 
cessity, the  doctrine  is  not  true  of  human  actions  ;  but  neither  is  it  then 
true  of  inanimate  objects.  It  would  be  more  correct  to  say  that  mat- 
ter is  not  bound  by  necessity  than  that  mind  is  so. 

That  the  free-will  j)hilosophers,  being  mostly  of  the  school  which 
rejects  Hume's  and  Brown's  analysis  of  Cause  and  Efl'ect,  should  miss 
their  way  for  want  of  the  light  which  that  analysis  attbrds,  cannot  sur- 
prise us.  The  wonder  is,  tliat  the  necessarians,  who  usually  admit  that 
philosophical  theory,  should  in  practice  etpially  lose  sight  of  it.  The 
very  same  mi.sconce])tion  of  the  doctrine  called  Philosophical  Neces- 
sity, which  prevents  the  opposite  party  from  recognizing  its  truth,  I 
believe  to  exist  more  or  less  obscurely  in  the  minds  of  most  necessa- 
rians, however  they  may  in  words  disavow  it.  I  am  much  mistaken 
if  they  habitually  feel  that  the  necessity  which  they  recogTiizi;  in  actions 
is  but  uniformity  of  order,  and  capability  of  being  predicted.  They 
have  a  feeling  as  if  there  were  at  bottom  a  stronger  tit;  between  the 
volitions  and  their  causes :  as  if,  when  they  asserted  that  our  will  is 
governed  by  the  balance  of  motives,  they  meant  something  more  co- 
gent than  if  they  had  only  said,  that  whoever  knew  the  motives,  and 
our  habitual  susceptibilities  to  them,  could  predict  how  we  should  will 
to  act.  They  commit,  in  opposition  to  their  own  philosophical  system, 
the  verj'  same  mistake  which  their  adversaries  commit  in  obedience 
to  theirs;  and  in  consequence  do  really  in  some  instances  (I  speak 
from  personal  experience)  suffer  those  depressing  consetjuences,  which 
their  opponents  eiToneously  impute  to  the  doctrine  itself. 

§  3.  I  am  inclined  to  think  that  this  error  is  almost  wholly  an  effect 
of  the  associations  with  a  word;  and  tliat  it  wouhl  be  prevented  by 
forbearing  to  em])loy,  for  the  expression  of  the  simple  fact  of  causa- 
tion, so  extremely  inappropriate  a  term  as  Necessity.  That  word,  in 
its  other  acceptaticjns,  involves  much  more  than  mere  uniformity  of 
Becpience ;  it  implies  in-esistibleness.  Ap|)lied  to  the  will,  it  only 
means  that  the  given  cause  will  be  followed  by  the  effect,  subject  to 
all  possibilities  of  counteraction  by  other  cau.ses :  but  in  common  use 
it  stands  for  the  operation  of  those  causes  exclusively,  which  are  sup- 
posed too  powerful  to  be  counteracted  at  all.  When  we  say  that  all 
human  acticnjs  take  place  of  necessity,  we  only  mean  that  they  will 
certaiidv  happen  if  nothing  prevents: — when  wc  say  that  dying  of 
want,  to  those  who  cannot  get  food,  is  a  necessity,  we  mean  that  it  will 
certainly  happen  whatever  may  be  done  to  pn-vent  it.  Tiie  applica- 
tion of  the  same  term  to  the  agencies  on  which  human  actions  depend, 
as  is  used  to  express  those  agencies  of  nature  which  are  really  uncon- 
trollable, cannot  fail,  when  habitual,  to  create  a  feeling  of  uncontroUa- 
bleness  in  the  former  also.  This  however  is  a  mere  illusion.  Thero 
are  physical  sequences  which  we  call  necessary,  as  dc^ath  for  want  of 
food  or  air ;  there  are  others  which  are  not  said  to  be  necessary,  as 


524  LOGIC    OF    THE   MORAL    SCIENCES. 

death  from  poison,  which  an  antidote,  or  the  use  of  the  stomach  pump, 
will  sometimes  avert.  It  is  apt  to  be  forgotten  by  people's  feelings, 
even  if  remembered  by  their  understandings,  that  human  actions  are 
in  this  last  predicament :  they  are  never  (except  in  some  cases  of 
mania)  ruled  by  any  one  motive  with  such  absolute  sway,  that  there 
is  no  room  for  the  influence  of  any  other.  The  causes,  therefore,  on 
which  action  depends,  are  never  uncontrollable ;  and  any  given  effect 
is  only  necessary  provided  that  the  causes  tending  to  produce  it  are 
not  controlled.  That  whatever  happens,  could  not  have  happened 
otherwise  unless  something  had  taken  place  which  was  capable  of 
preventing  it,  no  one  surely  needs  hesitate  to  admit.  But  to  call  this 
by  the  name  necessity  is  to  use  the  term  in  a  sense  so  different  from 
its  primitive  and  familiar  meaning,  from  that  which  it  bears  in  the 
common  occasions  of  life,  as  to  amoimt  almost  to  a  play  upon  words. 
The  associations  derived  from  the  ordinary  sense  of  the  term  will  ad- 
here to  it  in  spite  of  all  we  can  do  :  and  though  the  doctrine  of  Neces- 
sity, as  stated  by  most  who  hold  it,  is  very  remote  from  fatalism,  it  is 
probable  that  most  necessarians  are  fatalists,  more  or  less,  in  their 
feelings. 

A  fatalist  believes,  or  half  believes  (for  nobody  is  a  consistent  fatal- 
ist) not  only  that  whatever  is  about  to  happen,  will  be  the  infallible 
result  of  the  causes  which  produce  it  (which  is  the  true  necessarian 
doctrine),  but  moreover  that  there  is  no  use  in  struggling  against  it; 
that  it  will  happen  however  we  may  strive  to  prevent  it.  Now,  a 
necessarian,  believing  that  our  actions  follow  fi-om  our  characters,  and 
that  our  characters  follow  from  our  organization,  our  education,  and 
our  circvimstances,  is  apt  to  be,  Avith  more  or  less  of  consciousness  on 
his  part,  a  fatalist  as  to  his  own  actions,  and  to  believe  that  his  nature 
is  such,  or  that  his  education  and  circumstances  have  so  moulded  his 
character,  that  nothing  can  now  prevent  him  from  feelhig  and  acting 
in  a  particular  way,  or  at  least  that  no  effort  of  his  own  can  hinder  it. 
In  the  words  of  the  sect  which  in  our  own  day  has  so  perseveringly 
inculcated  and  so  perversely  misunderstood  this  gi-eat  doctrine,  his 
character  is  formed  for  him,  and  not  hy  him ;  therefore  his  wishing 
that  it  had  been  formed  differently  is  of  no  use ;  he  has  no  power  to 
alter  it.  But  this  is  a  grand  error.  He  has,  to  a  certain  extent,  a 
power  to  alter  his  character.  Its  being,  in  the  ultimate  resort,  formed 
for  him,  is  not  inconsistent  with  its  being,  in  part,  formed  liy  him  as 
one  of  the  intermediate  agents.  His  character  is  formed  by  his  cir- 
cumstances (including  among  these  his  particular  organization) ;  but 
his  own  desire  to  mould  it  in  a  particular  way,  is  one  of  those  circum- 
stances, and  by  no  means  one  of  the  least  influential.  We  cannot, 
indeed,  directly  will  to  be  different  from  what  we  are.  But  neither  did 
those  who  are  supposed  to  have  formed  our  characters,  directly  will 
that  we  should  be  what  we  are.  Their  will  had  no  direct  power 
except  over  their  own  actions.  They  made  us  what  they  did  make 
us,  by  willing,  not  the  end,  but  the  requisite  means  :  and  we,  when  our 
habits  are  not  too  inveterate,  can,  by  similarly  willing  the  requisite 
means,  make  ourselves  different.  If  they  could  place  us  under  the 
influence  of  certain  circumstances,  we,  in  like  manner,  can  place  our- 
selves under  the  influence  of  other  circumstances.  We  are  exactly  as 
capable  of  making  our  own  character,  ?/"  we  will,  as  others  are  of  mak- 
ing it  for  us. 


LIBERTY    AND    NECESSITY.  525 

Yes  (answers  the  Owenitc),  but  these  words,  "  if  we  will,"  surrender 
the  whole  point :  since  the  will  to  alter  our  own  cliaracter  is  given  us, 
not  by  any  efforts  of  ours,  but  by  circumstances  which  we  cannot  lu^ln ; 
it  comes  to  us  eitlicr  from  external  causes,  or  not  at  all.  Most  true  : 
if  the  Owenite  stops  here,  he  is  in  a  position  from  which  nijthing  can 
expel  him.  Our  character  is  fomied  by  us  as  well  as  for  us  ;  but  the 
wish  which  induces  us  to  attempt  to  form  it  is  formed  for  us:  and  how'? 
not,  in  general,  by  our  organization  or  education,  but  by  our  experi- 
ence ;  experience  of  the  painful  consequences  of  the  character  we 
previously  had  :  or  by  some  strong  feeling  of  admiration  or  asjnration, 
accidentally  aroused.  But  to  think  that  we  have  no  power  of  altering 
our  characters,  and  to  think  that  we  shall  not  use  our  power  unless  wc 
have  a  motive,  are  very  different  things,  and  have  a  very  different  effect 
upon  the  mind.  A  person  who  does  not  wish  to  alter  his  character, 
cannot  be  the  person  who  is  supposed  to  feel  discouraged  or  paralyzed 
by  thinking  himself  unable  to  do  it.  The  depressing  effect  of  the  fatalist 
doctrine  can  oidy  be  felt  where  there  is  a  wish  to  do  what  that  doctrine 
rejiresents  as  impossible.  It  is  of  no  consequence  what  we  think  fonns 
our  character  when  we  have  no  desire  of  our  own  about  forming  it ; 
but  it  is  of  great  consequence  that  we  should  not  be  prevented  from 
foi-ming  such  a  desire  by  thinking  the  attainment  impracticable,  and 
that  if  we  have  the  desire,  we  should  know  that  the  work  is  not  so 
in-evocably  done  as  to  be  incapable  of  being  altered. 

And  indeed,  if  we  examine  closely,  we  shall  find  that  this  feeling,  of 
our  being  able  to  modify  our  own  character  If  wc  icish,  is  itself  the 
feeling  of  moral  freedom  which  we  are  conscious  of.  A  person  feels 
morally  free,  who  feels  that  his  habits  or  his  temptations  are  not  his 
masters,  but  he  theirs  :  who  even  in  yielding  to  them  knows  that  he 
could  resist ;  that  were  he,  for  any  reason,  desirous  of  altogether  throw- 
ing them  off",  there  would  not  be  recjuired  for  that  purjjose  a  stronger 
desire  than  he  knows  himself  to  be  capable  of  feuling.  It  is  of  course 
necessary,  to  render  our  consciousness  of  freedom  complete,  that  we 
vshould  actually  have  made  our  character  all  we  have  liithorto  wished 
to  make  it;  for  if  we  have  wished,  and  not  attained,  we  have  not  ])ower 
over  our  ovati  character,  we  are  not  free.  Or  at  least,  we  must  feel 
that  our  wish,  if  not  strong  enough  to  alter  our  character,  is  strong 
enough  to  conquer  our  character  when  the  two  are  brought  into  conflict 
in  any  particular  case  of  conduct. 

The  application  of  so  improper  a  term  as  Necessity  to  the  doctrine 
of  cause  and  effect  in  the  matter  of  human  character,  seems  to  me  one 
of  the  most  signal  instances  in  philosophy  of  the  abuse  of  tenns,  and  its 
practical  consequences  one  of  the  most  striking  examples  of  the  j)owor 
of  language  over  om'  associations.  The  subject  will  never  be  generally 
understood,  until  that  objectionable  term  is  (b'opped.  The  frci'-will 
doctiine,  by  keeping  in  view  precisely  that  portion  of  the  truth  which 
the  word  Necessity  puts  out  of  sight,  namely,  the  power  of  the  mind  to 
cooperate  in  the  fonnation  of  its  own  character,  has  given  to  its  adher- 
ents a  practical  feeling  much  nearer  to  the  truth  than  has  generally  (I 
believe)  existed  in  the  minds  of  necessarians.  The  latter  may  have  had 
a  stronger  sense  «jf  the  importance  of  what  human  beings  can  do  to 
shape  the  characters  of  one  another  ;  but  the  free-will  doctrine  ha-s,  I 
believe,  fostered,  especially  in  the  younger  of  its  supporters,  a  much 
stronger  spirit  of  self-culture. 


526  LOGIC    OF    THE    MORAL    SCIENCES. 

§  4.  There  is  still  one  fact  which  requires  to  be  noticed  (in  addition 
to  the  existence  of  a  power  of  self-formation)  before  the  doctrine  of 
tbe  causation  of  human  actions  can  be  freed  from  the  confusion  and 
misapprehensions  which  surround  it  in  many  minds.  When  the  will 
is  said  to  be  detennined  by  motives,  a  motive  does  not  mean  always, 
or  solely,  the  anticipation  of  a  pleasure  or  of  a  pain.  I  shall  not  here 
inquire  whether  it  be  true  that,  in  the  commencement,  a.ll  our  volun- 
tary actions  are  mere  means  consciously  employed  to  obtain  some  pleas- 
ure, or  avoid  some  pain.  It  is  at  least  certain  that  we  gradually, 
through  the  influence  of  association,  come  to  desire  the  means  without 
thinking  of  the  end:  the  action  itself  becomes  an  object  of  desire,  and 
is  performed  without  reference  to  any  motive  beyond  itself.  Thus 
far,  it  may  still  be  objected,  that,  the  action  having  through  association 
become  pleasurable,  we  are,  as  much  as  before,  moved  to  act  by  the 
anticipation  of  a  pleasure,  namely,  the  pleasure  of  the  action  itself. 
But  granting  this,  the  matter  does  not  end  here.  As  we  proceed  in 
the  formation  of  habits,  and  become  accustomed  to  will  a  particular 
act  or  a  particular  course  of  conduct  because  it  is  pleasurable,  we  at 
last  continue  to  will  it  whether  it  is  pleasurable  or  not.  Although, 
from  some  change  in  us  or  in  our  circumstances,  we  have  ceased  to 
find  any  pleasure  in  the  action,  or  to  anticipate  any  pleasure  as  the 
consequence  of  it,  we  still  continue  to  desire  the  action,  and  conse- 
quently to  do  it.  In  this  manner  it  is  that  habits  of  hurtful  indulgence 
continue  to  be  practised  although  they  have  ceased  to  be  pleasm^able ; 
and  in  this  manner  also  it  is  that  the  habit  of  willing  to  persevere  in  a 
prescribed  course  does  not  desert  the  moral  hero,  even  when  the  re- 
ward, however  real,  which  he  doubtless  receives  from  the  conscious- 
ness of  well-doing,  is  anything  but  an  eqiiivalent  for  the  sufferings  he 
undergoes,  or  the  wishes  which  he  may  have  to  renounce. 

A  habit  of  %'\alling  is  commonly  called  a  purpose  ;  and  among  the 
causes  of  our  volitions,  and  of  the  actions  which  flow  fi-om  them,  must 
be  reckoned  not  only  likings  and  aversions,  but  also  purposes.  It  is 
only  when  our  purposes  have  become  independent  of  the  feelings  of 
pain  or  pleasure  from  which  they  originally  took  their  rise,  that  we  are 
said  to  have  a  confirmed  character.  "A  character,"  says  Novalis,  "  is 
a  completely  fashioned  will :"  and  the  will,  once  so  fashioned,  may  be 
steady  and  constant,  when  the  passive  susceptibilities  of  pleasure  and 
pain  are  gi-eatly  weakened,  or  materially  changed. 

With  the  coiTections  and  explanations  now  given,  the  doctrine  of 
the  causation  of  our  volitions  by  motives,  and  of  motives  by  the  desi- 
rable objects  offered  to  us,  combined  with  our  particular  susceptibilities 
of  desire,  may  be  considered,  I  hope,  as  sufficiently  established;  and 
I  shall  henceforth  assume  its  truth  without  any  further  discussion. 


HUMAN    NATURE    A    SUBJECT    OF    SCIENCE.  527 

CHAPTER  HI. 

THAT  THERE  IS,  OR   MAY  BE,   A  SCIENCE  OF   HUMAN   NATURE. 

§  1.  It  is  a  common  notion,  or  at  least  it  is  implied  in  many  common 
modes  of  speech,  that  the  thoughts,  tcelings,  and  actions  of  sentient 
beings  are  not  a  subject  of  science,  in  the  same  strict  sense  in  which 
this  is  true  of  the  objects  of  outward  Nature.  This  notion  seems  to 
involve  some  confusion  of  ideas,  which  it  is  necessary  to  begin  by 
clearing  up. 

Any  facts  are  fitted,  in  themselves,  to  be  a  subject  of  science,  which 
follow  one  another  according  to  constant  laws ;  although  those  laws 
may  not  have  been  discovered,  nor  even  be  discoveral)lc  by  our  exist- 
ing resources.  Take,  for  instance,  the  most  familiar  class  of  meteor- 
ological phenomena,  those  of  rain  and  sunshine.  Scientific  intjuiry 
has  not  yet  succeeded  in  ascertaining  the  order  of  antecedence  and 
consequence  among  these  jilicnomcna,  so  as  to  be  able,  at  least  in  our 
regions  of  the  earth,  to  predict  them  with  certainty,  or  even  witli  any 
high  degree  of  probability.  Yet  no  one  doubts  that  the  phenomena 
depend  upon  laws,  and  that  these  must  be  derivative  laws  resulting 
from  known  ultimate  laws,  those  of  heat,  vaporization,  and  elastic 
fluids.  Nor  can  it  be  doubted  that  if  we  were  acquainted  witli  all  the 
antecedent  circumstances,  we  could,  even  fi'om  those  more  general 
laws,  predict  (saving  difficulties  of  calculation)  the  state  of  the  weather 
at  any  future  time.  Meteorology,  therefore,  not  only  has  in  itself 
every  natural  requisite  for  being,  but  actually  is,  a  science ;  although, 
from  the  difficulty  of  observing  the  facts  upon  which  the  phenomcMia 
depend  (a  difficulty  inherent  in  the  peculiar  nature  of  those  phe- 
nomena) the  science  is  still  very  imperfect ;  and  were  it  perfect,  might 
probably  be  of  little  avail  in  practice,  since  the  data  requisite  for 
applying  its  jirinciples  to  particular  instances  would  rarely  be  pro- 
curable. 

A  case  may  be  conceived,  of  an  intermediate  character  between  the 
perfection  of  science,  and  this  its  extremi;  imperfection.  It  may  hap- 
pen that  the  greater  causes,  those  on  which  the  principal  part  of  a 
phenomenon  depends,  are  within  the  reach  of  obsei'vation  and 
measurement ;  so  that  if  no  other  causes  intervened,  a  complete 
explanation  could  be  given  not  only  of  the  })henomenon  in  general,  but 
of  all  the  variations  and  modifications  wliich  it  admitted  of  Jiut  inas- 
much as  other,  perhaps  many  other  causes,  separately  insignificant  in 
their  effects,  cooperate  or  conflict  in  many  or  in  all  cases  with  those 
greater  causes  ;  the  effect,  accordingly,  presents  more  or  less  of  aberra- 
tion from  what  would  be  produced  by  the  greater  causes  alone.  Now, 
if  these  minor  causes  are  not  so  constantly  accessible,  or  not  accessible 
at  all,  to  accurate  observation  ;  tlu;  principal  mass  of  the  eflect  may 
still,  as  before,  be  accounted  f  )r,  and  even  predicted  ;  but  tlnire  will 
be  variations  and  modifications  which  we  arc  not  comnetent  to  explain 
thoroughly,  and  our  predictions  will  not  be  fulfillea  accurately,  but 
only  approximately. 

It  is  thus,  for  example,  with  the  theory  of  the  tides.  No  one  doubts 
that  Tidology  (as  Mr.  Whewell  proposes  to  call  it)  Ls  really  a  science. 


528  LOGIC    OF    THE    MORAL    SCIENCES. 

As  much  of  tlie  phenomena  as  depends  upon  the  attraction  of  the  sun 
and  moon  is  completely  understood,  and  may  in  any,  even  unknowTi, 
part  of  the  earth's  surface,  be  foretold  with  certainty;  and  the  far 
greater  part  of  the  phenomena  depends  upon  those  causes.  But  cir- 
cumstances of  a  local  or  casual  nature,  such  as  the  configuration  of  the 
bottom  of  the  ocean,  the  degree  of  confinement  from  shores,  the  direc- 
tion of  the  wind,  &:c.,  influence,  in  many  or  in  all  places,  the  height 
and  time  of  the  tide  ;  and  a  portion  of  these  circumstances  being  either 
not  accurately  knowable,  not  precisely  measurable,  or  at  least  not 
capable  of  being  certainly  foreseen,  the  tide  in  known  places  com- 
monly varies  from  the  calculated  result  of  general  principles  by  some 
difference  that  we  cannot  explain,  and  in  unknown  ones  may  vary  from 
it  by  a  difference  that  we  are  not  able  to  foresee  or  conjecture.  Never- 
theless, not  only  is  it  certain  that  these  variations  depend  upon  causes, 
and  follow  their  causes  by  laws  of  unerring  uniformity ;  not  only, 
therefore,  is  tidology  a  science,  like  meteorology,  but  it  is,  what 
meteorology  perhaps  will  never  be,  a  science  largely  available  in 
practice.  General  laws  may  be  laid  down  respecting  the  tides,  pre- 
dictions may  be  founded  upon  those  laws,  and  the  result  will  in  the 
main,  though  often  not  \nth  complete  accuracy,  correspond  to  the 
predictions. 

And  this  is  what  is  or  ought  to  be  meant  by  those  who  speak  of 
sciences  which  are  not  exact  sciences.  Astronomy  Avas  once  a  science, 
without  being  an  exact  science.  It  could  not  become  exact  until  not 
only  the  general  course  of  the  planetary  motions,  but  the  perturbations 
also,  were  accounted  for,  and  refeiTed  to  their  causes.  It  has  now  be- 
come an  exact  science,  because  its  phenomena  have  been  brought  under 
laws  comprehending  the  whole  of  the  causes  by  which  the  phenomena 
are  influenced,  whether  in  a  great  or  only  in  a  trifling  de,gi"ee,  whether 
in  all  or  only  in  some  cases,  and  assigning  to  each  of  those  causes  the 
share  of  effect  which  really  belongs  to  it.  But  in  tidology  the  only  laws 
as  yet  accurately  ascertained,  are  those  of  the  causes  which  affect  the 
phenomenon  in  all  cases,  and  in  a  considerable  degree ;  while  others 
which  affect  it  in  some  cases  only,  or,  if  in  all,  only  in  a  slight  degree, 
have  not  yet  been  sufficiently  ascertained  and  studied  to  enable  us  to 
lay  doMTi  their  laws  ;  still  less  to  deduce  the  completed  law  of  the  phe- 
nomenon, by  compounding  the  effects  of  the  greater  with  those  of  the 
minor  causes.  Tidology,  therefore,  is  not  yet  an  exact  science ;  not 
from  any  inherent  incapacity  of  being  so,  but  from  the  difficulty  of 
ascertaining  with  complete  precision  the  real  derivative  uniformities. 
By  combining,  however,  the  exact  laws  of  the  greater  causes,  and  of 
such  of  the  minor  ones  as  are  sufficiently  known,  with  such  empirical 
laws  or  such  approximate  generalizations  respecting  the  miscellaneous 
variations  as  can  be  obtained  by  specific  observation,  we  can  lay  down 
general  propositions  which  will  be  true  in  the  main,  and  upon  which, 
with  allowance  for  the  degree  of  their  probable  inaccuracy,  we  may 
safely  gi-ound  om-  expectations  and  om-  conduct. 

§  2.  The  science  of  human  nature  is  of  this  description.  It  falls  far 
short  of  the  standard  of  exactness  now  realized  in  Astronomy;  but 
there  is  no  reason  that  it  should  not  be  as  much  a  science  as  Tidology 
is,  or  as  Astronomy  was  when  its  calculations  had  only  mastered  the 
main  phenomena,  but  not  the  perturbations. 


HUMAN    NATURE    A    SUBJECT    OF    SCIENCE.  529 

The  phenomena  with  which  tliis  science  is  conversant  bein"-  the 
thouglits,  fcehngs,  and  actions  of  human  beings,  it  wouhl  have  attained 
the  ideal  perfection  of  a  science  if  it  enabled  us  to  foretell  how  an  indi- 
vidual would  think,  feel,  or  act,  throughout  life,  with  the  same  certainly 
with  which  astronomy  enables  tis  to  predict  the  jdaces  and  the  occulla- 
tions  of  the  heavenly  bodies.  It  needs  scarcely  be  stated  that  nothing 
approaching  to  this  can  be  done.  The  actions  of  individuals  could  not 
be  predicted  with  scientific  accuracy,  were  it  only  because  we  cannot 
foresee  the  whole  of  the  circumstances  in  which  those  individuals  will 
be  placed.  But  further,  even  in  any  given  combination  of  (present) 
circumstances,  no  assertion,  which  is  both  precise  and  imiversally  true, 
can  be  made  respecting  the  manner  in  which  human  beings  will  think, 
feel,  or  act.  This  is  not,  however,  because  every  person's  modes  of 
thinking,  feeling,  and  acting,  do  not  depend  upon  causes ;  nor  can  we 
doubt  that  if,  in  the  case  of  any  individual,  our  data  could  be  complete, 
we  even  now  know  enough  of  the  ultimate  laws  by  which  mental  phe- 
nomena are  determined  to  enable  us  to  predict  with  tolerable  certainty, 
if  not  ^\•ith  perfect  precision,  what,  under  any  given  set  of  circumstances, 
his  conduct  or  sentiments  would  be.  But  the  impressions  and  actions 
of  human  beings  are  not  solely  the  result  of  their  present  circumstances, 
but  the  joint  result  of  those  circinnstances  and  of  the  characters  of  the 
individuals  :  and  the  agencies  which  determine  human  character  are  so 
numerous  and  diversified  (nothing  which  has  hapjiened  to  the  person 
throughout  life  being  without  its  portion  of  influence),  that  in  the  ag- 
gi-egate  they  are  never  in  any  two  cases  exactly  similar.  Hence,  even 
if  our  science  of  human  nature  were  theoretically  jserfect,  that  is,  if  we 
could  calculate  any  character  as  we  can  calculate  the  orbit  of  any 
planet,  from  given  data  ;  still  as  the  data  are  never  all  given,  nor  ever 
precisely  alike  in  different  cases,  we  could  neither  make  infallible  pre- 
dictions, nor  lay  down  universal  propositions. 

Inasmuch,  however,  as  many  of  those  effects  which  it  is  of  most  im- 
portance to  render  amenable  to  human  foresight  and  control,  are  de- 
termined, like  the  tides,  in  an  incomparably  greater  degree  by  general 
causes,  than  by  all  partial  causes  taken  together  ;  depending  in  the  main 
on  those  circumstances  and  those  qualities  which  are  common  to  all 
mankind,  or  common  at  least  to  large  bodies  of  them,  and  only  in  a 
small  degree  on  the  idiosyncracies  of  organization  or  the  peculiar  his- 
tory of  individuals ;  it  is  evidently  possible,  with  regard  to  all  such 
effects,  to  make  predictions  which  will  almost  always  be  verified,  and 
general  propositions  which  are  almost  always  true.  And  whenever  it 
is  sufficient  to  know  how  the  great  majority  of  the  human  race,  or  of 
some  nation  or  class  of  persons,  will  think,  feel,  and  act,  these  jiroposi- 
tions  are  equivalent  to  universal  ones.  For  the  purposes  of  political 
and  social  science  this  is  sufficient.  As  we  formerly  remarked,*  an 
approximate  generalization  is  practically,  in  social  intjuiries,  equivalent 
to  an  exact  one ;  that  which  is  only  prcibable  when  asserted  of  human 
beings  taken  individually,  being  certain  when  affirmed  of  the  character 
and  collective  conduct  of  masses. 

It  is  no  disparagement,  therefore,  to  the  science  of  Human  Nature, 
that  those  of  its  general  propositions  which  descend  sufficiently  into 
detail  to  serve  as  a  foundation  for  predicting  phenomena  in  the  con- 

*  Supra,  p.  35'J. 

3X 


530  LOGIC    OF    THE    MORAL    SCIENCES. 

Crete,  are  for  the  most  part  only  approximately  true.  But  in  order  to 
give  a  genuinely  scientific  character  to  the  study,  it  is  indispensable 
that  these  approximate  generalizations,  which  in  themselves  would 
amount  only  to  the  lowest  kind  of  empirical  laws,  should  be  connected 
deductively  with  the  laws  of  nature  from  which  they  result ;  should  be 
resolved  into  the  properties  of  the  causes  on  which  the  phenomena 
depend.  In  other  words,  the  science  of  Human  Nature  may  be  said 
to  exist,  in  proportion  as  those  approximate  truths,  which  compose  a 
practical  knowledge  of  mankind,  can  be  exhibited  as  corollaries  from 
the  universal  laws  of  human  nature  on  which  they  rest ;  whereby  the 
proper  limits  of  those  approximate  truths  would  be  shown,  and  we 
should  be  enabled  to  deduce  others  for  any  new  state  of  circumstances, 
in  anticipation  of  specific  experience. 

The  proposition  now  stated  is  the  text  on  which  the  two  succeeding 
chapters  will  furnish  the  comment. 


CHAPTER  IV. 

OF  THE   LAWS  OF  MIND. 


§  1.  "What  the  Mind  is,  as  well  as  what  Matter  is,  or  any  other 
question  respecting  Things  in  themselves,  as  distinguished  from  their 
sensible  manifestations,  it  would  be  foreign  to  the  purposes  of  this 
Treatise  to  consider.  Here,  as  throughout  our  inquiry,  we  shall  keep 
clear  of  all  speculations  respecting  the  Mind's  own  nature,  and  shall 
understand  by  the  Laws  of  JNIind,  those  of  mental  Phenomena;  of  the 
various  feelings  or  states  of  consciousness  of  sentient  beings.  These, 
according  to  the  classification  we  have  uniformly  followed,  consist  of 
Thoughts,  Emotions,  Volitions,  and  Sensations  :  the  last  being  as  truly 
States  of  Mind  as  the  three  former.  It  is  usual  indeed  to  speak  of 
Sensations  as  states  of  body,  not  of  mind.  But  this  is  the  common 
confusion  of  giving  one  and  the  same  name  to  a  phenomenon  and  to 
the  proximate  cause  or  conditions  of  the  phenomenon.  The  immediate 
antecedent  of  a  Sensation  is  a  state  of  Body,  but  the  sensation  itself  is 
a  state  of  Mind.  If  the  word  Mind  means  anything,  it  means  that  which 
feels.  If  we  allow  ourselves  to  use  language  implying  that  the  Body 
feels,  there  is  no  reason  against  being  consistent  in  that  language,  and 
saying  that  the  Body  also  thinks. 

The  phenomena  of  Mind,  then,  are  the  various  feelings  of  our 
nature,  both  those  called  physical,  and  those  peculiarly  designated  as 
Mental :  and  by  the  Laws  of  Mind,  I  mean  the  laws  according  to  which 
those  feelings  generate  one  another. 

§  2.  All  states  of  mind  are  immediately  caused  either  by  other  states 
of  mind,  or  by  states  of  body.  AVhen  a  state  of  mind  is  produced  by 
a  state  of  mind,  I  call  the  law  concerned  in  the  case,  a  law  of  Mind. 
When  a  state  of  mind  is  produced  directly  by  a  state  of  body,  the  law 
is  a  law  of  Body,  and  belongs  to  physical  science. 

With  regard  to  those  states  of  mind  which  are  called  Sensations,  all 
are  agreed  that  these  have  for  their  immediate  antecedents,  states  of 


LAWS    OF    MINO.  531 

body.  Every  sensation  luis  for  its  proximate  cause  sonie  afloctiim  of 
the  portion  ot"  our  frame  called  the  nervous  system;  whether  this  aH'cc- 
tion  originate  in  the  action  of  some  external  object,  or  in  sonu-  patho- 
logical condition  of  the  nervous  organization  itself.  The  laws  of  this 
portion  of  our  nature — tnc  varieties  of  our  sensations,  and  the  physi* 
cal  ci>nditions  on  which  they  proximately  depend — manifestly  fall 
under  the  province  of  Physiology. 

W'liether  any  other  portion  of  our  mental  states  arc  similarly  de- 
pendent on  physical  conditions,  is  one  of  those  scientific  questions 
respecting  human  nature  which  are  still  in  abeyance.  It  is  yet  unde- 
cided whether  our  thouglits,  emotions,  and  volitions  arc  generated 
through  the  intervention  of  material  mechanism ;  wliether  wo  have 
oi-gans  of  thought  and  of  emotion,  in  the  same  sense  in  which  we  have 
organs  of  sensation.  Many  eminent  physi(»logists  hold  the  aflirmative. 
These  contend,  that  a  thought  (for  example)  is  as  much  the  result  of 
nervous  agency,  as  a  sensation:  that  some  particuhir  state  of  our  ner\'ou8 
system,  in  particular  of  that  central  portion  of  it  called  the  brain,  invaria- 
bly precedes,  and  is  presupposed  by,  every  state  of  our  cimsciousness. 
According  to  this  theory,  one  state  of  mhid  is  never  really  produced  by 
another:  all  are  produced  by  states  of  body.  When  one  thought  seems  to 
call  up  another  by  association,  it  is  not  really  a  thought  which  recalls  a 
thought ;  the  association  did  not  exist  between  the  two  thoughts,  but 
between  the  two  states  of  the  brain  or  nerves  which  preceded  the 
tlioughts ;  one  of  those  states  recalls  the  other,  each  being  attended,  in 
its  passage,  by  the  particular  mental  state  which  is  consequent  upon  it. 
On  this  theory,  the  unifonnities  of  succession  among  states  of  mind 
would  be  mere  derivative  uniformities,  resulting  from  tlie  laws  of  suc- 
cession of  the  bodily  states  Avhich  cause  them.  There  would  be  no 
original  mental  laws,  no  Laws  of  Mind  in  the  sense  in  which  I  use  the 
term,  at  all ;  but  Mental  ^Science  would  be  a  mere  brandi,  though  the 
highest  and  most  recondite  branch,  of  the  .Science  of  Physiology. 
This  is  what  ^L  Comte  must  be  understood  to  mean,  when  he  claims 
the  scientific  cognizance  of  moral  and  intellectual  phenomena  exclu- 
sively for  physiologists;  and  not  only  denies  to  Psychology,  or  Mental 
Philosophy  properly  so  called,  the  character  of  a  science,  but  places  it, 
in  the  chimerical  nature  of  its  objects  and  pretensions,  almost  on  a  par 
with  Astrology. 

But,  after  all  has  been  said  which  can  be  said,  it  remains  incontest- 
able by  M.  Comte  and  by  all  others,  that  there  do  exist  uniformities  of 
succession  among  .states  of  mind,  and  that  these  can  be  ascertained  by 
obser\'ation  and  experiment.  Moreover,  even  if  it  were  rendered  far 
more  certain  than  I  believe  it  as  yet  to  be,  that  every  mental  state  has 
a  nervous  state  for  its  immediate  antecedent  and  proximate  cause  ;  yet 
every  one  must  admit  that  we  are  wholly  ignorant  of  the  characteristics 
of  these  nervous  states;  we  know  not,  nor  can  hope  to  know,  in  what 
respect  one  of  them  differs  from  another;  and  our  only  nio<le  of  study- 
ing their  successions  or  coexistences  must  be  by  observing  the  succes- 
sions and  coexi.stences  of  the  mental  .states  of  whicli  they  are  supposed 
to  be  the  generators  or  causes.  The  succ«;ssions,  therefiire.  which  <»b- 
tain  among  mental  pluniomcna,  do  not  admit  of  lii'ing  deduced  from 
the  physifjloijical  laws  (jf  our  ner^•ous  organization;  and  all  real 
knowledge  of  them  must  contiimo,  for  a  long  time  at  lea.st,  if  not  for 
ever,  to  be  sought  in  the  direct  study,  by  obsunalion  and  experiment. 


532  LOGIC    OF    THE   MORAL    SCIENCES. 

of  the  mental  successions  themselves.  Since  therefore  the  order  of  our 
mental  phenomena  must  be  studied  in  those  phenomena,  and  not  in- 
ferred from  the  laws  of  any  phenomena  more  general,  there  is  a  dis- 
tinct and  separate  Science  of  Mind.  The  relations,  indeed,  of  that 
science  to  the  Science  of  Physiology  must  never  be  overlooked  or  un- 
dervalued. It  must  by  no  means  be  forgotten  that  the  law^s  of  mind 
may  be  derivative  laws  resulting  from  laws  of  animal  life,  and  that 
their  ti-uth,  therefore,  may  ultimately  depend  upon  physical  conditions ; 
and  the  influence  of  physiological  states  or  physiological  changes  in 
altering  or  counteracting  the  mental  successions,  is  one  of  the  most 
important  departments  of  psychological  study. 

§  3.  The  subject,  then,  of  Psychology,  is  the  uniformities  of  succes- 
sion, the  laws,  whether  ultimate  or  derivative,  according  to  which  one 
mental  state  succeeds  another ;  is  caused  by,  or  at  the  least,  is  caused 
to  follow,  another.  Of  these  laws,  some  are  general,  others  more 
special.     The  following  are  examples  of  the  most  general  laws. 

First :  Whenever  any  state  of  consciousness  has  once  been  excited 
in  us,  no  matter  by  what  cause  ;  an  inferior  degree  of  the  same  state  of 
consciousness,  a  state  of  consciousness  resembling  the  former,  but 
inferior  in  intensity,  is  capable  of  being  reproduced  in  us,  without 
the  presence  of  any  such  cause  as  excited  it  at  first.  Thus,  if  we  have 
once  seen  or  touched  an  object,  we  can  afterwards  think  of  the  object 
although  it  be  absent  from  our  sight  or  from  our  touch.  If  we  have 
been  joyful  or  grieved  at  some  event,  we  can  think  of,  or  remember, 
our  past  joy  or  gi'ief,  although  no  new  event  of  a  happy  or  a  painful 
nature  has  taken  place.  When  a  poet  has  put  together  a  mental  pic- 
ture of  an  imaginary  object,  a  Castle  of  Indolence,  a  Una,  or  a  Juliet, 
he  can  afterwards  think  of  the  ideal  object  he  has  created,  without  any 
fresh  act  of  intellectual  combination.  This  law  is  expressed  by  saying, 
in  the  language  of  Hume,  that  every  mental  impression  has  its  idea. 

Secondly :  These  Ideas,  or  secondary  mental  states,  are  excited  by 
our  impressions,  or  by  other  ideas,  according  to  certain  laws  which 
are  called  Laws  of  Association.  Of  these  laws  the  first  is,  that  simi- 
lar ideas  tend  to  excite  one  another.  The  second  is,  that  when  two 
impressions  have  been  frequently  experienced  (or  even  thought  of) 
either  simultaneously  or  in  immediate  succession,  then  whenever 
either  of  these  impressions  or  the  idea  of  it  recurs,  it  tends  to  excite 
the  idea  of  the  other.  The  third  law  is,  that  gi'eater  intensity,  in  either 
or  both  of  the  impressions,  is  equivalent,  in  rendering  them  excitable 
by  one  another,  to  a  greater  frequency  of  conjunction.  These  are  the 
laws  of  Ideas  :  upon  which  I  shall  not  enlarge  in  this  place,  but 
refer  the  reader  to  works  professedly  psychological,  in  particular  to 
Mr.  Mill's  Analysis  of  the  Phenomena  of  the  Human  Mind,  where  the 
principal  laws  of  association,  both  in  themselves  and  in  many  of  their 
applications,  are  copiously  exemplified,  and  with  a  masterly  hand. 

These  simple  or  elementary  Laws  of  Mind  have  long  been  ascer- 
tained by  the  ordinary  methods  of  experimental  inquiry ;  nor  could 
they  have  been  ascertained  in  any  other  manner.  But  a  certain  num- 
ber of  elementary  laws  having  thus  been  obtained,  it  is  a  fair  subject 
of  scientific  inquiry  how  far  those  laws  can  be  made  to  go  in  explain- 
ing the  actual  phenomena.  It  is  obvious  that  complex  laws  of  thought 
and  feeling  not  only  may,  but  must,  be  generated  from  these  simple 


LAWS  OF  Mr\n.  533 

laws.  And  it  is  to  be  remarked,  that  the  ease  is  not  always  one  of 
Composition  of  Causes:  the  eflect  of  concurrinir  causes  is  not  always 
precisely  the  sum  of  the  eflects  of  those  causes  when  separate-,  nor  even 
always  an  ett'ect  of  the  same  kind  with  them.  Hevertin»?  to  the  dis- 
tinction which  occupies  so  prominent  a  place  in  the  theory  of  induc- 
tion ;  the  laws  of  the  phenomena  of  mind  are  sometimes  analot^ous  to 
mechanical,  but  sometimes  also  to  chemical  laws.  When  many  im- 
pressions or  ideas  are  operatinej  in  the  mind  together,  th»'n!  sometimes 
takes  place  a  process  of  a  similar  kind  to  chemical  combination. 
Wlien  inipressii>ns  have  been  so  often  experienced  in  conjunction,  that 
each  of  them  calls  up  readily  and  instantaneously  the  ideas  of  the  whole 
group,  those  ideas  sometimes  tnelt  and  coalesce  into  one  another,  and 
appear  not  several  ideas  but  one  ;  in  the  same  manner  as  when  the 
seven  prismatic  colors  are  jiresented  to  the  eye  in  rapid  siuxession, 
the  sensation  produced  is  that  of  ^vhite.  J^ut  as  in  this  bust  case  it  is 
correct  to  say  that  the  seven  colors  when  they  rapidly  follow  one 
another  generate  white,  but  not  that  they  actually  are.  white;  so  it 
appears  to  me  that  the  Complex  Idea,  formed  by  the  blending  together 
of  several  simpler  ones,  should,  when  it  really  appears  simple,  (that  is 
when  the  separate  elements  are  not  consciously  distinguishable  in  it,) 
be  said  to  result  from,  or  be  getierated  hi/,  the  simple  ideas,  not  to  cu/i- 
sist  of  them.  Our  idea  of  an  orange  really  consists  of  the  simple  ideas 
of  a  certain  color,  a  certain  form,  a  certain  taste  and  smell,  &c.,  be- 
cause we  can  by  interrogating  our  consciousness,  perceive  all  these  ele- 
ments in  the  idea.  But  we  cannot  perceive,  in  so  apparently  simple  a 
feeling  as  our  perception  of  the  shape  of  an  object  by  the  eye,  all  that 
multitude  of  ideas  derived  from  other  senses,  without  which  it  is  well 
ascertained  that  no  such  visual  perception  would  ever  have  had  exist- 
ence ;  nor,  in  our  idea  of  Extension,  can  we  discover  those  elementary 
ideas  of  resistance,  derived  from  f)ur  muscular  frame,  in  which  Dr. 
Brown  has  rendered  it  highly  probable  that  the  idea  originates.  These 
therefore  are  cases  of  mental  chemistry  :  in  which  it  is  proper  to  say 
that  the  simple  ideas  generate,  rather  than  that  they  compose,  the  com- 
plex ones.  * 

With  respect  to  all  the  other  constituents  of  the  mind,  its  beliefs, 
its  abstruser  conceptions,  its  sentiments,  emotions,  and  volitions  ;  there 
are  some  (among  whom  are  Hartley,  and  the  author  of  the  Analysis) 
who  think  that  the  whole  of  these  are  [generated  from  simple  ideas  of 
sensation,  by  a  chemistry  similar  to  that  which  we  have  just  cxemj)li- 
fied.  I  am  unable  to  satisfy  myself  that  this  conclusion  is,  in  the  pres- 
ent state  of  our  knowledge,  fully  made  out.  In  many  cases  I  cannot 
even  perceive,  that  the  line  of  argument  adopted  has  much  tendency 
to  establish  it.  The  philosophers  to  whom  I  have  referred  have,  in- 
deed, conclusively  .shown  that  there  is  such  a  thing  as  mental  chemis- 
try;  that  the  heterogeneous  nature  of  a  feeling.  A,  c(msidered  iu 
relation  to  B  and  C,  is  no  conclusive  argument  against  its  being  gener- 
ated from  B  and  C.  Ha\-ing  prove<l  this,  ihvy  proceed  to  show,  that 
where  A  is  found,  B  and  C  were,  or  may  have  been,  present,  and  why 
therefore,  they  say,  should  not  A  have  been  generated  from  B  and  C  ] 
But  even  if  this  evidence  were  canied  to  the  highest  degree  of  com- 
pleteness which  it  admits  of;  if  it  wtjn;  shown  that  certain  groups  of 
associated  ideas  not  only  might  have  been,  but  actually  were,  present 
whenever  the  raoro  recondite  mental  feeling  was  exponenced ;  tliis 


534  LOGIC    OF    THE    MORAL  SCIENCES. 

would  amount  only  to  the  Method  of  Agreement,  and  could  not  prove 
causation  until  confirmed  by  the  more  conclusive  evidence  of  the 
Method  of  Difference.  If  the  question  be  whether  Belief  is  a  mere 
case  of  close  association  of  ideas,  it  would  be  necessary  to  examine 
experimentally  if  it  be  true  that  any  ideas  whatever,  provided  they  are 
associated  together  with  the  required  degiee  of  closeness,  are  suffi- 
cient to  give  rise  to  belief  If  the  inquiry  be  into  the  origin  of  moral 
feelings,  the  feelings  for  example  of  moral  reprobation,  the  first  step 
must  be  to  compare  all  the  varieties  of  actions  or  states  of  mind  which 
are  ever  morally  disapproved,  and  see  whether  in  all  these  cases  it  can 
be  shown  that  the  action  or  state  of  mind  had  become  connected  by 
association,  in  the  disapproving  mind,  with  some  particular  class  of 
hateful  or  disgusting  ideas ;  and  the  method  employed  is,  thus  far,  that 
of  Agreement.  But  this  is  not  enough.  Supposing  this  proved,  we 
must  try  further,  by  the  Method  of  Difference,  whether  this  particular 
kind  of  hateful  or  disgusting  ideas,  when  it  becomes  associated  with  an 
action  previously  indifferent,  will  render  that  action  a  subject  of  moral 
disapproval.  If  this  question  can  be  answered  in  the  affirmative,  it  is 
shown  to  be  a  law  of  the  human  mind,  that  an  association  of  that  par- 
ticular description  is  the  generating  cause  of  moral  reprobation.  But 
these  experiments  have  either  never  been  tried,  or  never  with  the  de- 
gree of  precision  indispensable  for  conclusiveness ;  and,  considering 
the  difficulty  of  accurate  experimentation  upon  the  human  mind,  it  will 
probably  be  long  before  they  are  so. 

i  It  is  further  to  be  remembered,  that  even  if  all  which  this  theory  of 
mental  phenomena  contends  for  could  be  proved,  we  should  not  be  the 
more  enabled  to  resolve  the  laws  of  the  more  complex  feelings  into 
those  of  the  simpler  ones.  The  generation  of  one  class  of  mental 
'.phenomena  from  another,  whenever  it  can  be  made  out,  is  a  highly 
interesting  fact  in  psychological  chemistry ;  but  it  no  more  supersedes 
jthe  necessity  of  an  experimental  study  of  the  generated  phenomenon, 
than  a  knowledge  of  the  properties  of  oxygen  and  sulphur  enables  us 
to  deduce  those  of  sulphuric  acid  without  specific  observation  and  ex- 
periment. Whatever,  therefore,  may  be  the  final  issue  of  the  attempt 
to  account  for  the  origin  of  our  judgments,  our  desires,  or  our  volitions, 
jfrom  simpler  mental  phenomena,  it  is  not  the  less  imperative  to  ascer- 
!tain  the  sequences  of  the  complex  phenomena  themselves,  by  special 
study  in  conformity  to  the  canons  of  Induction.  Thus,  in  respect  of 
Belief,  the  psychologist  will  always  have  to  inquire,  what  beliefs  we 
have  intuitively,  and  according  to  what  laws  one  belief  produces 
another ;  what  are  the  laws  in  virtue  of  which  one  thing  is  recognized 
by  the  mind,  either  rightly  or  erroneously,  as  e\ddence  of  another 
, thing.  In  regai'd  to  Desire,  he  will  examine  what  objects  we  desire 
naturally,  and  by  what  causes  we  are  made  to  desire  things  originally 
indifferent  or  even  disagreeable  to  us ;  and  so  forth.  It  may  be  re- 
marked, that  the  general  laws  of  association  prevail  among  these  more 
intricate  states  of  mind,  in  the  same  manner  as  among  the  simpler 
ones.  A  desire,  an  emotion,  an  idea  of  the  higher  order  of  abstrac- 
tion, even  our  judgments  and  volitions  when  they  have  become  habitual, 
are  called  up  by  association,  according  to  precisely  the  same  laws  as 
our  simple  ideas. 

§  4.  In  the  course  of  these  inquiries  it  will  be  natural  and  necessary 


1 


LAWS    OF    MIND.  535 

to  examine,  how  far  the  production  of  one  state  of  mind  by  another  is 
influenced  by  any  assignable  state  of  body.  The  commonest  obsei-va- 
tion  shows  that  dilferent  minds  are  susceptible  in  very  diflercnt  degrees 
to  the  action  of  the  same  psychologic-al  causes.  The  idea,  for  example, 
of  a  given  desirable  object,  will  excite  in  dilferent  minds  very  diflercnt 
degrees  of  intensity  of  desire.  The  same  subject  of  meditation,  pre- 
sented to  diflercnt  minds,  will  excite  in  them  very  unecpial  degrees  of 
intellectual  action.  These  diflerences  of  mental  susceptibility  in  dif- 
ferent individuals  may  ho,  Ji/sl,  original  and  ultimate  iacXs,  or,  secondly, 
they  may  be  consequences  of  the  previous  mental  history  of  those  in- 
dividuals, or,  thirdly  and  lastly,  they  may  depend  upon  varieties  of 
physical  organization.  That  the  previous  mental  history  of  the  indi- 
viduals must  have  some  share  in  pnjducing  or  in  modifying  the  whole 
of  their  present  mental  character,  is  an  inevitable  consecjuence  of  the 
laws  of  mhid ;  but  that  diflerences  of  bodily  structure  also  cobpt-rate, 
is  the  assertion  not  only  of  phrenologists,  but,  to  a  greater  or  less 
extent,  of  all  physiologists  who  lay  any  stress  upon  the  magnitude  of 
the  hemispheres  of  the  brain,  indicated  by  the  facial  angle,  as  a  meas- 
ure of  natural  intelligence,  or  upon  temperament  as  a  source  of 
moral  and  emotional  peculiarities. 

AVTiat  portion  of  these  assertions  the  physiological  school  of  psychol- 
ogists, whether  phrenologists  or  otherwise,  have  either  succeeded  in 
establishing,  or  shown  ground  for  supposing  it  possible  to  establish 
hereafter,  1  would  not  undertake  to  say.  Nor  do  I  believe  that  the 
inquiry  will  be  brought  to  a  satisfactory  issue,  while  it  is  abandoned, 
as  unfortunately  it  has  hitherto  been,  to  physiologists  who  have  no 
adequate  knowledge  of  mental  laws,  or  psychologists  who  have  no 
sufficient  acquaintance  with  j)hysiology. 

It  is  certain  that  the  natural  diflerences  which  really  exist  in  the 
mental  predispositions  or  susceptibilities  of  diflercnt  persons,  arc  often 
not  uncomiected  with  diversities  in  their  f)rganic  constitution.  But  it 
does  not  therefore  follow  that  these  organic  diflerences  must  in  all 
cases  influence  the  mental  phenomena  directly  and  immediately.  They 
may  often  aflect  them  through  the  medium  of  their  psychological 
causes.  For  example,  the  idea  of  some  particular  pleasure  may  excite 
in  different  persons,  even  indej)endently  of  habit  or  education,  very 
different  strengths  of  desire,  and  this  may  be  the  effect  of  their  dif- 
ferent degrees  or  kinds  of  nerv(»us  susceptibility ;  but  these  organic 
diflerences,  we  must  remember,  will  render  the  pleasurable  sensation 
itself  more  inten.se  in  one  of  these  ])erson8  than  in  the  other ;  .so  that 
the  idea  of  the  pleasure  will  also  be  an  intenser  feeling,  and  will,  by 
the  operation  of  mere  mental  laws,  excite  an  intenser  desire,  without 
its  being  necessary  to  suppose  that  tlu;  desire  itself  is  directly  influ- 
enced by  the  physical  peculiarity.  As  in  this,  so  in  many  cases,  such 
differences  in  the  kind  or  in  the  intensity  of  the  physical  sensations  as 
must  necessarily  result  from  diflV'rences  of  bodily  organization,  will  of 
themselves  account  for  many  dilferences  not  only  in  the  di-gree,  but 
even  in  the  kind,  of  the  other  mental  phenomena.  So  true  is  this,  that 
even  diff'erent  qualities  of  mind,  different  ty]>es  of  mental  character, 
will  naturally  be  produced  by  mere  differences  of  intensity  in  the  sen- 
sations generally.  This  truth  is  so  well  exemplified,  and  in  so  short  a 
compass,  in  a  very  able  e.ssay  on  Dr.  Priestley,  mentioned  in  a  former 
chapter,  that  I  think  it  right  to  quote  the  passage  : — 


536  LOGIC    OF    THE    MORAL   SCIENCES. 

"The  sensations  which  form  the  elements  of  all  knowledge  are 
received  either  simultaneously  or  successively ;  when  several  are 
received  simultaneously,  as  the  smell,  the  taste,  the  color,  the  form, 
&c.,  of  a  fruit,  their  association  together  constitutes  our  idea  of  an 
object;  when  received  successively,  their  association  makes  up  the 
idea  of  an  event.  Anything,  then,  which  favors  the  associations  of 
synchronous  ideas,  will  tend  to  produce  a  knowledge  of  objects,  a 
perception  of  qualities ;  while  anything  which  favors  association  in  the 
successive  order,  will  tend  to  produce  a  knowledge  of  events,  of  the 
order  of  occuri'ences,  and  of  the  connexion  of  cause  and  eifect :  in 
other  words,  in  the  one  case  a  perceptive  mind,  with  a  discriminative 
feeling  of  the  pleasurable  and  painful  properties  of  things,  a  sense  of 
the  grand  and  the  beautiful,  will  be  the  result :  in  the  other,  a  mind 
attentive  to  the  movements  and  phenomena,  a  ratiocinative  and  philo- 
sophic intellect.  Now  it  is  an  acknowledged  principle,  that  all  sensa- 
tions experienced  during  the  presence  of  any  vivid  impression,  become 
strongly  associated  with  it,  and  with  each  other ;  and  does  it  not  follow, 
that  the  synchronous  feelings  of  a  sensitive  constitution  (/.e.  the  one 
which  has  vivid  impressions)  will  be  more  intimately  blended  than  in 
a  differently  formed  mind  1  If  this  suggestion  has  any  foundation  in 
truth,  it  leads  to  an  inference  not  unimportant;  that  where  nature  has 
endowed  an  individual  with  great  original  susceptibility,  he  will  proba- 
bly be  distinguished  by  fondness  for  natural  history,  a  relish  for  the 
beautiful  and  great,  and  moral  enthusiasm  ;  where  there  is  but  a 
mediocrity  of  sensibility,  a  love  of  science,  of  abstract  truth,  with  a 
deficiency  of  taste  and  of  fervor,  is  likely  to  be  the  result." 

We  see  from  this  example,  that  when  the  general  laws  of  mind  are 
more  accurately  known,  and  above  all,  more  skillfully  applied  to  the 
detailed  explanation  of  mental  peculiarities,  they  will  account  for  many 
more  of  those  peculiarities  than  is  ordinarily  supposed.  I  by  no  means 
seek  to  imply  from  this  that  they  will  account  for  all  ;  but  that  which 
remains  to  be  otherwise  accounted  for  is  merely  a  residual  phenomenon ; 
and  the  amount  of  the  residue  can  only  be  determined  by  persons  already 
familiar  with  the  expla,nation  of  phenomena  by  psychological  laws. 

On  the  other  hand,  it  is  equally  clear  that  when  physiologists,  taking 
into  account  the  whole  animal  creation,  attempt,  by  a  judicious  appli- 
cation of  the  Method  of  Concomitant  Variations,  grounded  chiefly  on 
extreme  cases,  to  establish  a  connexion  between  the  strength  of  differ- 
ent mental  propensities  or  capacities  and  the  proportional  or  absolute 
magnitudes  of  different  regions  of  the  brain ;  the  evidences  which  are 
or  may  be  produced  in  support  of  this  pretension,  ought  to  be  taken 
into  serious  consideration  by  psychologists.  Nor  will  this  part  of  the 
science  of  mind  be  ever  cleared  up,  until  those  evidences  shall  be  not 
only  sifted  and  analyzed,  but,  when  necessary,  added  to  and  completed, 
by  persons  sufficiently  versed  in  psychological  laws  to  be  capable  of 
discriminating  how  much  of  each  phenomenon  such  laws  will  suffice  to 
explain. 

Even  admitting  the  influence  of  cerebral  conformation  to  be  as  gi-eat 
as  is  contended  for,  it  would  still  be  a  question  how  far  the  cerebral 
development  determined  the  propensity  itself,  and  how  far  it  only  acted 
by  modifying  the  nature  and  degree  of  the  sensations  on  which  the 
propensity  may  be  psychologically  dependent.  And  it  is  certain  that, 
an  human  beings  at  least,  differences  in  education  and  in  outward  cir- 


ETHOLOGY.  537 

cunistanroa,  togothor  with  pliysical  didiTcncps  in  tlio  sonsatioiis  jinxlu- 
ced  in  (.lifll'rout  individuals  by  the  sainr  external  or  internal  cause,  are 
capable  ot"  accounting  for  a  far  i^reater  portion  of  character  than  is 
supposed  even  by  the  most  moderate  phrenologists.  There  are,  how- 
ever, many  mental  facts  which  do  not  seem  to  arlinit  of  tliis  mode  of 
explanation.  Such,  to  take  the  srTon<X(^st  case,  are  the  various  instincts 
of  animals,  the  portion  of  human  nature  which  corresponils  to  those 
instincts.  No  mode  h;is  been  suggested,  even  by  way  of  hypothesis, 
in  which  these  can  receive  any  satisfactory,  or  even  plausible,  expla- 
nation from  psychological  causes  ahme  ;  and  they  may  probably  be 
found  to  have  as  positive,  and  even  perhaps  as  direct  and  innnediate,  a 
•coimexion  with  physical  conditions  of  the  brain  and  nerves,  as  any  of 
our  mere  sensations  have. 

How  much  further  this  remark  might  be  extended,  I  do  not  pretend 
to  determine.  My  object  is  not  to  establish  the  doctrines,  but  to  dis- 
criminate the  true  Method,  of  mental  science  ;  and  this,  so  far  as 
regards  the  establishment  of  the  general  and  elementary  laws,  maybe 
considered  to  be  sufficiently  accomplished. 


CHAPTER  V. 

OF   ETHOLOGY,  OR   THE    SCIENCE   OF  THE   FORMATION'  OF   CHARACTER. 

§  1.  The  Laws  of  Mind,  as  characterized  in  the  preceding  chapter, 
constitute  the  universal  or  abstract  portion  of  the  philosophy  of  human 
nature  ;  and  all  the  various  truths  of  common  experience,  constitutinf 
a  practical  knowledge  of  mankind,  must,  to  tlie  extent  to  which  they 
are  truths,  be  results  or  conseipiences  of  these.  Such  familiar  maxims, 
when  collected  d  poxtcriorl  from  observation  of  life,  occupy  among  the 
truths  of  the  science  the  place  of  what,  in  our  analysis  of  Induction, 
have  so  often  been  spoken  of  under  the  title  of  Empirical  Laws. 

An  Empirical  Law  (it  will  be  remembered)  is  an  unifomiitv,  whether 
of  succession  or  of  coexistence,  which  holds  true  in  all  instances  within 
our  limits  of  observation,  but  is  not  of  a  nature  to  afford  any  assurance 
that  it  would  hold  beyond  those  limits  ;  eithi^r  because  the  consiMiucnt 
is  not  really  the  effect  of  the  antecedt-nt,  but  forms  part  along  with  it 
of  a  chain  of  effects,  flowing  from  pri(jr  causes  not  yet  ascertained;  or 
because  there  is  ground  to  believe  that  the  .secjuence  (though  a  case  of 
causation)  is  resolvable  into  simpler  sefpiences,  and,  depending  there- 
fore upon  a  concurrence  of  several  natural  agencies,  is  exposed  to  an 
unknown  multitude  of  possibilities  of  counteraction,  in  (fiber  words, 
an  empirical  law  is  a  generalization,  of  which,  not  content  with  fniding 
it  true,  we  are  obliged  to  ask,  why  is  it  true  %  knowing  that  its  truth  is 
not  absolute,  but  depends  upon  some  mtjre  general  conditions,  and  that 
it  can  only  be  relied  on  in  so  far  as  there  is  ground  of  assurance  that 
those  conditions  are  realized. 

Now,  the  observations  concerning  human  affairs  collected  from  com- 
mon experience,  are  precisely  of  this  nature.  Evcjn  if  they  were  uni- 
versally and  exactly  true  within  the  bounds  of  cxperi«;nco,  which  they 
never  are,  still  they  are  not  the  ultimate  laws  of  human  action  ;  they 
3Y 


538  LOGIC    OF    THE    MORAL    SCIENCES. 

are  not  the  principles  of  human  nature,  but  results  of  those  principles 
under  the  circumstances  in  which  mankind  have  happened  to  be  placed. 
When  the  Psalmist  "said  in  his  wrath  that  all  men  are  bars,"  he  enun- 
ciated what  in  some  ages  and  countries  is  borne  out  by  ample  experi- 
ence •  but  it  is  not  a  law  of  man's  nature  to  lie  ;  though  it  is  one  of  the 
consequences  of  the  laws  of  his  nature,  that  the  habit  of  lying  is  nearly 
universal  when  certain  external  circumstances  exist  universally,  espe- 
cially circumstances  productive  of  habitual  distrust  and  fear.     When 
the  character  of  the  old  is  asserted  to  be  cautious,  and  of  the  young 
impetuous,  this,  again,  is  but  an  empirical  law;  for  it  is  not  because  of 
their  youth  that  the  young  are  impetuous,  nor  because  of  their  age  that 
the  old  are  cautious.     It  is  because  the  old,  during  their-  many  years  of 
life,  have  generally  had  much  experience  of  its  various  evils,  and  having 
suffered  or  seen  others  suffer  much  from  incautious  exposure  to  them, 
have   acquired   associations    favorable    to    circumspection  :  while  the 
young,  as  well  from  the  absence  of  similar  experience  as  from  the 
greater  strength  of  the    inclinations  which  tempt  them  into  danger, 
expose  themselves  to  it  more  readily.     Here,  then,  is  the  explanation 
of  the  empirical  law  ;  here  are  the  conditions  which  ultimately  deter- 
mine whether  the  law  holds  good  or  not.     If  an  old  man  has  not  been 
oftener  than  most  young  men  in  contact  with  danger  and  difficulty,  he 
will  be  equally  incautious  :  if  a  youth  has  not  stronger  passions  than  an 
old  man,  he  probably  will  be  as  little  enterprising.      The  empirical  law 
derives  whatever  truth  it  has,  fi-om  the  causal  laws  of  which  it  is  a 
consequence.     If  we  know  those  laws,  we  know  what  are  the  limits  to 
the  derivative  law :  while,  if  we  have  not  yet  accounted  for  the  empir- 
ical law — if  it  rests  only  upon  observation — there  is  no  safety  in  apply- 
ing it  far  beyond  the  hmits  of  time,  place,  and  circumstance,  in  which 
the  observations  were  made. 

The  really  scientific  truths,  then,  are  not  these  empirical  laws,  but 
the  causal  law^s  which  explain  them.  The  empirical  laws  of  those 
phenomena  which  depend  on  known  causes,  and  of  which  a  general 
theory  can  therefore  be  constructed,  have,  whatever  may  be  their 
value  in  practice,  no  other  function  in  science  than  that  of  verifying 
the  conclusions  of  theory.  Still  more  must  this  be  the  case  when  most 
of  the  empirical  laws  amount,  even  within  the  limits  of  obsei-vation, 
only  to  approximate  generalizations. 

§  2.  This  however  is  not,  so  much  as  is  sometimes  supposed,  a  pe- 
culiarity of  the  sciences  called  moral.  It  is  only  in  the  simplest 
branches  of  science  that  empirical  laws  are  ever  exactly  true  ;  and 
not  always  in  those.  Astronomy,  for  example,  is  the  simplest  of  all 
the  sciences  which  explain,  in  the  concrete,  the  actual  course  of  natu- 
ral events.  The  causes,  or  forces,  on  which  astronomical  phenomena 
depend,  are  fewer  in  number  than  those  which  determine  any  other  of 
the  great  phenomena  of  nature.  Accordingly,  as  each  effect  results 
from  the  conflict  of  but  few  causes,  a  great  degi-ee  of  regularity  and 
uniformity  might  be  expected  to  exist  among  the  effects ;  and  such  is 
really  the  case  :  they  have  a  fixed  order,  and  return  in  cycles.  But 
propositions  which  should  express,  with  absolute  con-ectness,  all  the 
successive  positions  of  a  planet  until  the  cycle  is  completed,  would  be 
of  almost  unmanageable  complexity,  and  could  be  obtained  from  the- 
ory alone.     The  generalizations  which  can  be  collected  on  the  subject 


ETHOLOGY.  539 

from  direct  observation,  even  sucli  as  Kepler's  law,  are  mere  aj)j)rox- 
imations:  the  planets,  owing  to  their  perturbations  by  one  another,  do 
not  move  in  exact  ellipses.  Thus,  even  in  astronomy,  perfect  exact- 
ness in  the  mere  empirical  laws  is  not  to  be  lot)kcd  for ;  nmch  less, 
then,  in  more  complex  subjects  of  in(iuiry. 

The  same  example  shows  how  little  can  be  inferred  against  the 
universality  or  even  the  simplicity  of  the  ultimate  laws,  from  the  im- 
possibiHty  of  establishing  any  but  approximate  empirical  laws  of  the 
eifects.  The  laws  of  causation  according  to  which  a  cIjlss  of  phenom- 
ena are  produced  may  be  very  few  and  simple,  and  yet  the  effects 
themselves  may  be  so  various  and  complicated  that  it  shall  be  impossi- 
ble to  trace  any  regularity  whatever,  extending  compU-tely  through 
them.  For  the  phenomena  in  question  may  be  of  an  eminently  modi- 
fiable character ;  insomuch  that  innumerable  circumstances  are  capa- 
ble of  influencing  the  efi'ect,  although  they  may  all  do  it  according  to  a 
very  small  number  of  laws.  Suppose  that  all  which  passes  in  the  mind 
of  man  is  determined  by  a  few  simple  laws  :  still,  if  those  laws  be  such 
that  there  is  not  one  of  the  facts  surroimding  a  human  being,  or  of  the 
events  which  happen  to  him,  that  docs  not  influence  in  some  mode  or 
degree  his  subsequent  mental  history,  and  if  the  circumstances  of  dil- 
ferent  human  beings  are  extremely  different,  it  will  be  no  wonder  if 
very  few  propositions  can  be  made  respecting  the  details  of  their  con- 
duct or  feelings,  which  will  be  true  of  all  mankind. 

Now,  without  deciding  whether  the  ultimate  laws  ofour  mental  nature 
are  few  or  many,  it  is  at  least  certain  that  they  are  of  the. above  descrip- 
tion. It  is  certain  that  our  mental  states,  and  our  mental  capacities 
and  susceptibilities,  are  modified,  either  for  a  time  or  permanently,  by 
everything  which  happens  to  us  in  life.  Considering,  therefiire,  how 
much  these  modifying  causes  differ  in  the  case  of  any  twc»  individuals, 
it  would  be  unreasonable  to  expect  that  the  empirical  laws  of  the  hu- 
man mind,  the  generalizations  we  make  respecting  the  feelings  or  ac- 
tions of  mankind  without  reference  to  the  causes  that  determine  them, 
should  be  anything  but  approximate  generalizations.  They  arc  the 
common  wisdom  of  common  life,  and  as  such  are  invaluable ;  espe- 
cially as  they  are  mostly  to  be  applied  to  cases  not  very  dissimilar  to 
those  from  which  they  were  collected.  But  if  maxims  of  this  sort,  col- 
lected from  Englishmen,  come  to  be  applied  to  Frenchmen,  or  col- 
lected from  the  present  day,  are  applied  to  past  or  future  generations, 
they  are  apt  to  be  very  much  at  fault.  Unless  we  have  resolved  the 
empirical  law  into  the  laws  of  the  causes  upon  which  it  depends,  and 
ascertained  that  those  causes  extend  to  the  case  which  we  have  in 
view,  there  can  be  no  reliance  placed  in  our  inferences.  For  every 
individual  is  surrounded  by  circumstances  different  iroin  those  f>f  every 
otlier  individual ;  every  nation  or  generation  of  mankind  from  every 
other  nation  or  generation :  and  none  of  these  differences  are  without 
their  influence  in  forming  a  different  type  of  character.  There  is,  in- 
deed, also  a  certain  general  resemblance ;  but  peculiarities  of  circum- 
stances are  continually  constituting  exceptions  even  to  the  projiositions 
which  are  true  in  the  great  majority  of  cases. 

Althf>ugh,  however,  there  is  scarcely  any  mode  of  feeling  or  conduct 
which  is,  in  the  absolute  sense,  common  t(j  all  mankind  ;  and  though 
the  generalizations  which  assert  that  any  given  variety  of  conduct  or 
feeling  will  be  found  universally  (however  nearly  they  may  approxi- 


540  LOGIC    OF    THE    MORAL   SCIENCES. 

mate  to  truth  within  given  limits  of  observation),  will  oe  considered  as 
scientific  propositions  by  no  one  who  is  at  all  familiar  with  scientific 
investigation  J  yet  all  modes  of  feeling  and  conduct  met.with  among 
mankind  have  causes  which  produce  them;  and  in  the  propositions 
which  assign  those  causes  will  be  found  the  explanation  of  the  empiri- 
cal laws,  and  the  limiting  principle  of  our  reliance  on  them.  Men  do 
not  all  feel  and  act  alike  in  the  same  circumstances ;  but  it  is  possible 
to  determine  what  makes  one  man,  in  a  given  position,  feel  or  act  in 
one  way,  another  in  another ;  how  any  given  mode  of  feeling  and  con- 
duct, compatible  with  the  general  laws  (physical  and  mental)  of  human 
nature,  has  been,  or  may  be,  formed.  In  other  words,  mankind  have 
not  one  universal  character,  but  there  exist  universal  laws  of  the  For- 
mation of  Character.  And  since  it  is  by  these  laws,  combined  with 
the  facts  of  each  particular  case,  that  the  whole  of  the  phenomena  of 
human  action  and  feeling  are  produced,  it  is  upon  these  that  every 
rational  attempt  to  construct  the  science  of  human  nature  in  the  con- 
crete, and  for  practical  pm^poses,  must  proceed. 

§  3.  The  laws  then  of  the  formation  of  character  being  the  principal 
object  of  scientific  inquiry  into  human  nature,  it  remains  to  determine 
the  method  of  investigation  best  fitted  for  ascertaining  them.  And  the 
logical  principles  according  to  which  this  question  is  to  be  decided, 
must  be  those  which  preside  over  every  other  attempt  to  investigate 
the  laws  of  very  complex  phenomena.  For  it  is  evident  that  both  the 
character  of  any  human  being,  and  the  aggregate  of  the  circumstances 
by  which  that  character  has  been  formed,  are  facts  of  a  high  order  of 
complexity.  Now  to  such  cases  we  have  seen  that  the  Deductive 
Method,  setting  out  from  general  laws,  and  verifying  their  conse- 
quences by  specific  experience,  is  alone  applicable.  The  grounds  of 
this  great  logical  doctrine  have  formerly  been  stated  :  and  its  truth 
will  derive  additional  support  from  a  brief  examination  of  the  speciali- 
ties of  the  present  case. 

There  are  only  two  modes  in  which  laws  of  nature  can  be  ascer- 
tained :  deductively,  and  experimentally  :  including  under  the  denomi- 
nation of  experimental  inquiry,  observation  as  well  as  artificial  experi- 
ment. Are  the  laws  of  the  formation  of  character  susceptible  of  a 
satisfactory  investigation  by  the  method  of  experimentation  ]  Evi- 
dently not ;  because  even  if  we  suppose  unlimited  power  of  varying 
the  experiment,  (which  is  abstractedly  possible,  though  no  one  but  an 
oriental  despot  either  has  that  power,  or  if  he  had,  would  be  disposed 
to  exercise  it,)  a  still  more  essential  condition  is  wanting  :  the  power  of 
performing  any  of  the  experiments  with  scientific  accuracy. 

The  instances  requisite  for  the  prosecution  of  a  directly  experimental 
inquiry  into  the  formation  of  character,  would  be  a  number  of  human 
beings  to  bring  up  and  educate,  from  infancy  to  mature  age.  And  to 
perform  any  one  of  these  experiments  with  scientific  propriety,  it  would 
be  necessary  to  know  and  record  every  sensation  or  impression  received 
by  the  young  pupil  from  a  period  long  before  it  could  speak ;  includ- 
ing its  own  notions  respecting  the  sources  of  all  those  sensations  and 
impressions.  It  is  not  only  imposssble  to  do  this  completely,  but  even 
to  do  so  much  of  it  as  should  constitute  a  tolerable  approximation. 
One  apparently  trivial  circumstance  which  eluded  our  vigilance,  might 
let  in  a  train  of  impressions  and  associations  sufficient  to  vitiate  the  ex- 


ETHOLOGY.  511 

perimcnt  as  an  authentic  exhibition  of  the  eflecls  flowing  from  given 
causes.  No  one  wlio  lias  sufficiently  refletted  on  education  is  i^Ml(>- 
rant  of  this  truth;  and  whoever  has  not,  will  fuid  it  most  instructivfly 
illustrated  in  the  writings  of  Rousseau  and  Hclvetius  on  that  great 
subject. 

Under  this  impossibility  of  studying  the  laws  of  the  formation  of 
character  by  experiments  purposely  contrived  to  elucidate  them,  there 
remains  the  resource  of  simple  observation.  But  if  it  be  impossible  to 
ascertain  the  inHuencing  circumstances  with  any  approach  to  complete- 
ness, even  when  we  have  the  shaping  of  them  ourselves,  much  more 
impossible  is  it  when  the  cases  are  further  removed  from  our  observa- 
tion, and  altogether  out  of  our  control.  Consider  tin-  diiliculty  of  the 
veiy  first  step — of  ascertaining  what  actually  is  the  character  of  the 
individual,  in  each  particular  case  that  we  examine.  There  is  hardly 
any  person  living,  concerning  some  essential  part  of  whoso  character 
there  are  not  differences  of  opinion  even  amotig  his  intimate  acfjuaint- 
ance  :  and  a  single  action,  or  conduct  continued  only  for  a  short  time, 
goes  a  very  little  way  indeed  towards  ascertaining  it.  We  can  only 
make  our  observations  in  a  rough  way,  and  en  maasc  ;  not  attempting 
to  ascertain  completely,  in  any  given  instance,  what  character  has  been 
formed,  and  still  less  by  what  causes  ;  but  only  observing  in  what  state 
of  previous  circumstances  it  is  found  that  certain  marked  mental  (piali- 
ties  or  deficiencies  oftcncst  exist.  These  conclusions,  besides  that  they 
are  mere  approximate  generalizations,  deserve  no  reliance  even  as 
such,  unless  the  instances  are  sufficiently  numerous  to  eliminate  not 
only  chance,  but  every  accidental  circumstance  in  which  a  number  of 
the  cases  examined  may  happen  to  have  resembled  one  another.  So 
numerous  and  various,  moreover,  are  the  circumstances  which  form 
individual  character,  that  the  consequence  of  any  particular  combina- 
tion is  hardly  ever  some  definite  and  strongly  marked  character,  always 
found  where  that  combination  exists,  and  not  otherwise.  What  is  ob- 
tained, even  after  the  most  extensive  and  accurate  observation,  is  mere- 
ly a  comparative  result ;  as  for  example,  that  in  a  given  number  of 
Frenchmen,  taken  indiscriminately,  there  will  be  found  more  persona 
of  a  particular  mental  tendency,  and  fewer  of  the  contrary  tendency, 
than  among  an  equal  number  of  Italians  or  English,  similarly  taken  ; 
or  thus  :  of  a  hundred  Frenchmen  and  an  equal  number  of  Englishmen, 
fairly  selected,  and  arranged  according  to  the  degree  in  which  they 
possess  a  particular  quality,  each  number,  1,  2,  3,  &c.,  of  the  one  series, 
wall  surpass  in  that  quality  the  corresponding  number  of  the  other. 
Since,  therefore,  the  comparison  is  not  one  of  kinds,  but  of  ratios  and 
degrees;  and  since  in  proportion  as  the  difl'crences  are  slight,  it  re- 
quires a  greater  number  of  instances  to  eliminate  chance;  it  cannot 
often  happen  to  any  one  to  know  a  sufficient  luimber  of  cases  with  tho 
accuracy  requisite  for  making  tho  sort  of  comparison  last  mentioned  ; 
less  than  which,  however,  would  not  constitute  a  real  induction.  Ac- 
cordingly there  is  hardly  one  current  opinion  respecting  the  characters 
of  nations,  classes,  or  descriptions  of  pei-sons,  which  is  universally  ac- 
knowledged as  indisputable.* 

*  The  most  favorable  cases  for  making  such  approximate  gpncraHzationii  are  what  may 
be  termed  collective  instances  ;  where  we  are  fortunately  enabled  to  see  the  whole  class 
respecting  which  we  are  inquiring,  in  action  at  once  ;  anil,  from  the  qualitieH  displayed  by 
the  collective  body,  arc  able  to  judge  what  must  bo  the  qualities  of  the  majority  of  the  in- 


542  LOGIC    OF    THE    MORAL    SCIENCES. 

And  finally,  if  we  could  even  obtain  by  way  of  experiment  a  much 
more  satisfactory  assurance  of  these  generalizations  than  is  really  possi- 
ble, they  would  still  be  only  empirical  laws.  They  would  show,  indeed, 
that  there  was  some  connexion  between  the  type  of  character  foiined, 
and  the  circumstances  existing  in  the  case ;  but  not  what  the  precise 
connexion  was,  nor  to  which  of  the  peculiarities  of  those  circumstances 
the  effect  was  really  owing.  They  could  only,  therefore,  be  received 
as  results  of  causation,  requiring  to  be  resolved  into  the  general  laws 
of  the  causes ;  until  the  determination  of  which,  we  could  not  judge 
within  what  limits  the  derivative  laws  might  serve  as  presumptions  in 
cases  yet  unknown,  or  even  be  depended  upon  as  permanent  in  the 
very  cases  from  which  they  were  collected.  The  French  people  had, 
or  were  supposed  to  have,  a  certain  national  character :  but  they  drive 
out  their  royal  family  and  aristocracy,  alter  their  institutions,  pass 
through  a  series  of  extraordinary  events  for  half  a  century,  and  at  the 
end  of  that  time  are  found  to  be,  in  many  respects,  totally  altered. 
The  laboring  classes  are  observed  to  be  different  from  the  higher  in  a 
long  series  of  qualities ;  but  it  becomes  customary,  perhaps,  to  give 
them  an  education  more  approximating  to  that  of  their  superiors  in 
station,  and  in  the  next  age  the  differences,  though  still  real,  are  no 
longer  the  same. 

But  if  the  differences  which  you  think  you  observe  between  French 
and  English,  or  between  persons  of  station  and  persons  of  no  station, 
can  be  connected  with  more  general  laws ;  if  they  be  such  as  would 
naturally  flow  from  the  differences  of  goveniment,  former  customs,  and 
physical  peculiarities  in  the  two  nations,  and  from  the  diversities  of 
education,  occupations,  and  social  position  in  the  different  classes  of 
society ;  then,  indeed,  the  coincidence  of  the  two  kinds  of  evidence 
justifies  us  in  believing  that  we  have  both  reasoned  rightly  and  observed 
rightly.  Our  observation,  though  not  sufficient  as  proof,  is  ample  as 
verification.  And  ha\'ing  ascertained  not  only  the  empirical  laws  but 
the  causes  of  the  peculiarities,  we  need  be  under  no  difficulty  in  judg- 
ing how  far  they  may  be  expected  to  be  permanent,  or  by  what  circum- 
stances they  would  be  modified  or  destroyed. 

§  4.  Since  then  it  is  impossible  to  obtain  really  accurate  propositions 
respecting  the  fonnation  of  character  froro  observation  and  experi- 
ment alone,  we  are  driven  perforce  to  that  which,  even  if  it  had  not 
been  the  indispensable,  would  have  been  the  most  perfect  mode  of  in- 
vestigation, and  which  it  is  one  of  the  principal  aims  of  philosophy  to 
extend ;  namely,  that  which  tries  its  experiments  not  upon  the  complex 


dividuals  composing  it.  Thus  the  character  of  a  nation  is  shown  in  its  acts  as  a  nation : 
not  so  much  in  the  acts  of  its  government,  for  those  are  much  influenced  by  other  causes ; 
but  in  the  current  popular  maxims,  and  other  marks  of  the  general  direction  of  pubUc 
opinion ;  in  the  character  of  the  men  or  v.'ritings  that  are  held  in  permanent  esteem  or 
admiration  ;  in  laws  and  institutions,  so  far  as  they  are  the  work  of  the  nation  itself,  or 
are  acknowledged  and  supported  by  it ;  and  so  forth.  But  even  here  there  is  a  large  mar- 
gin of  doubt  and  uncertainty.  These  things  are  liable  to  be  influenced  by  many  circum- 
stances :  they  are  partly  determined  by  the  distinctive  qualities  of  that  nation  or  body  of 
persons,  but  partly  also  by  external  causes  which  would  influence  any  other  body  of  per- 
sons in  the  same  manner.  In  order,  therefore,  to  make  the  experiment  really  complete,  we 
ought  to  be  able  to  try  it  without  variation  upon  other  nations :  to  try  how  Englishmen 
would  act  or  feel  if  placed  in  the  same  circumstances  in  which  we  have  supposed  French- 
men to  be  placed  ;  to  apply,  in  short,  the  Method  of  Difference  as  well  as  that  of  Agree- 
ment.   Now  these  experiments  we  cannot  try,  nor  even  approximate  to. 


ETHOLOGY.  513 

facts,  but  xiyton  the  simple  ones  of  wliich  tlioy  art3  conipouiKltd  ;  and 
after  ascertaining  the  laws  of  the  causes,  the  composition  of  which 
gives  rise  to  the  complex  phenomena,  then  considers  whether  those 
will  not  explain  and  account  for  the  a{>proximati^  jrenerali/ations  which 
have  been  framed  iMupirically  res]ieitin<i  the  scijuenccs  of  those  com- 
plex phenomena.  The  laws  of  the  formiitioii  of  ciiaracter  arc,  in  short, 
derivative  laws,  resultinrr  from  the  general  laws  of  the  mind;  and  they 
are  to  be  obtained  by  dt'ducing  them  from  those  general  laws;  by  sup- 
posing any  given  set  of  circumstances,  and  then  considering  what, 
according  to  the  laws  of  mind,  will  be  the  influence  of  those  circum- 
stances on  the  formation  of  character. 

A  science  is  thus  formed,  to  which  I  would  propose  to  give  the 
name  of  Ethology,  or  the  Science  of  Character ;  from  ijOo^,  a  word 
more  nearly  coiTt;sponding  to  the  term  "  character"  as  I  here  use  it, 
than  any  other  word  in  the  same  language.  The  name  is  perhaps 
etymologically  applicable  to  the  entire  science  of  our  mental  and  moral 
nature;  but  if  as  is  usual  and  convenient,  we  em])loy  the  name  l*sy- 
chology  for  the  science  of  the  elementary  laws  of  mind,  Ethology  will 
sei"\e  for  the  subordinate  science  which  determines  the  kind  of  charac- 
ter produced,  in  conformity  to  those  general  laws,  by  any  set  of  cir- 
cumstances, physical  and  moral.  According  to  this  <lefinition,  Etliology 
is  the  science  which  corresponds  to  the  art  of  e<lucation  ;  in  the  widest 
sense  of  the  term,  including  the  formation  of  national  character  as  well 
as  individual.  It  would  indeed  be  vain  to  expect  (however  completely 
the  laws  of  the  formation  of  character  might  be  ascertained)  that  we 
could  know  so  accurately  the  circumstances  of  any  given  case  as  to  be 
able  positively  to  predict  the  character  that  would  be  produced  in  that 
case.  But  we  must  i-emembcr  that  a  degree  of  knowledge  far  short  of 
the  power  of  actual  prediction,  is  often  of  great  practical  value.  There 
may  be  great  power  of  influencing  phenomena,  with  a  very  imj)erfect 
knowledge  of  the  causes  by  which  they  are  in  any  given  instance  de- 
termined. It  is  enough  that  wo  know  that  certain  meaius  have  a  ten- 
dency/ to  produce  a  given  effect,  and  that  others  have  a  tendency  to 
frustrate  it.  When  the  circumstances  of  an  individual  or  of  a  nation 
are  in  any  considerable  degree  under  our  control,  we  may,  by  our 
knowledge  of  tendencies,  be  enabled  to  shape  those  circumstances  in 
a  maimer  much  more  favorable  to  the  ends  we  desire  than  the  shape 
which  they  would  of  themselves  assume.  This  is  the  limit  of  our 
power  ;  but  within  this  limit  the  power  is  a  most  important  one. 

The  science  of  Ethology  may  be  called  the  Exact  Science  of  Human 
Nature  ;  for  its  truths  are  not,  lik(!  the  iinpirical  laws  which  depend 
upon  them,  approximate  generalizations,  but  real  laws.  It  is,  Imw ever, 
(as  in  all  cases  of  complex  phenomena,)  necessary  to  the  exactnt-ss  of 
the  prf)positions,  that  they  shouhl  be  hypothetical  only,  and  atlirm 
tendencies,  not  facts.  They  must  not  a-ssert  that  something  will  always, 
or  certainly,  happen ;  but  only  that  such  and  such  will  be  the  effect  of 
a  o-iven  cause,  so  far  a.s  it  operates  uncounteracted.  It  is  a  scientific 
proptisition,  that  cowardice  tr-nds  to  make  men  cruel ;  not  that  it 
always  makes  them  so :  that  an  interest  on  one  side  of  a  question 
tends  to  biius  the  judgment;  not  that  it  invariably  does  so:  that  expe- 
rience tends  to  give  wisdom  ;  not  that  such  is  always  its  effect.  These 
propositions,  being  assertive  only  (»f  tendencies,  are  not  the  less  univer- 
sally ti-ue  because  the  tendencies  may  be  counteracted. 


544  LOGIC    OF    THE    MORAL    SCIENCES. 

§  5.  While  on  the  one  hand  Psychology  is  altogether,  or  principally, 
a  science  of  observation  and  experiment,  Ethology,  as  I  have  conceived 
it,  is,  as  I  have  already  remarked,  altogether  deductive.  The  one 
ascertains  the  simple  laws  of  Mind  in  general,  the  other  traces  their 
operation  in  complex  combinations  of  circumstances.  Ethology  stands 
to  Psychology  in  a  relation  very  similar  to  that  in  which  the  various 
branches  of  natural  philosophy  stand  to  mechanics.  The  principles  of 
Ethology  are  properly  the  middle  principles,  the  axiomata  media  (as 
Bacon  would  have  said)  of  the  science  of  mind  :  as  distinguished,  on 
the  one  hand  from  the  empirical  laws  resulting  from  simple  observa- 
tion, and  on  the  other  from  the  highest  generalizations. 

And  this  seems  a  very  proper  place  for  a  logical  remark,  which, 
though  of  general  application,  is  of  peculiar  importance  in  reference  to 
the  present  subject.  Bacon  has  judiciously  observed  that  the  axiomata 
media  of  every  science  principally  constitute  its  value.  The  lowest 
generalizations,  until  explained  by  and  resolved  into  the  middle  princi- 
ples of  which  they  are  the  consequences,  have  only  the  imperfect 
accuracy  of  empirical  laws;  while  the  most  general  laws  are  too 
general,  and  include  too  few  circumstances,  to  give  sufficient  indica- 
tion of  what  happens  in  individual  cases,  where  the  circumstances  are 
almost  always  immensely  numerous.  In  the  importance,  therefore, 
which  Bacon  assigns,  in  every  science,  to  the  middle  principles,  it  is 
impossible  not  to  agree  with  him.  But  I  conceive  him  to  have  been 
radically  wrong  in  his  doctrine  respecting  the  mode  in  which  these 
axiomata  media  should  be  arrived  at ;  although  there  is  no  one  propo- 
sition laid  do^vn  in  his  works  for  which  he  has  been  so  extravagantly 
eulogized.  He  enunciates  as  an  universal  rule,  that  induction  should 
proceed  fi'om  the  lowest  to  the  middle  principles,  and  fi-om  those  to  the 
highest,  never  I'eversing  that  order,  and  consequently  leaving  no  room 
for  the  discovery  of  new  principles  by  way  of  deduction  at  all.  It  is 
not  to  be  conceived  that  a  man  of  Bacon's  sagacity  could  have  fallen 
into  this  mistake,  if  there  had  existed  in  his  time,  among  the  sciences 
which  treat  of  successive  phenomena,  one  single  instance  of  a  deduc- 
tive science,  such  as  mechanics,  astronomy,  optics,  acoustics,  &:c.,  now 
are.  In  those  sciences  it  is  evident  that  the  higher  and  middle  princi- 
ples ai-e  by  no  means  derived  from  the  lowest,  but  the  reverse.  In 
some  of  them  the  very  highest  generalizations  were  those  earliest  as- 
certained with  any  scientific  exactness ;  as,  for  example  (in  mechanics), 
the  laws  of  motion.  Those  general  laws  had  not  indeed  at  first  the 
acknowledged  universality  which  they  acquired  after  having  been  suc- 
cessfully employed  to  explain  many  classes  of  phenomena  to  which 
they  were  not  originally  seen  to  be  applicable :  as  when  the  laws  of 
motion  were  einployed  in  conjunction  with  otlier  laws  to  explain  de- 
ductively the  celestial  phenomena.  Still,  the  fact  remains,  that  the 
propositions  which  were  afterwards  recognized  as  the  most  general 
truths  of  the  science,  were,  of  all  its  accurate  generalizations,  those 
earliest  arrived  at.  Bacon's  greatest  mei'it  cannot,  therefore,  consist, 
as  we  are  so  often  told  that  it  did,  in  exploding  the  vicious  method 
pursued  by  the  ancients  of  flying  to  the  highest  generalizations  first, 
and  deducing  the  middle  principles  from  them ;  since  this  is  neither  a 
^^cious  nor  an  exploded,  but  the  universally  accredited  method  of 
modern  science,  and  that  to  which  it  owes  its  greatest  triumphs.  The 
error  of  ancient  speculation  did  not  consist  in  making  the  largest 


KTllOI.OGV.  515 

generalizations  first,  hut  in  niakiiiij;^  tlu-in  willinut  tlu>  aid  or  wini-nnt  of 
rigorous  inchictive  niotlnxls,  and  applyinLr  tliein  dodurtivoly  witliout 
tlic  needful  use  of  that  important  part  of  the  Deductive  Method  termed 
Verification. 

The  order  in  which  truths  of  the  various  deirrees  of  generality 
should  be  ascertained,  cannot,  I  apprehend,  be  prescribed  by  any  un- 
bending rule.  I  know  of  no  maxim  which  can  be  laid  dou-n  on  the 
subject,  hut  to  obtain  those  first,  in  respect  to  which  the  conditions  of 
a  real  induction  can  be  first  and  most  comphtely  realized.  Now, 
wherever  our  means  of  investiirafion  can  reach  causes,  without  stopping 
at  the  empirical  laws  of  the  ell'ects,  the  simplest  cases,  being  those  in 
which  fewest  causes  are  simultaneously  concerned,  will  be  most 
amenable  to  the  inductive  process ;  and  tliese  are  the  cases  which 
elicit  laws  of  the  greatest  comprehensiveness.  In  every  science,  there- 
fore, which  has  reached  the  stage  at  which  it  becomes  a  .science  of 
causes,  it  will  be  usual,  as  well  as  desirable,  first  to  obtain  tin-  hitrhcst 
generalizations,  and  then  deduce  the  more  special  ones  from  them. 
Nor  can  I  discover  any  foundation  for  the  Baconian  maxim,  so  much 
extolled  by  subsequent  writers,  except  this :  That  before  we  attempt 
to  explain  "deductively  from  more  general  laws  any  new  class  of  phe- 
nomena, it  is  desirable  to  have  gone  as  far  as  is  practicable  in  ascer- 
taining the  emf)irical  laws  of  those  phenomena ;  so  as  to  compare  the 
results  of  deduction,  not  with  one  individual  instance  after  another, 
but  Avith  sjcneral  propositions  expressive  of  the  points  of  agreement 
which  have  been  found  among  many  instances.  For  if  Newton  had 
been  obliged  to  verify  the  theory  of  gravitation,  not  by  deducing  from 
it  Kepler's  laws,  but  by  deducing  all  the  observed  planetary  positions 
which  had  served  Kepler  to  establish  those  laws,  the  Newtonian  theory 
would  probably  never  have  emerged  from  the  state  of  an  hypothesis. 

The  applicability  of  these  remarks  to  the  special  ca.se  under  con- 
sideration, cannot  admit  of  question.  The  science  of  the  formation  of 
character  is  a  science  of  causes.  The  subject  is  one  to  which  those 
among  the  canons  of  induction,  by  which  laws  of  causation  are  ascer- 
tained, can  be  rigorously  aj)plied.  It  is,  therefore,  both  natural  and 
advisable  to  ascertain  the  simplest,  which  are  necessarily  the  most 
general,  laws  of  causation  first,  and  to  deduce  the  middle  principles 
from  them.  In  other  wortLs,  Ethology,  the  deductive  science,  is  a  sys- 
tem of  corollaries  firom  Psychology,  tin?  experimental  science. 

§  G.  Of  these,  the  earlier  alone  has  been,  as  yet,  really  conceived  or 
studied  as  a  science:  the  other,  Ethology,  is  still  to  be  created.  Hut 
all  things  are  prepared  for  its  creation.  The  em})iri<  al  laws,  destined 
to  verify  its  dedtictions,  have  been  afforded  in  abundance  by  every 
successive  age  of  humanity ;  and  the  premisses  for  the  deductions  are 
now  sufficiently  complete.  Excepting  the  degree  of  uncertainty  which 
still  exists  as  to  the  extent  of  the  natural  differences  of  human  minds, 
and  the  physical  circumstances  on  which  these  rnay  be  dependent, 
(considerations  which  are  of  secondai-y  importance  when  we  are  con- 
sidenng  mankind  in  the  average,  or  en  vki.ssp,)  I  believe  most  compe- 
tent judges  will  agree  that  the  general  laws  of  the  difii-rcnt  constituent 
elements  of  human  nature  are  now  sufficiently  understood,  to  render 
it  pos.sii)le  for  a  competent  thinker  to  deduce  from  those  laws  the 
particular  type  of  character  which  would  be  formed,  in  mankind  gen- 
3Z 


546  LOGIC    OF    THE    MORAL    SCIENCES. 

erally,  by  any  assumed  set  of  circumstances.  A  science  of  Ethology, 
founded  upon  the  laws  of  Psychology,  is  therefore  possible;  though 
little  has  yet  been  done,  and  that  little  not  at  all  systematically,  towards 
formino-  it.  The  progress  of  this  important  but  most  imperfect  science 
will  depend  upon  a  double  process  :  first,  that  of  deducing  theoreti- 
cally the  ethological  consequences  of  particular  circumstances  of 
position,  and  comparing  them  with  the  recognized  results  of  common 
experience ;  and  secondly,  the  reverse  operation  ;  increased  study  of 
the  various  types  of  human  nature  that  are  to  be  found  in  the  world, 
conducted  by  persons  not  only  capable  of  analyzing  and  recording  the 
circumstances  in  which  these  types  severally  prevail,  but  also  suf- 
ficiently acqviainted  with  psychological  laws,  to  be  able  to  explain  and 
account  for  the  characteristics  of  the  type  by  the  peculiarities  of  the 
circumstances  :  the  residuum,  if  any,  being  set  down  to  the  account  of 
congenital  predispositions. 

The"  experimental  or  a  posteriori  part  of  this  process  is  carried  on  in 
our  own  day  with  much  gi-eater  activity  than  heretofore.  The  gi-eat 
step,  therefore,  which  remains  to  be  taken  in  Ethology,  is  to  deduce 
the  requisite  middle  principles  from  the  general  laws  of  Psychology. 
The  subject  to  be  studied  is,  the  origin  and  sources  of  all  those  quahties 
in  human  beings  which  are  most  interesting  to  us,  either  as  facts  to  be 
produced,  to  be  avoided,  or  merely  to  be  understood-  and  the  object 
is,  to  determine,  from  the  general  laws  of  mind,  combined  with  the 
general  position  of  our  species  in  the  universe,  what  actual  or  possible 
combinations  of  circumstances  are  capable  of  promoting  or  of  pre- 
venting the  production  of  those  qualities.  A  science  which  possesses 
middle  principles  of  this  kind,  aiTanged  in  the  order,  not  of  causes, 
but  of  the  effects  which  it  is  desirable  to  produce  or  to  prevent,  is 
duly  prepared  to  be  the  foundation  of  the  corresponding  Art.  And 
when  Ethology  shall  be  thus  prepared,  practical  education  will  be  the 
mere  transformation  of  those  principles  into  a  parallel  system  of  pre- 
cepts, and  the  adaptation  of  these  to  the  sum  total  of  the  individual 
circumstances  which  exist  in  each  particular  case. 

It  is  hardly  necessary  again  to  repeat  that,  as  in  every  other  deduc- 
tive science,  the  work  of  verification  a  j^ostcriori  must  proceed  pan 
passu  with  that  of  deduction  a  priori.  The  inference  given  by  theory 
as  to  the  type  of  character  which  would  be  formed  by  any  given  cir- 
cumstances, must  be  tested  by  specific  experience  of  those  circum- 
stances whenever  obtainable;  and  the  whole  conclusions  of  the  science 
must  undergo  a  perpetual  verification  and  correction  from  tlie  general 
remarks  afforded  by  common  experience  respecting  human  nature  in 
our  own  age,  and  by  history  respecting  times  gone  by.  The  conclusions 
of  theory  cannot  be  trusted,  unless  confirmed  by  observation ;  nor  those 
of  observation,  unless  they  can  be  affiliated  to  the  theory,  by  deducing 
them  from  the  laws  of  human  nature  and  from  a  close  analysis  of  the 
circumstances  of  the  particular  situation.  It  is  the  accordance  of 
tliese  two  kinds  o.f  evidence,  separately  taken  —  the  consilience  (as  Mr. 
Whewell  would  express  it)  of  a  jjriori  reasoning  and  specific  expeii- 
ence  —  which  forms  the  only  sufficient  ground  for  the  principles  of  any 
science  so  "immersed  in  matter,"  dealing  with  so  complex  and  so 
concrete  phenomena,  as  Ethology. 


SOCIAL    SCIENCE.  547 

CHAPTER  VI. 

GENERAL   CONSIDERATIONS   ON   THE   SOCIAL  SCIENCE. 

§  1.  Next  after  the  science  of  individual  man,  comes  the  science  of 
man  in  society  :  of  the  actions  of  collective  masses  of  mankind,  and.  the 
various  phenomena  which  constitute  social  life. 

If  the  formation  of  individual  character  is  already  a  complex  sub- 
ject of  study,  this  subject,  it  is  evident,  must  be  greatly  more  complex ; 
because  the  number  of  concurrent  causes,  all  exercising  more  or  less 
influence  on  the  total  eftect,  is  greater,  in  the  proportion  iji  which  a 
nation,  or  the  species  at  large,  exposes  a  larger  surface  to  tlir  upera- 
tion  of  agents,  psychological  and  physical,  than  any  single  individual. 
If  it  was  necessary  to  prove,  in  opposition  to  an  existing  prejudice,  that 
the  siTTipler  of  the  two  is  capable  of  being  a  subject  of  science ;  the 
prejudice  is  likely  to  be  yet  stronger  against  the  possibility  of  giving  a 
scientific  character  to  the  study  of  Politics,  and  ui'  the  phenomena  of 
Society.  It  is,  accordingly,  but  of  yesterday  that  the  conception  of  a 
political  or  social  science  has  existed,  anywhere  but  in  the  mind  of 
here  and  there  an  insulated  thinker,  generally  very  ill  prepared  for  its 
realization  :  although  the  subject  itself  has  of  all  others  engaged  the 
most  general  attention,  and  been  a  theme  of  interested  and  earnest  dis- 
cussions almost  from  the  beginning  of  recorded  time. 

The  condition  indeed  of  politics,  as  a  branch  of  knowledge,  was 
until  very  lately,  and  has  scarcely  even  yet  ceased  to  be,  that  which 
Bacon  animadverted  upon,  as  the  natural  state  of  the  sciences  while 
their  cultivation  is  abandoned  to  practitioners ;  not  being  can-ieti  on  as 
a  branch  of  speculative  inquiry,  but  only  with  a  view  to  the  exigencies 
of  daily  practice,  and  x\\cj'ructifcra  expcrbnenta,  therefore,  being  aimed 
at,  almost  to  the  exclusion  of  the  lucifcra.  Such  was  medical  science, 
before  physiology  and  natural  history  began  to  be  cultivated  a-j 
branches  of  general  knowledge.  The  only  questions  examined  were, 
what  diet  is  wholesome,  or  what  medicine  will  cure  some  given  dis- 
ease ;  without  any  previous  systematic  intjuiry  into  the  laws  of  nutrition, 
and  of  the  healthy  and  morbid  action  of  the  different  organs,  on  which 
laws  the  effect  of  any  diet  or  medicine  must  evidently  depend.  And  in 
pohtics,  the  questions  which  engaged  general  attention  weri>  similar. 
Is  such  an  enactment,  or  such  a  form  of  g<)vennnent,  b(nie(icial  or  the 
reverse — either  universally,  or  to  some  particular  community  \  without 
inquiry  into  the  general  conditions  by  wliich  the  operation  of  legisla- 
tive measures,  or  the  effects  produced  by  forms  of  goverimient,  are 
determined. 

And  even  among  the  fevf  who  did  carry  their  speculations  to  that 
greater  lengtli,  it  is  only  at  a  still  more  recent  date  that  .social  phe- 
nomena, properly  so  called,  have  begun  to  be  looked  upon  as  having 
any  natural  tendencies  of  their  own.  It  is  hardly  an  exaggeration  to 
say  that  society  ha.i  usually,  b(»th  by  practitioners  in  politics  and  by 
philosophical  speculators  on  forms  of  goverimient,  from  Plato  to 
IJentham,  been  deemed  to  be  whatever  tin;  men  who  c()ni{)ose  it 
choose  to  make  it.  The  only  questions  which  people  thought  of  pro- 
posing to  themselves  were,  Would  such  and  such  a  law  or  iualilution 


548  LOGIC    OF    THE    MORAL    SCIENCES. 

be  beneficial  1  and,  if  so,  can  legislators  or  the  public  be  persuaded,  or 
Otherwise  induced,  to  adopt  it  1  For  hardly  any  notion  was  enter- 
tained that  there  were  limits  to  the  power  of  human  will  over  the  phe- 
nomena of  society,  or  that  any  social  arrangements  which  would  be 
desirable,  could  be  impracticable  from  incompatibility  with  the  proper- 
ties of  the  subject  matter  :  the  only  obstacle  was  supposed  to  lie  in  the 
private  interests  or  prejudices,  which  hindered  men  from  being  willing 
lo  see  them  tried.  Students  in  politics  thus  attempted  to  study  the 
p-at^iology  and  therapeutics  of  the  social  body,  before  they  had  laid  the 
necessary  foundation  in  its  physiology  ;  to  cure  disease,  without  under- 
standing the  laws  of  health.  And  the  result  was  such  as  it  must  always 
be  when  men  even  of  gi-eat  ability  attempt  to  deal  with  the  complex 
questions  of  a  science  before  its  simpler  and  mere  elementary  pi-oposi- 
tions  have  been  established. 

No  wonder  that  when  the  phenomena  of  society  have  so  rarely  been 
contemplated  in  the  point  of  view  characteristic  of  science,  the  philo- 
sophy of  society  should  have  made  little  progi-ess  ;  should  contain  few 
general  propositions  sufficiently  precise  and  certain,  for  common  in- 
quirers to  recognize  in  them  a  scientific  character.  The  vulgar  notion 
accordingly  is,  that  all  pretension  to  lay  down  general  truths  on  politics 
and  society  is  quackery  ;  that  no  universality  and  no  certainty  are 
attainable  in  such  matters.  What  partly  excuses  this  common  notion 
is,  that  it  is  really  not  without  foundation  in  one  particular  sense.  A 
large  proportion  of  those  who  have  laid  claim  to  the  character  of  philo- 
sophic politicians,  have  attempted,  not  to  ascertain  universal  sequences, 
but  to  frame  universal  precepts.  They  have  had  some  one  form  of 
government,  or  system  of  laws,  to  fit  all  cases;  a  pretension  well 
meriting  the  ridicule  with  which  it  is  treated  by  practitioners,  and 
wholly  unsupported  by  the  analogy  of  the  art  to  which,  from  the  nature 
of  its  subject,  that  of  politics  must  be  the  most  nearly  allied.  No  one 
now  supposes  it  possible  that  one  remedy  can  cure  all  diseases,  or  even 
the  same  disease  in  all  constitutions  and  habits  of  body.  Yet  physi- 
ology is  admitted  to  be  a  science,  and  medical  practice,  when  it  disre- 
gards the  indications  of  the  science,  to  be  criminal  quackery. 

It  is  not  necessary  to  even  the  perfection  of  a  science,  that  the 
corresponding  art  should  possess  universal,  or  even  general  rules. 
The  phenomena  of  society  might  not  only  be  completely  dependent 
upon  known  causes,  but  the  mode  of  action  of  all  those  causes  might 
be  reducible  to  laws  of  considerable  simplicity,  and  yet  no  two  cases 
might  admit  of  being  treated  in  precisely  the  same  manner.  So  great 
might  be  the  variety  of  circumstances  on  which  the  results  in  different 
cases  depend,  that  art  might  not  have  a  single  general  precept  to  give, 
except  that  of  watching  the  circumstances  of  the  case,  and  adapting 
our  measures  to  the  effects  which,  according  to  the  pi'inciples  of  the 
science,  result  from  those  cii'cumstances.  But  because,  in  so  compli- 
cated a  class  of  subjects,  it  is  absurd  to  lay  down  practical  maxims  of 
universal  application,  it  does  not  follow  that  the  phenomena  do  not 
conform  to  universal  laws. 

§  2.  All  phenomena  of  society  are  phenomena  of  human  nature, 
generated  by  the  action  of  outward  circumstances  upon  masses  of 
human  beings :  and  if,  therefore,  the  phenomena  of  human  thought, 
feeling,  and  action,  are  subject  to  fixed  laws,  the  phenomena  of  society 


I 


SOCIAL    SCIENCE.  549 

cannot  but  conform  to  fixed  laws,  the  consequences  of  the  procedinp. 
There  is,  indeed,  no  hope  that  those  laws,  though  our  knowledire  of 
them  were  as  certain  and  a.s  coin])leto  as  it  is  in  astronomy,  would 
enable  us  to  predict  the  history  of  society,  like  that  of  the  celestial 
appearances,  for  thousands  of  years  to  come.  But  the  difierence  of 
certainty  is  not  in  the  laws  themselves,  it  is  in  the  data  to  which  these 
laws  are  to  be  applied.  In  astronomy  the  causes  iuHueucing  the  result 
are  few,  and  change  little,  and  that  little  according  to  known  laws  :  we 
can  ascertain  what  they  are  now,  and  thence  determine  what  they  will 
be  at  any  epoch  of  a  distant  future.  The  data,  therefore,  in  astronomy, 
are  as  certain  as  the  laws  themselves.  The  circumstances,  on  the  con- 
trary, which  influence  the  condition  and  progress  of  society,  are  in- 
numerable, and  perpetually  changing;  and  though  they  all  change  in 
obedience  to  causes,  and  therefore  to  laws,  the  multitude  of  the  causes 
is  so  great  as  to  defy  our  limited  powers  of  calculation.  Not  to  say 
that  the  impossibility  of  applying  precise  numbers  to  facts  of  such  a 
description,  would  set  an  impassable  limit  to  the  possibility  of  calcu- 
lating them  beforehand,  even  if  the  powers  of  the  human  intellect 
were  otherwise  adequate  to  the  task. 

But,  as  we  before  remarked,  an  amount  of  knowledge  quite  insuffi- 
cient for  prediction,  may  be  most  valuable  for  guidance.  The  science 
of  society  would  have  attained  a  very  high  point  of  perfection,  if  it 
enabled  us,  in  any  given  condition  of  social  aflairs,  in  the  condition  for 
instance  of  Europe  or  any  European  country  at  the  present  time,  to 
understand  by  what  causes  it  had,  in  any  and  every  particular,  been 
made  what  it  was  ;  whether  it  was  tending  to  any,  and  to  what, 
changes ;  what  effects  each  feature  of  its  existing  state  was  likely  to 
produce  in  the  future ;  and  by  what  means  any  of  those  effects  might 
be  prevented,  modified,  or  accelerated,  or  a  different  cla-ss  of  effects 
superinduced.  There  is  nothing  chimerical  in  the  hope  that  general 
laws,  sufficient  to  enable  us  to  answer  these  various  questions  for  any 
country  or  time  with  the  individual  circumstances  of  which  we  are 
well  acquainted,  do  really  admit  of  being  ascertained ;  and  moreover, 
that  the  other  branches  of  human  knowledge,  which  this  undertaking 
presupposes,  are  so  far  advanced  that  the  time  is  ripe  for  its  accom- 
plishment.    Such  is  the  object  of  the  Social  Scituice. 

That  the  nature  of  what  I  consider  the  true  method  of  the  science 
may  be  made  more  palpable,  by  first  .showing  what  that  method  is  not; 
it  will  be  expedient  to  characterize  briefly  two  radical  misconceptions 
of  the  proper  mode  of  philosophizing  on  society  and  government,  one 
or  other  of  which  is,  either  explicitly  or  more  often  unconsciously, 
entertained  by  almost  all  who  have  meditated  or  argued  resjiecting  the 
logic  of  politics  since  the  notion  of  treating  it  by  strict  rules,  and  on 
Baconian  principles,  has  been  current  among  the  more  advanced 
thinkers.  These  erroneous  methods,  if  the  word  method  can  be 
applied  to  erroneous  tendencies  arising  from  the  absence  of  any  suf- 
ficiently distinct  conception  of  method,  may  be  aptly  termed  the 
Experimental,  or  Chemical,  mode  of  investigation,  and  the  Abstract, 
dj  Geometrical  mode.     We  shall  begin  with  the  former. 


550*  LOGIC    OF    TFIE    MORAL    SCIENCES. 

CHAPTER  VII. 

OP   THE   CHEMICAL,  OR  EXPERIMENTAL,  METHOD   IN  THE   SOCIAL   SCIENCE. 

§  1.  The  laws  of  the  phenomena  of  society  are,  and  can  be,  nothing 
but  the  laws  of  the  actions  and  passions  of  human  beings  united  to- 
gether in  the  social  state.  Men,  however,  in  a  state  of  society,  are 
still  men  ;  their  actions  and  passions  are  obedient  to  the  laws  of  indi- 
vidual human  nature.  Men  are  not,  when  brought  together,  converted 
into  another  kind  of  substance,  with  different  properties  ;  as  hydrogen 
and  oxygen  are  different  from  water,  or  as  hydrogen,  oxygen,  carbon, 
and  azote,  are  different  from  nerves,  muscles,  and  tendons.  Human 
beings  in  society  have  no  properties  but  those  which  are  derived  from, 
and  may  be  resolved  into,  the  laws  of  the  nature  of  individual  man.  In 
social  phenomena  the  Composition  of  Causes  is  the  universal  law. 

Now,  the  method  of  philosophizing  which  may  be  termed  chemical, 
overlooks  this  fact,  and  proceeds  as  if  the  nature  of  man  as  an  indi- 
vidual were  not  concerned  at  all,  or  concerned  in  a  very  inferior  de- 
gree, in  the  operations  of  man  in  society.  All  reasoning  in  politics  or 
social  affairs,  grounded  upon  principles  of  human  nature,  is  objected 
to  by  reasoners  of  this  sort,  under  such  names  as  "  abstract  theory." 
For  governing  their  opinions  and  conduct,  they  profess  to  demand,  in 
all  cases  without  exception,  specific  experience. 

This  mode  of  thinking  is  not  only  general  with  practitioners  in 
politics,  and  \vith  that  very  numerous  class  who  (on  a  subject  which  no 
one,  however  ignorant,  thinks  himself  incompetent  to  discuss)  profess 
to  guide  themselves  by  common  sense  rather  than  by  science ;  but  is 
,  often  countenanced  by  persons  with  greater  pretensions  to  instruction ; 
pe  sons  who,  having  sufficient  acquaintance  with  books  and  with  the 
current  ideas  to  have  heard  that  Bacon  taught  men  to  follow  expe- 
rience, and  to  ground  their  conclusions  upon  facts  instead  of  meta- 
physical dogmas,  think  that  by  treating  political  facts  in  as  directly 
experimental  a  method  as  chemical  facts,  they  are  showing  themselves 
true  Baconians,  and  proving  their  adversaries  to  be  mere  syllogizers 
and  schoolmen.  As,  however,  the  notion  of  the  applicability  of  experi- 
mental methods  to  political  philosophy  cannot  coexist  with  any  just 
conception  of  these  methods  themselves,  the  kind  of  aiguments  from 
experience  which  the  chemical  theory  brings  forth  as  its  fruits  (and 
which  form  the  staple,  in  this  country  especially,  of  parliamentary  and 
hustings'  oratory)  are  such  as,  at  no  time  since  Bacon,  would  have 
been  admitted  to  be  valid  in  chemistry  itself,  or  in  any  other  branch  of 
experimental  science.  They  are  such  as  these  :  that  the  prohibition  of 
foreign  commodities  must  conduce  to  national  wealth,  because  England 
has  flourished  under  it,  or  because  countries  in  general  which  have 
adopted  it  have  flourished ;  that  our  laws,  or  our  internal  administra- 
tion, or  our  constitution,  are  excellent  for  a  similar  reason ;  and  tho 
eternal  arguments  from  historical  examples,  from  Athens  or  Rome, 
from  the  fires  in  Smithfield,  or  the  French  Revolution. 

I  will  not  waste  time  iii  contending  against  modes  of  argumentation 
which  no  person,  with  the  smallest  practice  in  estimating  evidence, 
could  possibly  be  betrayed  into ;  which  draw  conclusions  of  general 


THE  CHEMICAL  METHOD.  551 

application  from  a  sinc;Io  unanalyzctl  instance,  or  arbitrarily  rt'fer  an 
ertcct  to  some  one  anionic  its  aiiti'c«ukMils,  witliont  any  process  of  flimi- 
nation  or  comparison  of  instances.  It  is  a  rnle  l)oth  of  justice  and  of  good 
sense  to  p^rapple  not  with  tin-  ahsurdi'st,  but  witii  tliu  most  reasonable 
form  of  a  wrong  opinion.  We  .shall  su])pos»'  our  impiirer  acquainted 
with  the  true  conditions  of  exiierimenlal  inveslicration,  and  competent  in 
point  of  acquirements  for  realizing  them,  if  lliey  can  be  realized  in  any 
case  of  the  kind.  He  shall  know  as  much  of  the  facts  of  history  as 
mere  erudition  can  teach — as  much  as  can  be  proved  Ijy  testimony, 
without  the  assistance  of  any'theory  ;  and  if  those  mere  facts,  properly 
collated,  can  fulfill  the  conditions  of  a  real  induction,  he  shall  be  (juali- 
lied  for  the  task. 

Uut,  that  no  such  attempt  can  have  the  smallest  chance;  of  success, 
has  been  abundantly  shown  in  the  tenth  chapter  of  the  Third  IJook.* 
We  there  examined  whether  eflects  which  depend  upon  a  complication 
of  causes,  can  be  made  the  subjects  of  a  true  induction  by  observation 
and  experiment;  and  concluded,  on  the  most  convincing  grounds,  that 
they  caimot.  Since,  of  all  effects,  none  depend  upon  so  great  a  com- 
plication of  causes  as  social  phenomena,  we  might  leave  our  case  to 
rest  in  safety  upon  that  previous  showing.  But  a  logical  princi|)le,  as 
yet  so  little  familiar  to  the  ordinary  run  of  thinkei-s,  re(|uires  to  be  in- 
sisted upon  more  than  once,  in  order  to  make  the  due  impression  ;  and 
the  present  being  the  case  which  of  all  others  exemplifies  it  the  nn>st 
strongly,  there  will  be  advantage  in  restating  the  grounds  of  the  general 
maxim,  as  applied  to  the  specialities  of  the  class  of  inquiries  now  under 
consideration. 

§  2.  The  first  difficulty  which  meets  us  in  the  attempt  to  apply  ex- 
perimental methods  for  ascertaining  the  laws  of  social  phenomena,  is 
that  we  are  without  the  means  of  making  artificial  experiments.  Even 
if  wo  could  contrive  experiments  at  leisure,  and  try  them  without 
limit,  we  should  do  so  under  immense  disadvantages;  both  from  the  im- 
possibility of  ascertaining  and  taking  note  of  all  the  facts  of  each  case, 
and  because  (those  facts  being  in  a  perpetual  state  of  change)  before 
sufhcient  time  had  elapsed  to  ascertain  the  result  of  the  experiment, 
some  material  circumstances  would  always  have  ceased  to  be  the  same. 
But  it  is  unnecessary  to  consider  the  logical  objections  which  would  exist 
to  the  conclusiveness  of  our  experiments,  since  we  palpably  never 
have  the  power  of  trying  any.  We  can  only  watch  those  wliich  nature 
produces,  or  those  which  are  produced  for  other  rea.sons.  We  cannot 
adapt  our  logical  means  to  our  wants,  by  varying  the  circumstances  as 
tlie  exigencies  of  elimination  may  recjuire.  If  the  spontaneous  instances, 
formed  by  contemporary  cvetits  and  l)y  the  successions  of  phenomena 
recorded  in  history,  afford  a  suflicient  variation  of  circumstances,  an 
inducticjn  from  specific  experience  is  attainable  ;  otherwi.se  not.  The 
question  to  be  resolved  is,  therefore,  wln-ther  the  requisites  for  induc- 
tion respecting  the  causes  of  political  effects  or  the  properties  of 
political  agents,  are  tr)  be  met  with  in  history  ?  including  under  the 
term,  contemporary  history.  And  in  onler  to  give  fixity  to  our  con- 
ceptions, it  will  be  advisable  to  suppose  this  (piestion  asked  in  n.'ferenco 
to  some  special  subject  of  political  inquiry  »jr  controversy  ;  such  as  that 

•  Supra,  pp.  2yj-2(H. 


552  LOGIC    OF    THE    MORAL    SCIENCES. 

great  topic  of  debate  in  the  present  day,  the  operation  of  restrictive  and 
prohibitory  commercial  legislation  upon  national  wealth.  Let  this,  then, 
be  the  scientific  question  to  be  investigated  by  specific  experience. 

§  3.  In  order  to  apply  to  the  case  the  most  perfect  of  the  methods 
of  experimental  inquiry,  the  Method  of  Difference,  we  require  to  find 
two  instances,  which  tally  in  every  particular  except  the  one  which  is 
the  subject  of  inquiry.  If  two  nations  can  be  found  which  are  alike  in 
all  natural  advantages  and  disadvantages  ;  whose  people  resemble  each 
other  in  every  quality,  physical  and  moral,  innate  and  acquired  ;  whose 
habits,  usages,  opinions,  laws,  and  institutions  are  the  same  in  all  re- 
spects, except  that  one  of  them  has  a  more  protective  tariff,  or  in  other 
respects  interferes  more  with  the  fieedom  of  industry  ;  and  if  one  of 
these  nations  is  found  to  be  rich,  and  the  other  poor,  or  one  richer 
than  the  other,  this  will  be  an  experhnentum  crucis:  a  real  proof,  by 
experience,  which  of  the  two  systems  is  most  favorable  to  national 
riches.  But  the  supposition  that  two  such  instances  can  be  met  with 
is  absurd  on  the  face  of  it.  Nor  is  such  a  concurrence  even  abstract- 
edly possible.  Two  nations  which  agreed  in  everything  except  their 
commercial  policy  would  agree  also  in  that.  Differences  of  legislation 
are  not  inherent  and  ultimate  diversities  ;  are  not  properties  of  Kinds. 
They  are  effects  of  preexisting  causes.  If  the  two  nations  differ  in 
this  pr)rtion  of  their  institutions,  it  is  from  some  difference  in  their 
position,  and  thence  in  their  apparent  interests,  or  in  some  portion  or 
other  of  their  opinions,  habits,  and  tendencies  ;  which  opens  a  view  of 
further  differences  without  any  assignable  limit,  capable  of  operating 
on  their  industrial  prosperity,  as  well  as  on  every  other  feature  of  their 
condition,  in  more  ways  than  can  be  enumerated  or  imagined.  There 
is  thus  a  demonstrated  impossibility  of  obtaining,  in  the  investigations 
of  the  social  science,  the  conditions  required  for  the  most  conclusive 
forai  of  inquiry  by  specific  experience. 

In  the  absence  of  the  direct,  we  may  next  try,  as  in  other  cases,  the 
supplementary  resource,  called  in  a  fonner  place  the  Indirect  Method 
of  Difference:  which,  instead  of  two  instances  differing  in  nothing  but 
the  presence  or  absence  of  a  given  circumstance,  compares  two  classes 
of  instances  respectively  agreeing  in  nothing  but  the  presence  of  a  cir- 
cumstance on  the  one  side  and  its  absence  on  the  other.  To  choose 
the  most  advantageous  case  conceivable  (a  case  far  too  advantageous 
to  be  ever  obtained),  suppose  that  we  compare  one  nation  which  has  a 
restrictive  policy,  with  two  or  more  nations  agi-eeing  in  nothing  but  in 
permitting  free  trade.  We  need  not  now  suppose  that  either  of  these 
nations  agrees  with  tlje  first  in  all  its  circumstances  ;  one  may  agree 
with  it  in  some  of  its  circumstances,  and  another  in  the  remainder. 
And  it  may  be  argued,  that  if  these  nations  remain  poorer  than 
the  restrictive  nation,  it  cannot  be  for  want  either  of  the  first  or  of  the 
second  set  of  circumstances,  but  it  must  be  for  want  of  the  protecting 
system.  If  (we  might  say)  the  restrictive  nation  had  prospered  from 
the  one  set  of  causes,  the  first  of  the  free-trade  nations  would  have 
prospered  equally  ;  if  by  I'eason  of  the  other,  the  second  would  :  but 
neither  has:  therefore  the  prosperity  was  owing  to  the  restrictions. 
This  will  be  allowed  to  be  a  very  favorable  specimen  of  an  argument 
from  specific  experience  in  politics,  and  if  this  be  inconclusive,  it  would 
not  be  easy  to  find  another  preferable  to  it. 


THE    CUEMICAL    METHOD.  r>53 

Yot,  that  it  is  incoiiclusive,  si-avccly  nvjuiros  to  bo  pointed  out.  W'iiy 
must  the  prosp«'rous  mitioii  have  piospcrt'tl  from  one  cuuso  exchisivcly  I 
National  pfosperity  is  always  the  coHoctivo  n\sult  of  a  muUitiKh^  of 
fuvorahle  ciiiumstam-rs  :  and  of  ihi-se,  tho  ivstrictivi- nation  may  unite 
a  i^ieater  number  than  either  of  the  others,  akhouirh  it  may  have  all  of 
those  cireumstantes  in  (-(mimon  with  either  one  or  the  other  of  tln'm. 
Its  prosperity  may  be  partly  owin<r  to  eircumslanees  «oiiun(»n  to  it 
with  one  of  those  nations,  and  partly  with  the  other,  while  tiury,  having 
each  of  them  only  half  the  number  of  favorable  cireumstances,  have 
remained  inferior.  So  that  the  closest  imitation  which  can  be  made,  in 
the  social  science,  of  a  genuine  induction  from  direct  experience,  gives 
but  a  specious  semblance  of  conclusiveness,  without  any  real  value 

§  4.  The  Method  of  Difference  in  cither  of  its  forms  being  thus 
completely  out  of  the  question,  there  remains  the  Method  of  Aijree- 
ment.  But  we  are  already  aware-  of  how  little  value  this  method  is, 
in  cases  admitting  Plurality  of  Causes  :  and  social  phenomena  are 
those  in  which  the  plurality  prevails  in  the  utmost  possible  ext(5nt. 

Suppose  that  the  observer  makes  the  luckiest  hit  which  could  bo 
given  him  by  any  conceivable  combination  of  chances  :  that  he  finds 
two  nations  which  agree  in  no  circumstance  whatever,  except  in  having 
a  restrictive  system,  and  in  being  prosperous;  or  a  lumiber  of  nations, 
all  prosperous,  which  have  no  atitecedent  circumstances  common  to 
them  all  but  that  of  having  a  restrictive  policy.  It  is  inuiecessary  to  go 
into  the  consideration  of  the  impossibility  oP  ascertaining  from  history, 
or  even  from  contemporary  observation,  that  such  is  nally  the  fact ; 
that  the  nations  agree  in  no  other  circumstance  capable  of  influencing 
the  case.  Let  us  suppose  this  impossibility  van(|uished,  and  the  fact 
ascertained  that  tliey  agreed  only  in  a  restrictive  system  as  an  antece- 
dent, and  industrial  prosperity  as  a  consequent.  What  degree  of  pro- 
sumption  does  this  raise,  that  the  restrictive  system  caused  the  pros- 
perity ]  One  so  trifling  as  to  be  ecjuivalent  to  none  at  all.  That  some 
one  antecedent  is  the  cause  of  a  given  effect,  because  all  otlu-r  antece- 
dents have  been  found  capable  of  being  eliminated,  is  a  just  inference, 
only  if  the  effect  can  have  but  one  cause.  If  it  admits  of  several,  no- 
thing is  more  natural  than  that  t;ach  of  these  should  separately  admit  of 
being  eliminated.  Now,  in  the  case  of  political  phenomena,  the  suppo- 
sition of  unity  of  cause  is  not  oidy  wide  of  the  truth,  but  at  an  immeas- 
urable distance  from  it.  The  causes  of  every  social  {ihenomenon  which 
we  arc  particularly  interested  about,  security,  wealth,  frced(»m,  good 
government,  jjublic  virtue,  public  intelligence,  or  their  oppositcK,  are 
infinitely  numerous  :  especially  the  external  or  remote  causes,  which 
alone  are.  for  the  most  part,  accessible  to  direct  obs»rvali<»n.  N(*  one 
cause  suffices  of  itself  to  produce  any  one  of  these  plienomena;  while 
there  are  countle.><8  causes  which  have  some  influence  over  them,  and 
may  cooperate  cither  in  their  production  nr  in  their  proventi«»ii.  From 
the  mere  fact,  therefore,  of  our  having  been  able  to  eliminate  some 
circumstances,  we  can  by  no  means  infer  that  this  circumstanct;  wa.H  not 
instrumental  to  the  efl\;ct  evi;n  in  the  very  instances  from  which  wo 
have  eliminated  it.  We  may  conclude  that  the  effect  is  sometimes 
produced  without  it;  but  not  that,  when  present,  it  docs  not  contribute 
its  part. 

Similar  objections  will  be  found  to  uj)ply  to  the  Method  of  Ct^nctJtn- 
4A 


554  LOGIC    OF    THE    MORAL    SCIENCES. 

itant  Variations.  If  the  causes  which  act  upon  the  state  of  any  society 
produced  effects  differing  from  one  another  in  kind;  if  wealth  depended 
upon  one  cause,  peace  upon  another,  a  third  made  a  people  virtuous,  a 
fourth  intelligent ;  we  might,  though  unable  to  sever  the  causes  from 
one  another,  refer  to  each  of  them  that  property  of  the  effect  which 
waxed  as  it  waxed,  and  which  waned  as  it  waned.  But  every  attribute 
of  the  social  body  is  influenced  by  innvimerable  causes;  and  such  is  the 
mutual  action  of  the  coexisting  elements  of  society,  that  whatever 
affects  any  one  of  the  more  important  of  them,  will  by  that  alone,  if  it 
does  not  affect  the  others  directly,  affect  them  indirectly.  The  effects, 
therefore,  of  different  agents  not  being  different  in  quality,  while  the 
quantity  of  each  is  the  mixed  result  of  all  the  agents,  the  variations  of 
the  aggregate  cannot  bear  any  uniform  proportion  to  those  of  any  one 
of  its  component  parts. 

§  5.  There  remains  the  Method  of  Residues ;  which  appears,  on  the 
first  view,  less  foreign  to  this  kind  of  inquiry  than  the  three  other  meth- 
ods, because  it  only  requires  that  we  should  accurately  note  the  circum- 
stances of  some  one  country,  or  state  of  society.  Making  allowance, 
thereupon,  for  the  effect  of  all  causes  whose  tendencies  are  known,  the 
residue  which  those  causes  are  inadequate  to  explain  may  plausibly  be 
imputed  to  the  remainder  of  the  circumstances  which  are  known  to 
have  existed  in  the  case.  Something  similar  to  this  is  the  method 
which  Coleridge*  describes  himself  as  having  followed  in  his  political 
essays  in  the  Morning  Post.  "  On  every  great  occurrence  I  endeav- 
ored to  discover  in  past  history  the  event  that  most  nearly  resembled 
it.  I  procured,  wherever  it  was  possible,  the  contemporary  historians, 
memorialists,  and  pamphleteers.  Then  fairly  subtracting  the  points  of 
diflerence  from  those  of  likeness,  as  the  balance  favored  the  former  or 
the  latter,  I  conjectured  that  the  result  would  be  the  same  or  different. 
As  for  instance  in  the  series  of  essays  entitled  '  A  comparison  of  France 
under  Napoleon  with  Rome  under  the  first  Caesars,'  and  in  those  which 
followed,  '  on  the  probable  final  restoration  of  the  Bourbons.'  The 
same  plan  I  pursued  at  the  commencement  of  the  Spanish  Revolution, 
and  with  the  same  success,  taking  the  war  of  the  United  Provinces 
with  Philip  II.  as  the  groundwork  of  the  comparison."  In  this  inquiry 
Coleridge  no  doubt  employed  the  Method  of  Resi^lues ;  for,  in  "  sub- 
tracting the  points  of  diflerence  from  those  of  likeness,"  he  doubtless 
weighed,  and  did  not  content  himself  with  numbering  them  :  he  doubt- 
less took  those  points  of  agreement  only,  which  might  be  known  from 
their  own  nature  to  be  capable  of  influencing  the  effect,  and,  allowing 
for  that  influence,  concluded  that  the  remainder  of  the  result  would  be 
referable  to  the  points  of  difference. 

Whatever  may  be  the  efficacy  of  this  method,  it  is,  as  we  long  ago 
remarked,  not  a  method  of  pure  observation  and  experiment ;  it  con- 
cludes, not  from  a  comparison  of  instances,  but  fi'om  the  comparison 
of  an  instance  with  the  result  of  a  previous  deduction.  Applied  to  so- 
cial phenomena,  it  presupposes  that  the  causes  from  which  part  of  the 
effect  proceeded  are  already  known  ;  and  as  we  have  shown  that  these 
cannot  have  been  known  by  specific  experience,  they  must  have  been 
learned  by  deduction  fi:om  the  principles  of  human  nature  ;  experience 

*  Biographia  Liieraria,  i.,  214. 


THE  GEOMETRICAL  METHOD.  555 

beirifT  called  in  only  as  a  supplementary  resource,  to  (letermino  the  causes 
wliich  produced  an  unexplained  residue.  ]?ut  if  the  principles  (if  Ini- 
man  nature  may  be  had  recourse  to  for  the  establishment  of  some  po- 
litical truths,  they  may  for  all.  If  it  be  admissible  to  say,  Enc^land 
must  have  prospered  by  reason  of  her  proliihitory  system,  because 
after  allowing  for  all  the  other  tendencies  which  have  bcuui  operating, 
there  is  a  portion  of  prosperity  still  to  be  accounted  for;  it  must  be 
admissible  to  go  to  the  same  source  for  the  eflect  of  the  prohibitory 
system,  and  examine  what  account  the  laws  of  human  motives  and  ac- 
tions will  enable  us  to  give  of  it.i  tendencies.  Nor,  in  tact,  will  the 
experimental  argument  amount  to  anything,  except  in  verification  of  a 
conclusion  drawn  from  those  general  laws.  For  we  may  sul)tract  the 
effect  of  one,  two,  three,  or  four  causes,  but  we  shall  never  succeed  in 
subtracting  the  effect  of  all  causes  except  one  ;  while  it  would  be  a 
curious  instance  of  the  dangers  of  too  much  caution,  if,  to  avoid 
depending  on  a  priori  reasoning  concerning  the  effect  of  a  single 
cause,  we  should  oblige  ourselves  to  depend  upon  as  many  separate 
a  priori  reasonings  as  there  are  causes  operating  concurrently  with 
that  particular  cause  in  some  given  instance. 

We  have  'now  sufficiently  characterized  the  absurd  misconception 
of  the  mode  of  investigation  proper  to  political  phenomena,  which  I 
have  termed  the  Chemical  Method.  So  lengthened  a  discussion  would 
not  have  been  necessary,  if  the  claim  to  decide  authoritatively  on  polit- 
ical doctrines  were  coniined  to  persons  who  had  competently  studied 
any  one  of  the  higher  departments  of  physical  science.  l?ut  since  the 
generality  of  those  who  reason  on  political  subjects,  satisfactorily  to 
themselves  and  to  a  more  or  less  numerous  body  of  admirers,  know 
nothing  whatever  of  the  methods  of  physical  investigation  beyond  a 
few  precepts  which  they  contiimc  to  parrot  after  liacon,  being  entirely 
unaware  that  Bacon's  conception  of  scientific  in(iuiry  has  done  its 
work,  and  that  science  has  now  advanced  into  a  higher  stage ;  there 
are  probably  many  to  whom  such  remarks  {is  the  foregoing  may  still 
be  useful.  In  an  age  in  which  chemistry  itself,  when  attempting  to 
deal  with  the  more  complex  chemical  sequences,  those  (jf  the  animal 
or  even  the  vegetable  organism,  has  found  it  necessary  to  become,  and 
has  succeeded  in  becoming,  a  Deductive  Science — it  is  not  to  he  ap- 
prehended that  any  person  of  scientific  habits,  who  has  kept  pace  with 
the  general  progress  of  the  knowledge  of  nature,  can  be  in  danger  of 
applying  the  methods  of  elementary  chemistry  to  explore  the  sequences 
of  the  moat  complex  order  of  phenomena  in  existence. 


CILVPTKR  VIII. 

OF  THE  GEOMETRICAI,,  OR   AD-STRACT   METHOD. 

§  1.  TiiK  misconc(!ption  discussed  in  the  preceding  chapter  is,  as  we 
said,  chiefly  committed  by  persons  not  much  accustomcju  to  scientific 
investigation  :  practitioners  in  politics,  who  rather  eni[)loy  the  common- 
places of  philosopliy  to  justify  their  practice;,  than  seek  to  guide  their 
2;)ractice  by  any  philosophic  views ;  or  imperfectly  educated  racn,  who, 


556  LOGIC    OF    THE    MORAL    SCIENCES. 

in  ignorance  of  the  careful  selection  and  elaborate  comparison  of 
instances  required  for  the  formation  of  a  sound  theory,  attempt  to 
found  one  upon  a  few  coincidences  which  they  have  casually  noticed. 

The  erroneous  method  of  which  we  are  now  to  treat  is,  on  the  con- 
trary, peculiar  to  thinking  and  studious  minds.  It  never  could  have 
suggested  itself  but  to  persons  of  some  familiarity  with  the  nature  of 
scientific  research ;  who — being  aware  of  the  impossibility  of  establish- 
ing, by  casual  observation  or  direct  experimentation,  a  true  theory  of 
sequences  so  complex  as  are  those  of  the  social  phenomena — have 
recourse  to  the  simpler  laws  which  are  immediately  operative  in  those 
phenomena,  and  which  are  no  other  than  the  laws  of  the  nature  of  the 
human  beings  therein  concerned.  These  thinkers  perceive  (what  the 
partisans  of  the  chemical  or  experimental  theory  do  not)  that  the  phi- 
losophy of  society  is  a  deductive  science.  But,  from  an  insufficient 
consideration  of  the  specific  nature  of  the  subject  matter — and  often 
because  (their  own  scientific  education  having  stopped  short  in  too 
early  a  stage)  geometry  stands  in  their  minds  as  the  type  of  all  deductive 
science ;  it  is  to  geometry,  rather  than  to  astronomy  and  natural  phi- 
losophy, that  they  unconsciously  assimilate  the  deductive  science  of 
society. 

Among  the  differences  between  geometry  (a  science  of  coexistent 
facts,  altogether  independent  of  the  laws  of  the  succession  of  phe- 
nomena) and  those  physical  Sciences  of  Causation  which  have  been 
rendered  deductive,  the  following  is  one  of  the  most  conspicuous  : 
That  geometry  affords  no  room  for  what  so  constantly  occurs  in  me- 
chanics and  its  applications,  the  case  of  conflicting  forces;  of  causes 
which  counteract  or  modify  one  another.  In  mechanics  we  continually 
find  two  or  more  moving  forces  pi'oducing,  not  motion,  but  rest ;  or 
motion  in  a  different  direction  fi'om  that  which  would  have  been  pro- 
duced by  either  of  the  generating  forces.  It  is  true  that  the  effect  of 
the  joint  forces  is  the  same  when  they  act  simultaneously,  as  if  they  had 
acted  one  after  another,  or  by  turns ;  and  it  is  in  this  that  the  difference 
between  mechanical  and  chemical  laws  consists.  But  still  the  effects, 
whether  produced  by  successive  or  by  simultaneous  action,  do,  wholly 
or  in  part,  cancel  one  another :  what  the  one  force  does,  the  other, 
partly  or  altogether,  undoes.  There  is  no  similar  state  of  things  in 
geometi-y.  The  result  which  follows  from  one  geometrical  principle 
has  nothing  that  contradicts  the  result  which  follows  from  another. 
What  is  proved  true  from  one  geometrical  theorem,  what  would  be 
true  if  no  other  geometrical  principles  existed,  cannot  be  altered  and 
made  no  longer  true  by  reason  of  some  other  principle.  What  is  once 
proved  true  must  be  true  in  all  cases,  whatever  supposition  may  be 
made  in  regard  to  any  other  matter. 

Now  a  conception,  similar  to  this  last,  would  appear  to  have  been 
formed  of  the  social  science,  in  the  minds  of  the  earlier  of  those  who 
have  attempted  to  cultivate  it  by  a  deductive  method.  Mechanics 
would  be  a  science  very  similar  to  geometry,  if  every  motion  resulted 
from  one  force  alone,  and  not  from  a  conflict  of  forces.  In  the 
geometrical  theory  of  society,  it  seems  to  be  supposed  that  this  is 
really  the  case  with  the  social  phenomena;  and  that  each  of  them 
results  always  from  only  one  force,  one  single  property  of  human 
nature. 

At  the  point  which  we  have  now  reached,  it  cannot  be  necessary  to 


THE    GEOMETRICAL    METHOD.  5r>7 

say  anything  cither  in  proof  or  in  ilhistration  of  the  assertion  that  such 
is  not  the  tiue  diarac-ter  of  the  social  jilienomena.  There  is  not, 
among  these  most  complex  and  (for  that  reason)  most  modiiiahle  of 
all  phenomena,  any  one  over  which  innuinerahle  ft)rce8  do  not  exercise 
influence  ;  which  does  not  depend  upon  a  conjunction  of  very  many 
causes.  We  have  not,  therefore,  to  prove  the  notion  in  question  to  be 
an  error,  but  to  prove  that  the  error  has  been  committed  ;  that  so  mis- 
taken a  conception  of  the  mode  in  which  the  plienomena  of  society 
are  produced,  has  actually  been  cntoitained. 

§  2.  One  numerous  division  of  the  reasoners  who  have  treated  social 
facts  according  to  geometrical  methoils,  not  admitting  of  any  modifica- 
tion of  one  law  by  another,  must  for  the  present  be  left  out  of  onsider- 
ation  :  because  in  them  this  error  is  complicated  with,  and  is  the  cHect 
of,  another  fundamental  misconception,  ot  which  we  have  already  taken 
some  notice,  and  which  will  be  trtvited  of  more  fully  before  we  con- 
clude. 1  speak  of  those  who  deduce  political  conclusions*  not  from 
laws  of  nature,  not  from  sequences  of  phenomena,  real  or  imaginary, 
but  from  unbending  practical  maxims.  Such,  f(U-  example,  are  all 
who  found  their  theories  of  politics  upon  what  is  called  abstract  right, 
that  is  to  say,  upon  universal  precepts  ;  a  pretension  of  which  we  have 
already  noticed  the  chimerical  nature.  Such,  in  like  manner,  arc  those 
who  make  the  assumption  of  a  social  contract,  or  any  other  kind  of 
original  obligation,  and  apply  it  to  particular  cases  by  mere  interpre- 
tation. But  in  this  the  fundamental  error  is  the  attempt  to  treat  an  art 
like  a  science,  and  to  have  a  deductive  art ;  the  irrationality  of  which 
will  be  sliown  in  a  future  chapter.  It  will  be  proper  to  take  our  ex- 
emplification of  the  geometrical  theory  from  those  thinkers  who  have 
avoided  this  additional  error,  and  who  entertain,  so  far,  a  juster  idea 
of  the  nature  of  political  inquiry. 

We  may  cite,  in  the  first  instance,  those  who  assume,  as  the  princi- 
ple of  their  political  philosophy,  that  government  is  founded  on  fear; 
that  the  dread  of  each  other  is  the  one  motive  by  which  human  beings 
were  originally  brought  into  a  state  of  society,  and  are  still  held  in  it. 
Some  of  the  earlier  scientitic  incpiirers  into  politics,  in  particular 
Hobbes,  assumed  this  proposition,  not  by  im])li(  alioii,  but  avowedly, 
as  the  foundation  of  their  doctnne,  and  attempted  to  buihl  a  complete 
philosophy  of  politics  thereupon.  It  is  ti'ue  that  Hobbes  (who  is  so 
much  the  most  considerable  of  these,  that  we  need  not  particularly  ad- 
vert to  any  of  the  rest)  did  not  find  this  one  maxim  sufficient  to  carry 
him  thnmgh  the  whole  of  his  sulyect,  but  wius  obliged  to  eke  it  out  by 
the  double  sophism  of  an  original  contract.  I  call  this  a  double 
sophism;  first,  as  passing  off  a  fiction  for  a  fact,  and  secondly,  as  as- 
suming a  practical  principle,  or  precept,  as  the  basis  of  a  theory ; 
which  is  a  pelitio  jtrmcipii,  since  (as  we  noticed  in  treating  of  that 
Fallacy)  every  rule  of  conduct,  even  though  it  be  so  binding  a  one  a« 
the  obsei-vance  of  a  promise,  must  rest  its  own  foundation.s  upon  the 
theory  of  the  subject,  and  the  theory,  therefore,  cannot  rest  U))on  it. 

§  3.  Passing  over  less  important  instances,  I  shall  come  at  «mce  to 
the  most  remarkable  example  afforded  by  our  owti  times  of  the 
geometrical  method  in  politics  ;  emanating  from  persons  who  were 
well  aware  of  the  distinction  between  Science  and  Art;  who  knew 


558  LOGIC    OF    THE    MORAL    SCIENCES. 

that  rules  of  conduct  must  follow,  not  precede,  the  ascertainment  of 
laws  of  nature,  and  that  the  latter,  not  the  former,  is  the  legitimate  field 
for  the  application  of  the  deductive  method.  I  allude  to  the  interest- 
philosophy  of  the  Bentham  school. 

The  profound  and  original  thinkers  who  are  commonly  known  under 
this  description,  founded  their  general  theory  of  government  upon  one 
comprehensive  premiss,  namely,  that  men's  actions  are  always  deter- 
mined by  their  interests.  There  is  an  ambiguity  in  this  last  expres- 
sion ;  for,  as  tlie  same  philosophers,  especially  Bentham,  systematical- 
ly gave  the  name  of  an  interest  to  anything  which  a  person  likes,  the 
proposition  may  be  understood  to  mean  only  this,  that  men's  actions 
are  always  determined  by  their  wishes.  In  this  sense,  however,  it 
would  not  bear  out  any  of  the  consequences  which  these  philosophers 
di-ew  from  it:  and  the  word,  therefore,  in  their  political  reasonings, 
must  be  understood  to  mean  (which  is  also  the  explanation  they  them- 
selves, on  such  occasions,  gave  of  it)  what  is  commonly  termed  pri- 
vate, or  worldly,  interest. 

Taking  the  doctrine,  then,  in  this  sense,  an  objection  presents  itself 
in  limine  which  might  be  deemed  a  fatal  one,  namely,  that  so  sweep- 
ing a  proposition  is  far  from  being  universally  true.  Men  are  not 
governed  in  all  their  actions  by  their  worldly  interests.  This,  how- 
ever, is  by  no  means  so  conclusive  an  objection  as  it  at  first  appears ; 
because  in  politics  we  are  for  the  most  part  conceraed  with  the  con- 
duct not  of  individual  men,  but  either  of  a  series  of  men  (as  a  succes- 
sion of  kings),  or  a  body  or  mass  of  men,  as  a  nation,  an  aristocracy, 
or  a  representative  assembly.  And  whatever  is  true  of  a  large  majori- 
ty of  mankind,  may,  without  much  error,  be  taken  for  true  o^any  suc- 
cession of  persons,  considered  as  a  whole,  or  of  any  collection  of  per- 
sons in  which  the  act  of  the  majority  becomes  the  act  of  the  whole 
body.  Although,  therefore,  the  maxim  is  sometimes  expressed  in  a 
manner  unnecessarily  paradoxical,  the  consequences  drawn  from  it  will 
hold  equally  good  if  the  assertion  be  limited  as  follows — Any  succes- 
sion of  men,  or  the  majority  of  any  body  of  men,  will  be  governed  in 
the  bulk  of  their  conduct  by  their  personal  interests.  We  are  bound 
to  allow  to  this  school  of  philosophers  the  benefit  of  this  more  rational 
statement  of  their  fundamental  maxim,  which  moreover  is  in  strict  con- 
formity to  the  explanations  which,  when  considered  to  be  called  for, 
have  been  given  by  themselves. 

The  theory  goes  on  to  infer,  correctly  enough,  that  if  the  actions  of 
mankind  are  determined  in  the  main  by  their  selfish  interests,  the  only 
rulers  who  will  govern  according  to  the  interest  of  the  governed,  are 
those  whose  selfish  interests  are  in  accordance  with  it.  And  to  this  is 
added  a  third  proposition,  namely,  that  no  rulers  have  their  selfish 
interest  identical  with  that  of  the  governed,  unless  it  be  rendered  so 
by  accountability,  that  is,  by  dependence  upon  the  will  of  the  governed. 
In  other  words  (and  as  the  result  of  the  whole),  that  the  desire  of  retain- 
ing or  the  fear  of  losing  their  power,  and  whatever  is  thereon  consequent, 
is  the  sole  motive  which  can  be  relied  on  for  producing,  on  the  part 
of  rulers,  a  course  of  conduct  in  accordance  with  the  general  interest. 

We  have  thus  a  fundamental  theorem  of  political  science,  consisting 
of  three  syllogisms,  and  depending  chiefly  upon  two  general  premisses, 
in  each  of  which  a  certain  effect  is  considered  as  determined  only  by 
one  cause,  not  by  a  concurrence  of  causes.     In  the  one,  it  is  assumed 


THE    GEOMETRICAL    METHOD.  559 

that  the  actions  of  average  rulei-s  arc  detennined  solely  by  solf-iiitcrest; 
in  the  otlicr,  that  the  sense  of  identity  of  interest  with  tlie  i^ovcirned, 
is  produced  and  producil)le  by  no  other  cause  than  lesponsiliiUty. 

Neither  of  tliese  propositions  is  by  any  means  true;  the  last  is  ex- 
tremely wide  of  the  truth. 

It  is  not  true  that  tlie  actions  even  of  average  rulers  arc  wholly,  or 
anything  approaching  to  wholly,  determined  by  their  personal  interest, 
or  even  by  their  own  opinion  tii"  their  personal  interest.  I  do  not  Speak 
of  the  intluence  of  a  sense  t)f  duty,  or  feehngs  of  phihuithropy,  mo- 
tives never  to  be  exclusively  relied  on,  although  (except  in  countries 
or  during  periods  of  great  moral  debasement)  they  inllueiice  almost  all 
rulers  in  some  degree,  and  some  rulers  in  a  very  great  degree.  JJut  I 
insist  oidy  upon  what  is  true  of  all  rulers,  viz.,  that  the  character  and 
course  of  their  actions  is  largely  influencetl  (independ(Mitly  of  personal 
calculation)  by  the  habitual  sentiments  and  feelings,  the  general  modes 
of  thinking  and  acting,  which  jirevail  throughout  tlio  community  of 
wliich  they  are  members;  as  well  ;ls  by  the  feelings,  habits,  an.l  imnles 
of  thought  which  characterize  the  particular  class  in  that  comnuinity 
to  which  they  themselves  belong.  And  no  one  will  undi-rsfand  or  bo 
able  to  decipher  their  system  of  conduct,  who  does  not  take  all  these 
things  into  account.  They  are  also  much  influenced  by  the  maxims  and 
traditions  which  have  descended  to  them  from  other  rulers,  their  pred- 
ecessors; and  which  have  been  known  to  maintain,  during  long  pe- 
riods, a  successful  struggle  in  a  direction  contrary  to  tlie  private 
interests  of  the  rulers  for  the  time  being.  I  put  aside  the  iiilluence  of 
other  less  general  causes.  Although,  therefore,  the  private  interest  of 
the  rulers  or  of  the  ruling  class  is  a  very  powerful  force,  constantly  in 
action,  and  exercising  the  most  important  influence  upon  their  con- 
duct; there  is  also,  in  what  they  do,  a  large  portion  whii  h  thiit  ])rivato 
interest  by  no  means  affords  a  suflicient  explanation  of:  and  evin  the 
particulars  which  constitute  the  goodness  or  badness  of  their  govern- 
ment, are  in  some,  and  no  small  degree,  influenced  by  tliose  among 
the  circumstances  acting  upon  them,  which  caunot,  with  any  propriety, 
be  included  in  the  term  self-interest. 

Turning  n(nv  to  the  other  proposition,  that  responsibility  to  the  gov- 
erned is  the  only  cause  capable  of  ])rodu(ing  in  tlir  rulers  a  sense  of 
identity  of  interest  with  the  community;  this  is  still  li-ss  admissible  as 
an  universal  truth,  than  even  the  former.  We  are  not  speaking  of 
perfect  identity  of  interest,  which  is  an  impracticable  chimera;  wliich, 
most  assuredly,  responsibility  to  the  people  does  not  give.  We  ^|>eak 
of  identity  in  essentials;  and  the  essentials  aro  different  at  difleronl 
places  and  times.  There  are  a  large  number  of  cases  in  which  those 
things  which  it  in  most  for  the  interest  of  the  people  that  thtsir  ruler 
should  do,  are  also  those  which  he  is  prompted  to  do  by  his  strongest 
personal  interest,  the  consolidation  of  his  power.  The  suppression, 
for  instance,  of  anarchy  and  resistance  to  law — the  comj)lete  establi«h- 
ment  of  the  authority  r»f  the  ctrntral  g»)vemmetit,  in  a  slate  of  society 
like  that  of  L^urojx-  in  the  middle  ages — is  the  strongest  int(M-est  of  the 
people,  and  also  of  the  rulers,  simply  because  they  aro  the  rulers;  and 
respoiisil)llity  on  their  part  could  not  strengthen,  though  in  many  con- 
ceivable ways  it  might  weaken,  the  motives  prompting  them  to  pursue 
this  object.  During  the  gr(;ater  part  of  the  reign  of  Queen  Elizabeth, 
and  of  many  other  monarchs  who  might  be  named,  the  sense  of  iJcn- 


560  LOGIC    OF    THE    MORAL    SCIENCES. 

tity  of  interest  between  the  sovereign  and  the  majority  of  the  peop]e 
was  probably  stronger  than  it  usually  is  in  responsible  governments  ; 
everything  that  the  people  had  most  at  heart,  the  monarch  had  at  heart 
too.  Had  Peter  the  Great,  or  the  rugged  savages  whom  he  began  to 
civilize,  the  truest  inclination  towards  the  things  which  were  for  the 
real  interest  of  those  savages  1 

I  am  not  here  attempting  to  establish  a  theory  of  government,  and 
am  not  called  upon  to  determine  the  proportional  weight  v/hich  ought 
to  be  given  to  the  circumstances  which  this  school  of  geometrical  poli- 
ticians left  out  of  their  system,  and  those  which  they  took  into  it.  I 
am  only  concerned  to  show  that  their  method  was  unscientific ;  not  to 
measure  the  amount  of  error  which  may  have  affected  their  practical 
conclusions. 

It  is  but  justice  to  them,  however,  to  remark,  that  their  mistake  was 
not  so  much  one  of  substance  as  of  form  ;  and  consisted  in  presenting 
in  a  systematic  shape,  and  as  the  scientific  treatment  of  a  great  philo- 
sophical question,  what  should  have  passed  for  that  which  it  really 
was,  the  mere  polemics  of  the  day.  Although  the  actions  of  rulers  are 
by  no  means  wholly  determined  by  their  selfish  interests,  it  is  as  a 
security  against  those  selfish  interests  that  constitutional  checks  are 
required;  and  for  that  purpose  such  checks,  in  England,  and  in  many 
other  countries,  can  in  no  manner  be  dispensed  with.  It  is  true,  more- 
over, that  in  the  particular  stage  of  civilization  through  which  Europe 
is  now  passing,  either  express  or  virtual  responsibility  to  the  governed 
is  the  only  means  practically  available  to  ci'eate  a  feeling  of  identity  of 
interest,  in  the  cases,  and  on  the  points,  where  that  feeling  does  not 
sufficiently  exist.  To  all  this,  and  to  the  arguments  which  may  be 
founded  upon  it  in  favor  of  measures  for  the  connection  of  our  repre- 
sentative system,  I  have  nothing  to  object;  but  I  confess  my  regret, 
that  the  small  though  highly  important  portion  of  the  philosophy  of 
government,  which  was  wanted  for  the  immediate  purpose  of  serving 
the  cause  of  parliamentary  reform,  should  have  been  held  forth  by  phi- 
losophers of  such  eminence  as  a  complete  theory. 

It  is  not  to  be  imagined  possible,  nor  is  it  true  in  point  of  fact,  that 
these  philosophers  regarded  the  few  premisses  of  their  theory  as  in- 
cluding all  that  is  required  for  explaining  social  phenomena,  or  for 
determining  the  choice  of  forms  of  government  and  measures  of  legis- 
lation and  administration.  They  were  too  highly  instructed,  of  too 
comprehensive  intellect,  and  some  of  them  of  too  sober  and  practical 
a  character,  for  such  an  error.  They  would  have  applied  and  did 
apply  their  principles  with  innumerable  allowances.  But  it  is  not 
allowances  that  are  wanted.  There  is  little  chance  of  making  due 
amends  in  the  superstructure  of  a  theory  for  the  want  of  sufficient 
breadth  in  its  foundations.  It  is  unphilosophical  to  construct  a  science 
out  of  a  few  of  the  agencies  by  which  the  phenomena  are  detennined, 
and  leave  the  rest  to  the  routine  of  practice  or  the  sagacity  of  conjec- 
ture. We  either  ought  not  to  pretend  to  scientific  forms,  or  we  ought 
to  study  all  the  detennining  agencies  equally,  and  endeavor,  so  far  as 
it  can  be  done,  to  include  all  of  them  within  the  pale  of  the  science ; 
else  we  shall  infallibly  bestow  a  disproportionate  attention  upon  those 
which  our  theory  takes  into  accoimt,  while  we  mis-estimate  the  rest, 
and  probably  underrate  their  importance.  That  the  deductions  should 
be  from  the  whole  and  not  from  a  part  only  of  the  laws  of  nature  that 


rUYSICAL    METHOD.  501 

are  concerned,  would  bo  drsirablo  v\cn  if  lliosc  omitted  were  so  iiisiir- 
nificant  in  cimiparLson  with  tlio  otliers,  that  lliey  might,  for  most  luii- 
poses  and  on  most  occasions,  hv  left  duI  of  iho  account.  But  this  is 
far  indeed  from  boins^  true  in  the  social  science.  The  phenomenii  ut 
societj'  do  not  depend,  in  essentials,  upon  any  <»ne  aifoncy  or  law  of 
human  nature,  with  only  inconsiderable  modihcations  from  others. 
The  whole  of  the  laws  of  human  nature  intluence  those  phenomena, 
and  there  is  not  one  which  influences  them  in  a  small  (lei,Mre.  There 
is  not  one,  the  removal  or  any  threat  alteration  of  wliicii  woidd  not 
materially  atl'ect  the  whole  aspect  of  society,  and  chani^e  more  or  less 
most  of  the  principal  seiiuences  of  the  social  phenomena. 

The  theory  which  has  been  the  subject  of  these  remarks  is,  in  this 
country  at  least,  the  prhicipal  contemporary  example  of  what  I  have 
styled  the  geometrical  method  of  philosophizing  in  the  social  science; 
and  our  examination  of  it  has,  for  this  reason,  been  more  detailed  than 
might  otherwise  have  been  deemed  necessary  in  a  work  like  the 
present.  Ha\ing'now  sufficiently  illustrated  the  two  erroneous  metliods, 
we  shall  pass  without  further  prclimiiuiry  to  the  true  method  ;  lliat 
which  proceeds  (conformably  to  the  practice  of  the  higher  branches 
of  physical  science)  deductively  indeed,  but  by  deduction  fnmi  many, 
not  from  one  or  a  veiy  few,  original  premisses  ;  cons-idering  each  efl'ect 
as  (what  it  really  is)  an  aggregate  result  of  many  causes,  operating 
sometimes  through  the  same,  sometimes  through  diflerent  mental  agen- 
cies, or  laws  of  human  nature. 


CHAPTER  IX. 

OF  THE  PIIVSICAL,   OR  CONXRETE  DEDUCTIVE,   METHOD. 

§  1.  After  what  has  been  said  to  illustrate  the  nature  of  the  inquiry 
into  the  social  phenomena,  the  general  character  of  the  method  pro- 
per to  that  inquiry  is  sufficiently  evident,  and  needs  only  to  be  recap- 
itulated, not  proved.  However  complex  the  phenomena,  all  their 
sequences  and  coexistences  result  fiom  the  laws  of  the  8«*parate  ele- 
ments. The  effect  which  is  produced,  in  social  phenomena,  by  any 
complex  set  of  circumstances,  amounts  precisely  to  the  sum  of  the 
effects  of  the  cirounstances  tcdven  singly:  and  the  comj)lexity  does  not 
arise  from  the  number  of  the  laws  themselves,  which  is  not  remarkably 
great;  but  fi-ora  the  extraordinary  number  and  variety  of  the  data  or 
elements — of  the  agents  which,  in  obedience  to  that  small  number  of 
laws,  cooperate  towards  the  effect.  The  Social  Science,  therefore, 
(which  I  shall  henceforth,  with  M.  Comte,  tlesignate  by  ihe  more  com- 
pact term  Sociology,)  is  a  deductive  .science ;  not,  indeed,  after  the 
model  of  geometr}',  but  after  that  of  the  higher  physical  scienccfl.  It 
infers  the  law  of  each  efTi'Ct  from  the  laws  of  causation  upon  which 
that  effect  depends ;  not,  hr)wever,  from  the  law  merely  of  one  cause, 
as  in  the  geometrical  method  ;  but  by  considering  all  the  caiusos  which 
conjunctly  influence  the  efFect,  and  C(»mj>ounding  their  laws  with  one 
another.  Its  method,  in  shf»rt,  is  the  Concrete  Dc-ductive  M»-thod  : 
that  of  which  a.sti-onomy  furnishes  the  most  perfect,  natural  philoso])hy 
4B 


562  LOGIC   OF    THE    MORAL  SCIENCES. 

a  somewhat  less  perfect  example,  and  the  employment  of  which,  with 
the  adaptations  and  precautions  required  by  the  subject,  is  beginning 
to  regenerate  physiology. 

Nor  does  it  admit  of  doubt,  that  similar  adaptations  and  precautions 
are  indispensable  in  sociology.  In  applying,  to  that  most  complex  of 
all  studies,  what  is  demonstrably  the  sole  method  capable  of  throwing 
the  light  of  science  even  upon  phenomena  of  a  far  inferior  degree  of 
complication,  we  ought  to  be  aware  that  the  same  superior  complexity 
which  renders  the  instrument  of  Deduction  more  necessary,  renders 
it  also  more  precarious ;  and  we  must  be  prepared  to  meet,  by  appro- 
priate contrivances,  this  increase  of  difficulty. 

The  actions  and  feelings  of  human  beings  in  the  social  state,  are,  no 
doubt,  entirely  governed  by  psychological  and  ethological  laws :  what- 
ever influence  any  cause  exercises  upon  the  social  phenomena,  it  exer- 
cises through  those  laws.  Supposing,  therefore,  the  laws  of  human 
actions  and  feelings  to  be  sufficiently  known,  there  is  no  extraordi- 
nary difficulty  in  determining  from  those  laws,  the  nature  of  the  social 
effects  which  any  given  cause  tends  to  produce.  But  when  the  ques- 
tion is  that  of  compounding  several  tendencies  together,  and  com- 
puting the  aggregate  result  of  many  coexistent  causes  ;  and  especially 
when,  by  attempting  to  predict  what  will  actually  occur  in  a  given 
case,  we  incur  the  obligation  of  estimating  and  compounding  together 
the  influences  of  all  the  causes  which  happen  to  exist  in  that  case  ;  we 
attempt  a  task,  to  proceed  far  in  which,  certainly  surpasses  the  com- 
pass of  the  human  faculties. 

If  all  the  resources  of  science  are  not  sufficient  to  enable  us  to  calcu- 
late a  priori,  with  complete  precision,  the  mutual  action  of  three 
bodies  gravitating  towards  one  another;  it  may  be  judged  with  what 
prospects  of  success  we  should  endeavor,  from  the  laws  of  human  na- 
ture only,  to  calculate  the  result  of  the  conflicting  tendencies  which 
are  acting  in  a  thousand  different  directions  and  promoting  a  thousand 
different  changes  at  a  given  instant  in  a  given  society :  although  we 
might  and  ought  to  be  able,  from  the  laws  of  human  nature,  to  distin- 
guish correctly  enough  the  tendencies  themselves,  so  far  as  they  de- 
pend on  causes  accessible  to  our  observation ;  and  to  determine  the 
direction  which  each  of  them,  if  acting  alone,  would  impress  upon 
society,  as  well  as,  in  a  general  way  at  least,  to  pronounce  that  some 
of  these  tendencies  are  more  powerful  than  others. 

But,  without  dissembling  the  necessary  imperfections  of  the  d  priori 
method  when  applied  to  such  a  subject,  neither  ought  we,  on  the  other 
hand,  to  exaggerate  them.  The  same  objections  which  apply  to  the 
Method  of  Deduction  in  this  its  most  difficult  employment,  apply  to  it, 
as  we  formerly  showed,*  in  its  easiest ;  and  would  even  there  have 
been  insuperable  if  there  had  not  existed,  as  was  then  fully  explained, 
an  appropriate  remedy.  This  remedy  consists  in  the  process  which, 
under  the  name  of  Verification,  we  have  characterized  as  the  third 
essential  constituent  part  of  the  Deductive  Method ;  that  of  collating 
the  conclusions  "of  the  ratiocination  either  with  the  concrete  phenom- 
ena themselves,  or,  when  such  are  obtainable,  with  their  empirical 
laws.  The  ground  of  confidence  in  any  concrete  deductive  science  is 
not  the  a  priori  reasoning,  but  the  consilience  between  its  results  and 

•  Supra,  pp.  268-9. 


PHYSICAL    METHOD.  5G3 

those  of  observation  a  posteriori.  Khhcr  of  these  processes  wlieii  di- 
vorceil  from  tlie  otlior  tHiniiiisht;s  in  vuhu?  ;ts  the  sul))(!ct  iinTt!;uscs  in 
complication,  and  tliis  in  so  rapid  a  ratio  as  soon  to  become  •■ntirely 
worthless;  but  the  reliance  to  be  placed  in  tin*  concurrence  of  the  two 
sorts  of  evidence,  not  only  does  not  diminish  in  anythinj^  like  the  same 
proportion,  but  is  not  necessarily  much  diminished  at  all.  Nothinuf 
more  rosuUs  than  a  disturbance  in  the  order  of  precedency  of  the  two 
processes,  sometimes  amountinji;  to  its  actual  invei-sion  :  insomuch  that 
instead  of  deducint^  our  conclusions  by  reasonin-,',  and  vc'riiyinir  thrm 
by  observation,  we  in  some  cases  bcfrin  by  obtaining  tlicm  conjccfu- 
rally  from  specific  experience,  and  afterwards  connect  them  with  the 
principles  of  human  nature  by  ii  j)riori  reasonings,  which  reasonings 
are  thus  a  real  A'erilication. 

The  greatest  living  authority  on  scientific  methods  in  general,  and 
the  only  philosopher  who,  with  a  competent  knowledge  of  those 
methods,  has  attempted  to  characterize  the  Method  of  Socioloqry,  M. 
Comte,  considers  this  inverse  order  as  inseparably  inherent  in  the 
nature  of  sociological  speculation.  He  looks  upon  the  social  science 
as  essentially  consisting  of  generalizations  from  history,  verified,  not 
originally  suggested,  by  deduction  from  the  laws  of  Imman  nature. 
Such  an  opinion,  from  such  a  thinker,  deserves  the  most  serious  con- 
sideration ;  but  though  I  shall  presently  endeavor  to  show  the  emi- 
nent importance  of  the  truth  which  it  contains,  I  cannot  but  think  that 
this  truth  is  enunciated  in  too  unlimited  a  manner,  and  that  there  is 
considerable  scope  in  sociological  inquiry  for  the  direct,  as  well  as  for 
the  inverse.  Deductive  Method. 

It  will,  in  fact,  be  shown  in  the  next  chapter,  that  there  is  a  kind  of 
sociological  inquiries  to  which,  from  their  prodigious  complication,  the 
method  of  direct  deduction  is  altogether  inapplicable,  while  by  a  hajijiy 
compensation  it  is  precisely  in  these  cases  that  we  are  ablo  to  obtain 
the  best  empirical  laws:  to  these  inquiries,  therefore,  the  Inverse 
Method  is  exclusively  adapted.  But  there  are  also,  as  will  presently 
appear,  other  cases  in  which  it  is  impossible  to  obtain  from  direct  ob- 
servation  anything  worthy  the  name  of  an  empirical  law ;  and  it  for- 
tunately happens  that  these  are  the  very  cjises  in  which  the  Direct 
Method  is  least  affected  by  the  objection  which  undoubtedly  must  al- 
ways affect  it  in  a  certain  degree. 

We  shall  begin,  then,  by  lo<jking  at  Sociology  as  a  science  of  direct 
Deduction,  and  considering  what  can  be  accomplished  in  it,  and  under 
what  limitations,  by  that  mode  of  investigation.  We  shall,  then,  in  a 
separate  chapter,  examine  and  endeavor  to  characterize  the  inverse 
process. 

§  2.  It  is,  in  the  first  place,  distinctly  apparent  that  Sociology,  con- 
sidered as  a  system  of  deductions  a  priori,  cannot  be  a  science  of  pos- 
itive predictions,  but  only  of  tendencies.  We  may  be  able  to  con- 
clude, from  the  laws  of  human  nature;  apjdied  to  the  circumstances  of 
a  given  state  of  society,  that  a  particular  cause  will  tjperatc  in  a  cer- 
tain maimer  uiih-ss  counteracted  ;  but  we  can  never  be  assured  to 
what  extent  (»r  amount  it  will  so  (jpcrate,  (»r  allirm  with  certainty  that 
it  will  not  be  counteracted;  because  we  can  seldcun  know,  even  ap- 
proximatively,  all  the  agencies  which  may  coexist  with  it,  and  still  less 
calculate  the  collective  result  of  so  many  combined  elements.     Tho 


564  LOGIC    OF    THE    MORAL    SCIENCES. 

remark,  however,  must  here  be  once  more  repeated,  that  knowledge 
insufficient  for  prediction  may  be  most  vakaable  for  guidance.  It  is 
not  necessary  for  the  wise  conduct  of  the  affairs  of  society,  no  more 
than  of  any  man's  private  concerns,  that  we  should  be  able  to  foresee 
infallibly  the  results  of  what  we  do.  We  must  seek  our  objects  by 
means  which  may  perhaps  be  defeated,  and  take  precautions  against 
dangers  which  possibly  may  never  be  realized.  The  aim  of  practical 
politics  is  to  surround  the  society  which  is  under  our  superintendence 
with  the  greatest  possible  number  of  circumstances  of  which  the  ten 
dencies  are  beneficial,  and  to  remove  or  counteract,  as  far  as  practi- 
cable, those  of  which  the  tendencies  are  injurious.  A  knowledge  of 
the  tendencies  only,  though  without  the  power  of  accurately  predicting 
their  conjunct  result,  gives  us  to  a  certain  extent  this  power. 

It  would,  however,  be  an  error  to  suppose  that  even  with  respect  to 
tendencies,  we  could  arrive  in  this  manner  at  any  great  number  of  prop- 
ositions which  will  be  true  in  all  societies  without  exception.  Such  a 
supposition  would  be  inconsistent  with  the  eminently  modifiable  nature 
of  the  social  phenomena,  and  the  multitude  and  variety  of  the  circum- 
stances by  which  they  are  modified;  circumstances  never  the  same,  or 
even  nearly  the  same,  in  two  different  societies,  or  in  two  different 
periods  of  the  same  society.  This  would  not  be  so  serious  an  obstacle 
if,  though  the  causes  acting  upon  society  in  general  are  numerous, 
those  which  influence  any  one  feature  of  society  were  limited  in  num- 
ber ;  for  we  might  then  insulate  any  particular  social  phenomenon,  and 
investigate  its  laws  without  disturbance  from  the  rest.  But  the  truth 
is  the  very  opposite  of  this.  Whatever  affects,  in  an  appreciable  degree, 
any  one  element  of  the  social  state,  affects  through  it  all  the  other  ele- 
ments. The  mode  of  production  of  all  social  phenomena  is  one  great 
case  of  Intermixture  of  Laws.  We  can  never  either  understand  in 
theory  or  command  in  practice  the  condition  of  a  society  in  any  one 
respect,  without  taking  into  consideration  its  condition  in  all  other 
respects.  There  is  no  social  phenomenon  which  is  not  more  or  less 
influenced  by  every  other  part  of  the  condition  of  the  same  society, 
and  therefore  by  every  cause  which  is  influencing  any  other  of  the 
contemporaneous  social  phenomena.  There  is,  in  short,  a  consensus 
(to  borrow  an  expression  from  physiology)  similar  to  that  existing 
among  the  various  organs  and  functions  of  the  physical  frame  of  man 
and  the  more  perfect  animals ;  and  constituting  one  of  the  many  anal- 
ogies which  have  rendered  universal  such  expressions  as  the  "  body 
politic  "  and  "  body  natural."  It  follows  from  this  consensus,  that  unless 
two  societies  could  be  alike  in  all  the  circumstances  which  surround 
and  influence  them  (which  would  imply  their  being  alike  in  their  pre- 
vious history),  no  portion  whatever  of  their  phenomena  will,  unless  by 
accident,  precisely  conespond  ;  no  one  cause  will  produce  exactly  the 
same  effect  in  both.  Every  cause,  as  its  effect  spreads  through  society, 
comes  somewhere  in  contact  with  different  sets  of  agencies,  and  thus  has 
its  effects  on  some  of  the  social  phenomena  differently  modified  ;  and 
these  differences,  by  their  reaction,  produce  a  difference  even  in  those  of 
the  effects  which  would  otherwise  have  been  the  same.  We  can  never, 
therefore,  affirm  with  certainty  that  a  cause  which  has  a  particular  ten- 
dency in  one  people  or  in  one  age  will  have  exactly  the  same  tendency 
in  another,  without  referring  back  to  our  premisses,  and  perforaiing 
over  again  for  the  second  age  or  nation,  that  analysis  of  the  whole  of 


I 


PHYSICAL    METHOD.  503 

its  influencin<r  circumstances  whidi  we  had  already  jierform.'d  fur  ilin 
tirsL  Tlie  detliictive  so  eiict;  oi'  Bociety  (l<»rs  not  lay  down  a  llicun-iii, 
asserting  in  an  universal  manner  the  t'H'ect  of  any 'cause  ;  but  rallior 
teaches  us  liovv  to  frame  the  proper  theorem  for  the  circumstances  of 
any  given  case.  It  does  not  give  us  the  laws  of  society  in  general,  but 
the  means  of  determining  the  phenomena  of  any  given  society  from  tho 
particular  elements  or  data  of  that  soci«'ty. 

All  the  general  propositions  of  the  deductive  science  arc  therefore, 
in  the  strictest  sense  of  the  word,  hypothetical.  They  are  grounded 
on  some  supposititious  set  of  circumstances,  and  declare  how  some 
given  cause  will  operate  in  those  circumstances,  supposing  tliat  no 
others  are  combined  with  them.  If  the  set  of  circumstances  supposed 
has  been  taken  from  those  of  any  existing  society,  the  conclusions 
will  be  true  of  that  society,  provided,  and  in  as  far  as,  tin;  effect  of  ihoso 
circumstances  shall  not  be  modified  by  others  which  liave  not  been 
taken  into  the  account.  If  wo  desire  a  nearer  approach  to  coiicrcto 
truth,  we  can  only  aim  at  it  by  taking,  or  endeavoring  to  take,  a  greater 
number  of  individualizing  circumstances  into  the  computation. 

Considering,  however,  in  how  accelerating  a  ratio  tho  uncertainty  of 
our  conclusions  increases,  as  we  attempt  to  take  the  efl'ect  of  a  greater 
number  of  concurrent  causes  into  our  calculations  ;  the  hypothetical 
combinations  of  circumstances  upon  which  we  construct  the  general 
theorems  of  the  science,  cannot  be  made  very  complex,  without  so 
rapidly  accumulating  a  liability  to  error  as  must  soon  deprive  our  con- 
clusions of  all  value.  This  mode  of  inquiry,  considered  as  a  mcai»s  of 
obtaining  general  propositions,  must  therefore,  on  pain  of  entin-  fri- 
volity, be  limited  to  those  classes  of  social  facts  wliich,  though  intluenrcd 
like  the  rest  by  all  sociological  agents,  are  under  tho  i/nmcdiatc  influ- 
ence, principally  at  least,  of  a  few  only. 

§  3.  Notwithstanding  the  universal  consensus  of  the  social  phenomena, 
whereby  nothing  which  takes  place  in  any  part  of  the  operations  of 
society  is  without  its  share  of  influence  on  every  other  part  ;  and  not- 
withstanding the  paramount  ascendency  which  the  general  state  of 
civilization  and  social  progress  in  any  given  society  must  hence  exercise 
over  all  the  partial  and  subordinate  phenomena ;  it  is  not  the  less  true 
that  different  species  of  social  facts  are  in  the  main  de])endent,  imme- 
diately and  in  the  first  resort,  upon  difl'en-nt  kinds  of  causes ;  and  there- 
fore not  only  may  with  advantage,  but  must,  be  stu<lied  apart :  just  as 
in  the  natural  body  we  study  separately  the  physiology  and  pathology 
of  each  of  the  principid  organs  and  tissues,  although  every  one  is  acted 
iijx)n  by  the  state  of  all  the  (jthers  ;  and  althougli  the  peculiar  consti- 
tution and  general  state  of  health  of  llie  organism  coopi.-rates  with  ami 
often  preponderates  over  the  local  causes,  in  determining  tho  slate  of 
any  particular  organ. 

On  these  considerations  is  grounded  the  existence  of  distinct  and 
separate,  though  not  independent,  branches  or  departments  of  socio- 
logical speculation. 

There  is,  for  example,  one  large  class  of  social  phenomena,  in  which 
the  immediately  determining  causes  are  prin<ipally  those  which  art 
through  the  desire  of  wealth;  and  in  which  the  jisychohfgical  law  main- 
ly concerned  is  the  familiar  one,  that  a  greater  gain  is  prefe-rred  to  a 
fimaller.     I  mean,  of  course,  that  portion  of  the  phenomena  of  society 


566  LOGIC    OF    THE    MORAL    SCIENCES. 

which  emanate  from  the  industrial,  or  productive,  operations  of  man- 
kind ;  and  from  those  of  their  acts  through  which  the  distribution  of 
the  products  of  those  industrial  operations  takes  place,  in  so  far  as  not 
effected  by  force,  or  modified  by  voluntary  gift.  By  reasoning  from 
that  one  law  of  human  nature,  and  from  the  principal  outward  circum- 
stances (whether  universal  or  confined  to  particular  states  of  society) 
which  operate  upon  the  human  mind  through  that  law,  we  may  be 
enabled  to  explain  and  predict  this  portion  of  the  phenomena  of  soci- 
ety, so  far  as  they  depend  upon  that  class  of  circumstances  only ;  over- 
looking the  influence  of  any  other  of  the  circumstances  of  society;  and 
therefore  neither  tracing  back  the  circumstances  which  we  do  take  into 
account,  to  their  possible  origin  in  some  other  facts  in  the  social  state, 
nor  making  allowance  for  the  manner  in  which  any  of  those  other 
circumstances  may  interfere  with,  and  counteract  or  modify,  the  effect 
of  the  former.  A  science  is  thus  constructed,  which  has  received  the 
name  of  Political  Economy. 

The  motive  which  suggests  the  separation  of  this  portion  of  the 
social  phenomena  from  the  rest,  and  the  creation  of  a  distinct  science 
relating  to  them,  is — that  they  do  mainly  depend,  at  least  in  the  first 
j:esort,  upon  one  class  of  circumstances  only ;  and  that  even  when 
other  circumstances  interfere,  the  ascertainment  of  the  effect  due  to 
the  one  class  of  circumstances  alone,  is  a  suflRciently  intricate  and 
difficult  business  to  make  it  expedient  to  perform  it  once  for  all,  and 
then  allow  for  the  effect  of  the  modifying  circumstances  ;  especially  as 
certain  fixed  combinations  of  the  former  are  apt  to  recur  often,  in  con- 
junction with  ever-varying  circumstances  of  the  latter  class. 

Political  Economy,  as  I  have  said  on  another  occasion,  concerns 
itself  only  with  "such  of  the  phenomena  of  the  social  state  as  take 
place  in  consequence  of  the  pursuit  of  wealth.  It  makes  entire  abstrac- 
tion of  every  other  human  passion  or  motive;  except  those  which  may 
be  regarded  as  perpetually  antagonizing  principles  to  the  desire  of 
wealth,  namely,  aversion  to  labor,  and  desire  of  the  present  enjoyment 
of  costly  indulgences.  These  it  takes,  to  a  certain  extent,  into  its  cal- 
culations, because  these  do  not  merely,  like  our  other  desires,  occa- 
sionally conflict  with  the  pursuit  of  wealth,  but  accompany  it  always 
as  a  drag  or  impediment,  and  are  therefore  inseparably  mixed  up  in 
the  consideration  of  it.  Political  Economy  considers  mankind  as  oc- 
cupied solely  in  acquiring  and  consuming  wealth  ;  and  aims  at  showing 
what  is  the  course  of  action  into  which  mankind,  living  in  a  state  of 
society,  would  be  impelled,  if  that  motive,  except  in  the  degree  in 
which  it  is  checked  by  the  two  perpetual  counter-motives  above  ad- 
verted to,  were  absolute  ruler  of  all  their  actions.  Under  the  influence 
of  this  desire,  it  shows  mankind  accumulating  wealth,  and  employing 
that  wealth  in  the  production  of  other  wealth  ;  sanctioning  by  mutual 
agreement  the  institution  of  property ;  establishing  laws  to  prevent 
individuals  from  encroaching  upon  the  property  of  others  by  force  or 
fraud  ;  adopting  various  contrivances  for  increasing  the  productiveness 
of  their  labor  ;  settling  the  division  of  the  produce  by  agi'eement,  under 
the  influence  of  competition  (competition  itself  being  governed  by  cer- 
tain laws,  which  laws  are  therefore  the  ultimate  regulators  of  the 
division  of  the  produce) ;  and  employing  certain  expedients  (as  money, 
credit,  &c.)  to  facilitate  the  distribution.  All  these  operations,  though 
many  of  them  are  really  the  result  of  a  plurality  of  motives,  arc  coi> 


niyaicAL  method.  507 

sidered  by  political  economy  as  flowing  solely  from  tlie  desire  of  wealtli. 
The  science  then  proceeds  to  investigate  the  laws  which  govern  these 
several  operations,  under  th<'  supposition  that  man  is  a  being  who  is 
determined,  by  the  necessity  of  his  nature,  to  prefer  a  gi-eater  portion 
of  wealth  to  a  smaller,  in  all  cases,  without  any  other  exception  than 
that  cotistituted  by  the  two  counter-motives  already  specified.  Not 
that  any  political  economist  was  ever  so  absurd  as  to  suppose  that 
mankind  are  really  thus  constituted,  but  because  this  is  the  mode  in 
which  science  must  necessarily  proceed.  When  an  cflt'ct  depends 
upon  a  concurrence  of  causes,  these  causes  must  be  studied  ouc,  at  a 
time,  and  their  laws  separately  investigated,  if  we  wish,  through  the 
causes,  to  obtain  the  j)ower  of  either  predicting  or  controlling  the 
effect;  since  the  law  of  the  effect  is  compounded  of  the  laws  of  all 
the  causes  which  determine  it.  The  law  of  the  centripetal  and  that  of 
the  tangential  force  must  have  been  known,  before  the  motions  of  the 
earth  and  planets  could  be  explained,  or  many  of  them  predicted. 
The  same  is  the  case  with  the  conduct  of  man  in  society.  In  order  to 
judge  how  he  will  act  under  the  variety  of  desires  and  aversions  which 
are  concurrently  operating  upon  him,  we  must  know  how  he  would  act 
under  the  exclusive  influence  of  each  one  in  particular.  There  is, 
perhaps,  no  action  of  a  man's  life  in  which  he  is  neither  under  the 
immediate  nor  under  the  remote  influence  of  any  impulse  but  the  mere 
desire  of  wealth.  There  are  many  parts  of  human  conduct  of  which 
wealth  is  not  even  the  principal  object,  and  to  these  political  economy 
does  not  pretend  that  its  conclusions  are  applicable.  But  there  are 
also  certain  departments  of  human  affairs,  in  which  the  acquisition  of 
wealth  is  the  main  and  acknowledged  end.  It  is  only  of  these  that 
political  economy  takes  notice.  The  manner  in  which  it  necessarily 
proceeds  is  that  of  treating  the  main  and  acknowledged  end  as  if  it 
were  the  sole  end;  which,  of  all  hypotheses  equally  simple,  is  the 
nearest  to  the  truth.  The  political  eccmomist  inquires,  what  are  the 
actions  which  would  be  produced  by  this  desire,  if  within  the  depart- 
ments in  question  it  were  unimpeded  by  any  other.  In  this  way  a 
nearer  approximation  is  obtained  than  would  otherwise  be  practicable 
to  the  real  oi'der  of  human  affairs  in  those  dcjiartmcnts.  This  approxi- 
mation has  then  to  be  corrected  by  making  proper  allowance  for  the 
effects  of  any  impulses  of  a  different  description,  which  can  be  shown 
to  interfere  with  the  result  in  any  particular  case.  Only  in  a  few  of 
the  most  striking  cases  (such  as  the  important  one  of  the  principle  of 
population)  are  these  corrections  interpolated  into  the  expositions  of 
political  economy  itself;  the  strictness  of  purely  scientific  anangement 
being  thereby  somewhat  departed  from,  fur  the  sake  of  j)ractical  utility. 
So  far  as  it  is  known,  or  may  be  presumed,  that  the  conduct  of  man- 
kind in  the  pursuit  of  wealth  is  under  the  collateral  influence  of  any 
other  of  the  properties  of  our  nature,  than  the  desire  of  obtaining  the 
greatest  quantity  of  wealth  with  the  least  labor  and  self-denial,  the 
conclusions  of  political  economy  will  so  far  fail  of  being  applicable  to 
the  explanation  or  pnjdiction  of  real  evt-nts,  utitil  tliey  are  modified  by 
a  correct  allowance  for  the;  degree  of  influence  exercised  by  the  other 
cause." 

When  M.  Comte  (for  of  the  objections  raised  by  inferior  thinkers  it 
is  unnecessary  here  to  take  account)  pronounces  the  attempt  to  treat 
political  economy,  even  provisionally,  as  a  science  apart,  to  be  a  mia- 


568  LOGIC    OF    THE   MORAL    SCIENCES. 

apprehension  of  the  scientific  method  proper  to  Sociology ;  I  cannot 
but  think  that  he  has  overlooked  the  extensive  and  important  practical 
guidance  which  may  be  derived,  in  any  given  state  of  society,  from 
general  propositions  such  as  those  above  indicated ;  even  though  the 
modifying  influence  of  the  miscellaneous  causes  which  the  theory  does 
not  take  into  account,  as  well  as  the  effect  of  the  general  social  changes 
in  progress,  be  provisionally  overlooked.  And  although  it  has  been 
a  very  common  error  of  political  economists  to  draw  conclusions 
from  the  elements  of  one  state  of  society,  and  apply  them  to  other 
states  in  which  many  of  the  elements  are  not  the  same;  it  is  even 
then  not  difficult,  by  tracing  back  the  demonstrations,  and  intro- 
ducing the  new  premisses  in  their  proper  places,  to  make  the  same 
general  course  of  argument  which  serve  for  the  one  case,  serve  for 
the  others  too. 

For  example,  it  has  been  greatly  the  custom  of  English  political 
economists  to  discuss  the  natural  laws  of  the  distribution  of  the  pro- 
duce of  industry,  on  a  supposition  which  is  scarcely  realized  anywhere 
out  of  England  and  Scotland,  namely,  that  the  produce  is  "shared 
among  three  classes,  altogether  distinct  fiom  one  another,  laborers, 
capitalists,  and  landlords ;  and  that  all  these  are  free  agents,  permitted 
in  law  and  in  fact  to  set  upon  their  labor,  their  capital,  and  their  land, 
whatever  price  they  are  able  to  get  for  it.  The  conclusions  of  the 
science,  being  all  adapted  to  a  society  thus  constituted,  require  to  be 
revised  whenever  they  are  applied  to  any  other.  They  are  inapplica- 
ble where  the  only  capitalists  are  the  landlords,  and  the  laborers  are 
their  property,  as  in  slave  countries.  They  are  inapplicable  where 
the  universal  landlord  is  the  state,  as  in  India.  They  are  inap])licable 
where  the  agricultural  laborer  is  generally  the  owner  both  of  the  land 
itself  and  of  the  capital,  as  in  France,  or  of  the  capital  only,  as  in 
Ireland."  But  although  it  may  often  be  very  justly  objected  to  the 
existing  race  of  political  economists  "  that  they  attempt  to  construct  a 
permanent  fabric  out  of  transitory  materials;  that  they  take  for  granted 
the  immutability  of  arrangements  of  society,  many  of  which  are  in 
their  nature  fluctuating  or  progressive,  and  enunciate  with  as  little 
qualification  as  if  they  were  universal  and  absolute  truths,  propositions 
which  are  perhaps  applicable  to  no  state  of  society  except  the  particular 
one  in  which  the  writer  happened  to  live ;"  this  does  not  take  away 
the  value  of  the  propositions,  considered  with  reference  to  the  state  of 
society  fi-om  which  they  were  drawn.  And  even  as  applicable  to  other 
states  of  society,  "  it  must  not  be  supposed  that  the  science  is  so  incom- 
plete and  unsatisfactory  as  this  might  seem  to  prove.  Though  many  of 
its  conclusions  are  only  locally  true,  its  method  of  investigation  is  appli- 
cable universally;  and  as  he  who  has  solved  a  certain  number  of  alge- 
braic equations,  can  without  difficulty  solve  all  others  of  the  same  kind, 
so  he  who  knows  the  political  economy  of  England,  or  even  of  York- 
shire, knows  that  of  all  nations,  actual  or  possible,  provided  he  have 
good  sense  enough  not  to  expect  the  same  conclusion  to  issue  from 
varying  premisses."  Whoever  is  thoroughly  master  of  the  laws  which, 
under  free  competition,  determine  the  rent,  profits,  and  wages,  received 
by  landlords,  capitalists,  and  laborers  in  a  state  of  society  in  which 
the  three  classes  are  completely  separate,  will  have  no  difficulty  in 
determining  the  very  different  laws  which  regulate  the  distribution 
of  the   produce   among   the   classes  interested  in  it,  in   any  of  the 


PHYSICAL    METHOD.  569 

States  of  cultivation  ami  laiuk'd  propeily  set  forth  in  tlio  foiiv!^n»iiig 
exti-act.* 

§  4.  I  woukl  not  here  undertake  to  decitle  what  other  hyj>othttical 
or  abstract  sciences,  similar  to  PoHtical  l^conomy,  may  admit  of  ht:\wr 
carved  out  of  the  c;eneral  body  of  the  social  science  ;  wiiat  other  ])or- 
tions  of  the  social  phenomena  are  in  a  sufHciently  close  and  complete 
dependence,  in  the  tirst  resort,  upon  a  peculiar  class  of  causes,  to  make 
it  convenient  to  create  a  preliminary  science  of  those  causes ;  post- 
poning the  consideration  of  the  causes  which  net  through  them,  or  in 
concurrence  with  them,  to  a  later  period  of  the  iiwpiiry.  Tlu're  is 
however  among  these  separate  departments  one  whicli  cannot  be 
passed  over  in  silence,  being  of  a  more  comprehensive  and  connnand- 
ing  character  than  any  of  the  other  branches  into  which  the  social 
science  may  admit  of  being  divided.  Like  them,  it  is  directly  con- 
versant with  the  causes  of  only  one  class  of  social  facts,  but  a  class 
which  exercises,  immediately  or  remotely,  a  paramount  influence  over 
the  rest.  I  allude  to  what  may  be  termed  Political  Ethology,  or  the 
science  of  the  causes  whicli  determine  the  typi'  of  character  Ijelonging 
to  a  people  or  to  an  age.  Of  all  the  subordinate  branches  of  the  social 
science,  this  is  the  most  completely  in  its  infancy.  The  causes  of 
national  character  are  scarcely  at  all  understood,  and  the  effect  of 
institutions  or  social  airangements  upon  national  character  is  generally 
that  portion  of  their  effects  which  is  least  attended  to,  and  least  com- 
prehended. Nor  is  this  wonderful,  when  we  consider  the  infant  state 
of  the  Science  of  Ethology  itself,  from  whence  the  laws  must  be  drawn 
of  which  the  truths  of  political  ethology  are  but  results  and  exemplifi- 
cations. 

Yet,  to  whoever  well  considers  the  matter,  it  must  appear  that  the 
laws  of  national  character  are  by  far  the  most  important  class  of  socio- 
logical laws.  In  the  first  place,  the  character  which  is  formed  by  any 
state  of  social  circumstances  is  in  itself  the  most  interesting  phe- 
nomenon which  that  state  of  society  can  possibly  present.  Secondly, 
it  is  also  a  fact  which  enters  largely  into  the  production  of  all  the  other 
phenomena.  And  above  all,  the  character,  that  is,  the  opinions,  feel- 
ings, and  habits,  of  the  people,  though  greatly  the  results  of  the  state 
of  society  which  precedes  them,  are  also  greatly  the  causes  of  the 
state  of  society  which  folhnvs  them  ;  and  are  th(!  power  by  which  all 
those  of  the  circumstances  of  society  whicli  are  artificial,  laws  and 
customs  for  instance,  are  altogether  moulded  :  customs  (evidently,  laws 
no  less  really,  either  by  the  direct  influence  of  public  sentiment  upon 
th(!  ruling  powers,  or  by  the  effect  which  the  state  of  national  opinion 
and  feeling  has  in  detennining  the  form  of  government  and  sliapiiig  the 
character  of  the  governors. 

As  might  be  expected,  the  mo.st  imperfect  part  of  those  brandies  of 
sociology  which  have  been  cultivated  as  separate  sciences,  is  the 
theory  of  the  manner  in  which  their  conclusions  are  aflectr-d  by  t^tho- 
logical  considerations.  The  omission  is  no  defect  in  them  as  abstract 
or  hypothetical  sciences,  but  it  vitiates  them  in  their  practical  applica- 
tion as  branches  of  the  comprehensive  social  science.     In  political 

*  The  quotations  in  this  parufraph  are  from  a  paper  wTittcn  by  Uio  author,  an'l  puhhshcd 
in  a  periodical  in  1934. 

4C 


570  LOGIC    OF    THE    MORAL    SCIENCES. 

economy,  for  instance,  empirical  laws  of  human  nature  are  tacitly 
assumed  by  English  thinkers,  which  are  calculated  only  for  Great 
Britain  and  the  United  States.  Among  other  things,  an  intensity  of 
competition  is  constantly  supposed,  which,  as  a  general  mercantile  tact, 
exists  in  no  country  in  the  world  except  those  two.  An  English  political 
economist,  like  his  countrymen  in  general,  has  seldom  learned  that  it 
is  possible  that  men,  in  conducting  the  business  of  selling  their  goods 
over  a  counter,  should  care  more  about  their  ease  or  their  vanity  than 
about  their  pecuniary  gain.  Yet  those  who  know  the  habits  of  the 
Continent  of  Eui'ope  ai-e  aware  how  apparently  small  a  motive  often 
outweighs  the  desire  of  money-getting,  even  in  the  operations  which 
have  money-getting  for  their  direct  object.  The  more  highly  the 
science  of  ethology  is  cultivated,  and  the  better  the  diversities  of 
national  character  are  understood,  the  smaller,  probably,  will  the 
number  of  propositions  become,  which  it  will  be  considered  safe  to 
build  upon  as  universal  principles  of  human  nature. 

These  considerations  show  that  the  process  of  dividing  oflT  the  social 
science  into  compartments,  in  order  that  each  may  be  studied  sepa- 
rately, and  its  conclusions  afterwards  corrected  for  practice  by  the 
modifications  supplied  by  the  others,  must  be  subject  to  at  least  one 
important  limitation.  Those  portions  alone  of  the  social  phenomena 
can  with  advantage  be  made  the  subjects,  even  provisionally,  of  dis- 
tinct branches  of  science,  into  which  the  diversities  of  character  be- 
tween different  nations  or  different  times  enter  as  influencing  causes 
only  in  a  secondary  degree.  Those  phenomena,  on  the  contrary,  with 
which  the  influences  of  the  ethological  state  of  the  people  are  mixed 
up  at  every  step  (so  that  the  connexion  of  effects  and  causes  cannot  be 
even  rudely  marked  out  without  taking  those  influences  into  considera- 
tion) could  not  with  any  advantage,  nor  without  great  disadvantage, 
be  treated  independently  of  political  ethology,  nor,  therefore,  of  all  the 
circumstances  by  which  the  qualities  of  a  people  are  influenced.  For 
this  reason  (as  well  as  for  others  which  will  hereafter  appear)  there 
can  be  no  separate  Science  of  Government ;  that  being  the  fact  which, 
of  all  others,  is  most  mixed  up,  both  as  cause  and  effect,  with  the 
qualities  of  the  particular  people  or  of  the  particular  age.  All 
questions  respecting  the  tendencies  of  forms  of  government  must 
stand  part  of  the  general  science  of  society,  not  of  any  separate  branch 
of  it. 

This  general  Science  of  Society,  as  distinguished  from  the  separate 
departments  of  the  science  (each  of  which  asserts  its  conclusions  only 
conditionally,  subject  to  the  paramount  control  of  the  laws  of  the 
general  science),  it  now  remains  for  us  to  characterize.  And,  as  will 
be  shown  presently,  nothing  of  a  really  scientific  character  is  here 
possible,  except  by  the  inverse  deductive  method.  But  befoj-e  we 
quit  the  subject  of  those  sociological  speculations  which  proceed  by 
way  of  direct  deduction,  we  must  examine  in  what  relation  they  stand 
to  that  indispensable  element  in  all  deductive  sciences.  Verification  by 
Specific  Experience — the  comparison  between  the  conclusions  of 
reasoning  and  the  results  of  observation. 

§  5.  We  have  seen  that,  in  most  deductive  sciences,  and  among  the 
rest  in  Ethology  itself,  which  is  the  immediate  foundation  of  the  Social 
Science,  a  preliminary  work  of  preparation  is  performed  upon  the 


PHYSICAL    METHOD.  571 

obsen-ed  facts,  to  fit  them  for  being  rapidly  and  accurately  collated, 
sometimes  even  for  being  collated  at  all,  with  the  conclusions  of  theory. 
This  preparatory  treatment  consists  in  finding  general  propositions 
which  express  concisely  what  is  common  to  large  classes  of  observed 
facts  :  and  these  are  called  tho  ompiricd  laws  of  the  phenomena.  We 
have,  therefore,  to  inquire,  whether  any  similar  preparatory  process 
can  be  performed  upon  tlie  facts  of  the  social  science  j  whether  there 
are  any  empirical  laws  in  history  or  statistics. 

In  statistics,  it  is  evident  that  empirical  laws  may  sometimes  be 
traced ;  and  the  tracing  them  forms  an  impt)rtant  part  of  that  system 
of  indirect  observation  on  which  we  must  often  rely  for  tho  data  of  the 
Deductive  Science.  The  process  of  the  science  consists  in  inferring 
eftects  from  their  causes  ;  but  we  have  often  no  means  of  observing 
the  causes,  except  through  the  medium  of  their  eflects.  In  such  cases 
the  deductive  science  is  unable  to  predict  the  eflects  for  want  of  the 
necessary  data ;  it  can  tell  us  what  causes  are  capable  of  producing 
any  given  eft'ect,  but  not  with  what  frequency  and  in  what  quantities 
those  causes  exist.  An  instance  in  point  is  aff'orded  by  a  newspaper 
now  lying  before  rae.  A  statement  was  furnished  by  one  of  the  oflicial 
assignees  in  bankruptcy,  showing,  among  the  various  bankruptcies 
which  it  had  been  his  duty  to  investigate,  in  how  many  cases  the  losses 
had  been  caused  by  misconduct  of  different  kinds,  and  in  liow  many 
by  unavoidable  misfortunes.  The  result  was,  that  the  number  of  fail- 
ures caused  by  misconduct  greatly  preponderated  over  those  arising 
from  all  other  causes  whatever.  Nothing  but  specific  experience 
could  have  given  sufficient  ground  for  a  conclusion  to  this  purport. 
To  collect,  therefore,  such  empirical  laws  (which  are  never  more  than 
approximate  generalizations)  from  direct  observation,  is  an  important 
part  of  the  process  of  sociological  inquiry. 

The  experimental  process  is  not  here  to  be  regarded  as  a  distinct 
road  to  the  truth,  but  as  a  means  (happening  accidentally  to  be  the 
only,  or  the  best  available)  for  obtaining  the  data  which  the  deductive 
science  cannot  do  without.  When  the  immediate  causes  of  social  facts 
are  not  open  to  direct  observation,  the  empirical  law  of  the  effects 
gives  us  the  empirical  law  (which  in  that  case  is  all  that  we  can  obtain) 
of  the  causes  likewise.  But  those  immediate  causes  depend  upon 
remote  causes ;  and  the  empirical  law,  obtained  by  this  indirect  mode 
of  observation,  can  only  be  relied  upon  as  applicable  to  unobserved 
cases,  so  long  as  there  is  reason  to  think  that  no  change  has  taken 
place  in  any  of  the  remote  causes  on  which  tho  immediate  causes  de- 
pend. In  making  use,  therefore,  of  even  tho  best  statistical  generali- 
zations for  the  purpose  of  inferrinir  (though  it  bo  only  conjecturally) 
that  the  same  empirical  laws  will  hold  in  any  new  case,  it  is  necessary 
that  we  be  perfectly  well  acquainted  with  the  remoter  causes,  in  order 
that  we  may  scrupulously  avoid  applying  tho  empirical  law  to  cases 
which  differ  in  any  of  the  circumstances  on  which  the  truth  of  the  law 
ultimately  depends.  And  thus,  oven  where  conclusions  derived  from 
specific  observation  are  available  for  practical  infiircnces  in  new  cases, 
it  is  necessary  that  the  deductive  scicMice  should  stand  sentinel  f)ver 
the  whole  process ;  that  it  should  be  constantly  referred  to,  and  its 
sanction  obtained  to  every  inference. 

The  same  thing  holds  true  of  all  generalizations  which  can  be 
grounded  on  history.     Not  only  there  are  such  generalizations,  but  it 


572  LOGIC    OF    THE    MORAL    SCIENCES. 

will  presently  be  shown  that  the  general  science  of  society,  which 
inquires  into  the  laws  of  succession  and  coexistence  of  the  great  facts 
constituting  the  state  of  society  and  civilization  at  any  time,  can  pro- 
ceed in  no  other  manner  than  by  making  such  generalizations — after- 
wards to  be  confirmed  by  connecting  them  with  the  psychological  and 
ethological  laws  on  which  they  must  really  depend. 

§  6.  But  (reserving  this  question  for  its  proper  place),  in  those  more 
special  sociological  inquiries  which  form  the  subject  of  the  separate 
branches  of  the  social  science,  this  two-fold  logical  process  and  recip- 
rocal verification  is  not  possible ;  specific  experience  affords  nothing 
amounting  to  empirical  laws.  This  is  particularly  the  case  where  the 
object  is  to  determine  the  effect  of  any  one  sociological  cause  among 
a  great  number  acting  simultaneously ;  the  effect,  for  example,  of 
corn  laws,  or  of  a  prohibitive  commercial  system  generally.  Although 
it  may  be  perfectly  certain,  from  theory,  what  kind  of  effects  corn  laws 
must  produce,  and  in  what  general  direction  their  influence  must  tell 
upon  industrial  prosperity  ;  their  effect  is  yet  of  necessity  so  much 
disguised  by  the  similar  or  contrary  effects  of  other  influencing 
agents,  that  specific  experience  can  at  most  only  show  that  in  the 
average  of  some  great  number  of  instances,  the  cases  where  there 
were  corn  laws  exhibited  the  effect  in  a  greater  degree  than  those 
where  there  were  not.  Now  the  number  of  instances  necessary  to 
take  in  the  whole  round  of  combinations  of  the  various  influential  cir- 
cumstances, and  thus  afford  a  fair  average,  never  can  be  obtained. 
Not  only  we  can  never  learn  with  sufficient  authenticity  the  facts  of  so 
many  instances,  but  the  world  itself  does  not  afford  them  in  sufficient 
numbers,  within  the  limits  of  the  given  state  of  society  and  civilization 
which  such  inquiries  always  presuppose.  Having  thus  no  previous 
empirical  generalizations  with  which  to  collate  the  conclusions  of  the- 
ory, the  only  mode  of  direct  verification  which  remains  is  to  compare 
those  conclusions  with  the  result  of  an  individual  experiment  or  in- 
stance. But  here  the  difficulty  is  equally  gi-cat.  For  in  order  to  ver- 
ify a  theory  by  an  experiment,  the  circumstances  of  the  experiment 
must  be  exactly  the  same  with  those  contemplated  in  the  theory.  But 
in  social  phenomena  the  circumstances  of  no  two  experiments  are  ex- 
actly alike.  A  ti-ial  of  com  laws  in  another  country,  or  in  a  former 
generation,  would  go  a  very  little  way  towards  verifying  a  conclusion 
drawn  respecting  their  effect  in  this  generation  and  in  this  country.  It 
thus  happens  in  most  cases  that  the  only  individual  instance  really  fitted 
to  verify  the  predictions  of  theory  is  the  very  instance  for  which  the 
predictions  were  made ;  and  the  verification  comes  too  late  to  be  of 
any  avail  for  practical  guidance. 

Although,  however,  direct  verification  is  impossible,  there  is  an  in- 
direct verification,  which  is  scarcely  of  less  value,  and  which  is  always 
practicable.  The  conclusion  drawn  as  to  the  individual  case,  can  only 
be  directly  verified  in  that  case  ;  but  it  is  verified  indirectly,  by  the 
verification  of  other  conclusions,  drawn  in  other  individual  cases  from 
the  same  laws.  The  experience  which  comes  too  late  to  verify  the 
particular  proposition  to  which  it  refers,  is  not  too  late  to  help  towards 
verifying  the  general  sufficiency  of  the  theory.  The  test  of  the  degree 
in  which  the  science  affords  safe  ground  for  predicting  (and  conse- 
quently for  practically  dealing  with)  what  has  not  yet  happened,  ia 


PHYSICAL    METHOD.  678 

the  degree  in  which  it  would  liave  enablrd  us  to  predict  what  has  ac- 
tually occurred.  Before  our  tlieory  of  tlio  influence  of  a  particular 
cause,  in  a  given  state  of  circumstances,  can  be  trusted,  we  must  he 
able  to  explain  and  account  for  the  existing  state  of  all  that  j)orli(»n  of 
the  social  phenomena  which  that  cause  has  a  tendency  to  innuencr. 
If,  for  instance,  we  would  a]iply  our  speculations  in  political  economy 
to  the  prediction  or  guidance  of  the  phenomena  ot  any  country,  wt; 
must  be  able  to  exphiin  all  tlie  mercantih:;  or  industrial  i'acts  of  a  ijcn- 
eral  character,  appertaining  to  the  pn\><ent  state  of  tliat  country  :  to  point 
out  causes  sufHcient  to  account  for  all  of  thorn,  and  prove,  or  show  good 
ground  for  supposing,  that  these  causes  did  really  exist.  If  we  cannot 
do  this,  it  is  a  proof  either  that  the  facts  which  ouijht  to  bo  taken  into 
account  are  not  yet  completely  kiKiwn  to  us,  or  that  ahhough  we  know 
the  facts,  we  are  not  masters  of  a  suHiciently  perfect  theory  to  enable 
us  to  assign  their  consequences.  In  cither  case  we  are  not,  in  the 
present  state  of  our  knowledge,  competent  to  draw  conclusions,  citlier 
speculative  or  practical,  for  that  country.  In  like  manner,  if  we  would 
attempt  to  judge  of  the  eflect  which  any  political  institution  would 
have,  supposing  that  it  could  be  introduced  into  any  given  country  ; 
we  must  be  able  to  show  that  the  existing  state  of  the  practical  govern- 
ment of  that  country,  and  of  whatever  else  depends  thereon,  togetlier 
^vith  the  particular  chaiacter  and  tendencies  of  the  people,  and  their 
state  in  respect  to  the  various  elements  of  social  well-being,  are  such 
as  the  institutions  they  have  lived  under,  in  conjunction  witli  the  other 
circumstances  of  their  nature  or  of  their  position,  were  calculated  to 
produce. 

It  is  therefore  well  said  by  M.  Comte,  that  in  order  to  prove  that 
our  science,  and  our  knowledge  of  the  particular  case,  render  us  com- 
petent to  predict  the  future,  we  must  show  that  they  would  have  ena- 
bled us  to  predict  the  present  and  the  past.  If  there  be  anjlhing 
which  we  could  not  have  predicted,  this  constitutes  a  residual  phenom- 
enon, requiring  further  study  for  the  puq)Ose  of  explanation  ;  and  we 
must  either  search  among  the  circumstances  of  tho  particular  case 
until  we  find  one  which,  on  the  principles  of  our  existing  theory,  ac- 
counts for  the  unexplained  phenomenon,  or  we  must  turn  back,  and 
seek  the  explanation  by  an  extension  and  improvement  of  the  theory 
itself. 


574  LOGIC    OF    THE    MORAL    SCIENCES. 

CHAPTER  X. 

OF  THE  INVERSE   DEDUCTIVE,    OR   HISTORICAL  METHOD. 

§  1.  There  are  two  kinds  of  sociological  inquiry.  In  the  first  kind, 
the  question  proposed  is,  what  effect  will  follow  from  a  given  cause,  a 
certain  general  condition  of  social  circumstances  being  presupposed. 
As,  for  example,  what  would  be  the  effect  of  imposing  or  of  repealing 
corn  laws,  of  abolishing  monarchy,  or  introducing  univei'sal  sufii-age, 
in  the  present  condition  of  society  and  civilization  in  any  European 
country,  or  under  any  other  given  supposition  with  regard  to  the  cir- 
cumstances of  society  in  general :  without  reference  to  the  changes 
which  might  take  place,  or  which  may  already  be  in  progress,  in  those 
circumstances.  But  there  is  also  a  second  inquiry,  namely,  what  are 
the  laws  which  determine  those  general  circumstances  themselves.  In 
this  last  the  question  is,  not  what  will  be  the  effect  of  a  given  cause  in 
a  certain  state  of  society,  but  what  are  the  causes  which  produce,  and 
the  phenomena  which  characterize,  States  of  Society  generally.  In 
the  solution  of  this  question  consists  the  general  Science  of  Society ;  by 
which  all  the  conclusions  of  the  other  and  more  special  kind  of  inquiry 
must  be  limited  and  controlled. 

§  2.  In  order  to  conceive  correctly  the  scope  of  this  general  science, 
and  distinguish  it  from  the  subordinate  departments  of  sociological 
speculation,  it  is  necessary  to  fix  with  precision  the  ideas  attached  to 
the  phrase,  "  A  State  of  Society."  What  is  called  a  state  of  society, 
is  the  simultaneous  state  of  all  the  greater  social  facts,  or  phenomena. 
Such  are,  the  degree  of  knowledge,  and  of  intellectual  and  moral  cul- 
ture, existing  in  the  community,  and  in  every  class  of  it ;  the  state  of 
industry,  of  wealth  and  its  distribution;  the  habitual  occupations  of  the 
community;  their  division  into  classes,  and  the  relations  of  those 
classes  to  one  another  ;  the  common  beliefs  which  they  entertain  on 
all  the  subjects  most  important  to  mankind,  and  the  degree  of  assur- 
ance with  which  those  beliefs  are  held  ;  their  tastes,  and  the  character 
and  degree  of  their  esthetic  development ;  their  form  of  government, 
and  the  more  important  of  their  laws  and  customs.  The  condition  of 
all  these  things,  and  of  many  more  which  will  spontaneously  suggest 
themselves,  constitute  the  state  of  society  or  the  state  of  civilization  at 
any  given  time. 

When  states  of  society,  and  the  causes  which  produce  them,  are 
spoken  of  as  a  subject  of  science,  it  is  implied  that  there  exists  a  natu- 
ral correlation  among  these  different  elements;  that  not  every  variety 
of  combination  of  these  general  social  facts  is  possible,  but  only  cer- 
tain combinations  ;  that,  in  short,  there  exist  Uniformities  of  Coexist- 
ence between  the  states  of  the  various  social  phenomena.  And  such 
is  the  truth :  as  is  indeed  a  necessary  consequence  of  the  influence  ex- 
ercised by  every  one  of  those  phenomena  over  every  other.  It  is  a 
fact  implied  in  the  consensus  of  the  various  parts  of  the  social  body.  ^ 

States  of  society  are  like  different  constitutions  or  different  ages  in 
the  physical  frame ;  they  are  conditions  not  of  one  or  a  few  organs  or 
functions,  but  of  the  whole  organism.     Accordingly,  the  information 


HISTORICAL    METHOD,  575 

which  we  possess  respecting  past  ages,  and  respecting  the  various  states 
of  society  now  existing  in  difierent  regions  of  tlie  earth,  does,  when 
duly  analyzed,  exhib  it  suchuniforniities.  It  is  found  that  when  ono 
of  the  features  of  society  is  in  a  [)articular  state,  a  state  of  all  the  other 
features,  more  or  less  precisely  detenninate,  always  coexists  witli  it. 

But  the  uniformities  of  coexistence  obtaining  among  phenomena 
which  are  effects  of  causes,  must  (as  we  have  so  often  observed)  be  mere 
corollaries  from  the  laws  of  causation  by  which  these  plicnoniena  are 
actually  determined.  The  mutual  correlation  between  tlio  different 
elements  of  each  state  of  society,  is  therefore  a  derivative  law,  result- 
ing from  the  laws  which  regulate  the  succession  between  one  state  of 
society  and  another:  for  the  proximate  cause  of  every  state  of  society 
is  the  state  of  society  immediately  preceding  it.  The  fundamental 
problem,  therefore,  of  sociology  is  to  rtnd  the  laws  according  to  which 
any  state  of  society  produces  the  state  which  succeeds  it  and  takes  its 
place.  This  opens  the  great  and  vexed  questioti  of  the  progressive- 
ness  of  man  and  society  ;  an  idea  involved  in  every  just  concej)tion  of 
social  phenomena  as  the  subject  of  a  science. 

§  3.  It  is  one  of  the  characters,  not  absolutely  peculiar  to  the 
sciences  of  human  nature  and  society,  but  belonging  to  them  in  a  pe- 
culiar degree,  to  be  conversant  with  a  subject  matter  whose  properties 
are  changeable.  I  do  not  mean  changeable  from  day  to  day,  but  from 
age  to  age  :  so  that  not  only  the  qualities  of  individuals  vary,  but  those 
of  the  majority  are  not  the  same  in  one  age  as  in  another. 

The  principal  cause  of  this  peculiarity  is  the  extensive  and  constant 
reaction  of  the  efl'ects  upon  their  causes.  The  circumstances  in  which 
mankind  are  placed,  operating  according  to  their  own  laws  and  to  the 
laws  of  human  nature,  form  the  characters  of  the  men  ;  but  the  men, 
in  their  turn,  mould  and  shape  the  circumstances,  for  themselves  and 
for  those  who  come  after  them.  From  this  reciprocal  action  there  must 
necessarily  result  either  a  cycle  or  a  progress.  In  astronomy  also 
every  fact  is  at  once  effect  and  cause  ;  the  successive  positions  of  the 
various  heavenly  bodies  produce  changes  both  in  the  direction  and  in 
the  intensity  of  the  forces  by  which  those  positions  are  determined. 
But,  in  the  case  of  the  solar  system,  these  mutual  actions  bring  round 
again,  after  a  certain  number  of  changes,  the  former  state  of  circum- 
stances, which  of  course  leads  to  the  perpetual  recurrence  of  the  same 
series  in  an  unvarying  order.  TIkjso  bodies,  in  short,  revolve  in 
orbits  :  but  there  are  (or,  conformably  to  the  laws  of  astronomy,  there 
might  be)  others  which,  instead  of  an  orbit,  describe  a  trajectory,  or  a 
course  not  returning  into  itself  One  or  other  of  these  must  be  the 
type  to  which  human  affairs  must  also  confonn. 

One  of  the  thinkers  who  earliest  conceived  the  succession  of  histori- 
cal events  as  subject  to  fixed  laws,  and  endeavored  to  discover  these 
laws  by  an  analytical  survey  of  history,  Vice,  the  celebr.ated  authyr  of 
the  Scieiiza  Nuoia,  adopted  the  former  of  these  opinions.  He  con- 
ceived the  phenomena  of  human  society  as  revolving  in  an  orbit ;  as 
going  through  periodically  the  same  series  of  changes.  Though  there 
were  not  wanting  circumstances  tending  to  give  some  plausibility  to 
this  vi(!W,  it  would  not  bear  a  close  scrutiny  :  and  those  who  have  suc- 
ceeded Vico  in  this  kind  of  speculations  have  universally  adopted  the 
idea  of  a  trajectory  or  progress,  in  lieu  of  an  orbit  or  cycle. 


576  LOGIC    OF    THE    MORAL    SCIENCES. 

The  words  Progress  and  Progresshenesa,  are  not  here  to  be  under- 
stood as  sjTionymous  with  improvement  and  tendency  to  improvement. 
It  is  conceivable  that  the  laws  of  human  nature  might  determine,  and 
even  necessitate,  a  certain  series  of  changes  in  man  and  society,  which 
might  not  in  every  case,  or  which  might  not  on  the  whole,  be  improve- 
ments. It  is  my  belief  indeed  that  the  general  tendency  is,  and  will 
continue  to  be,  saving  occa.sional  exceptions,  one  of  improvement ;  a 
tendency  towards  a  better  and  happier  state.  But  this  is  not  a  ques- 
tion of  the  method  of  the  social  science,  but  an  ultimate  result  of  the 
science  itself.  For  our  purpose  it  is  sufficient,  that  there  is  a  progress- 
ive change  both  in  the  character  of  the  human  race,  and  in  their  out- 
ward circumstances  so  far  as  moulded  by  themselves :  that  in  each  suc- 
cessive age  the  principal  phenomena  of  society  are  different  from  what 
they  were  in  the  age  preceding,  and  still  more  different  from  any  pre- 
vious age.  The  periods  at  which  these  successive  changes  are  most 
apparent  (according  to  the  judicious  remark  of  M.  Comte)  are  inter- 
vals of  one  generation,  during  which  a  new  set  of  human  beings  have 
been  educated,  have  grown  uj)  from  childhood,  and  taken  possession 
of  society. 

The  progi-essiveness  of  the  human  race  is  the  foundation  on  which  a 
method  of  philosophizing  in  the  social  science  has  been  of  late  years 
erected,  far  superior  to  either  of  the  two  modes  which  had  previously 
been  prevalent,  the  chemical  or  experimental,  and  the  geometrical 
modes.  This  method,  which  is  now  generally  adopted  by  the  most 
advanced  thinkers  on  the  Continent,  and  especially  in  France,  consists 
in  attempting,  by  a  study  and  analysis  of  the  general  facts  of  history, 
to  discover  (what  these  philosophers  term)  the  law  of  progress  :  which 
law,  once  ascertained,  must  according  to  them  enable  us  to  predict 
future  events,  just  as  after  a  few  terms  of  an  infinite  series  in  algebra 
we  are  able  to  detect  the  principle  of  regularity  in  their  recurrence, 
and  to  predict  the  rest  of  the  series  to  any  number  of  teiTns  we  please. 
The  principal  aim  of  historical  speculation  in  France,  of  late  years, 
has  been  to  ascertain  the  law.  But  while  I  gladly  acknowledge  the 
great  sei-vices  which  have  been  rendered  to  historical  knowledge  by 
this  school,  I  cannot  but  deem  them  (with  the  single  exception  of  M. 
Comte)  to  be  chargeable  M-ith  a  fundamental  misconception  of  the 
true  method  of  social  philosophy.  The  misconception  consists  in  sup- 
posing that  the  order  of  succession  which  we  may  be  able  to  trace 
among  the  different  states  of  society  and  civilization  which  history 
presents  to  us,  even  if  that  order  were  more  rigidly  uniform  than  it 
has  yet  been  proved  to  be,  could  ever  amount  to  a  law  of  nature.  It 
can  only  be  an  empirical  law.  The  succession  of  states  of  the  human 
mind  and  of  human  society  cannot  have  an  independent  law  of  its  own; 
it  must  depend  upon  the  psychological  and  ethological  laws  which 
govern  the  action  of  circumstances  on  men  and  of  men  on  circum- 
stances. It  is  conceivable  that  those  laws  may  be  such,  and  the 
general  circumstances  of  the  human  race  such,  as  to  deteiTnine  the 
successive  transformations  of  man  and  society  to  one  given  and  un- 
varying order.  But  even  if  the  case  be  so,  it  cannot  be  the  ultimate 
aim  of  science  to  discover  an  empirical  law.  Until  that  law  can  be 
connected  with  the  psychological  and  ethological  laws  upon  which  it 
depends,  and,  by  the  consilience  of  deduction  a  priori  with  historical 
evidence,  can  be  converted  from  an  empirical  law  into  a  scientific  one, 


HISTORICAL    METHOD.  577 

it  cannot  be  relied  upon  for  tlie  prediction  of  future  events,  beyond,  at 
most,  strictly  adjacent  cases.  Now,  M.  Corate  alono  has  seen  thr 
necessity  of  thus  connectiiiiT  all  our  irciieralizations  from  history  with 
the  laws  of  human  nature ;  and  he  alone,  therefore,  lias  arrivi-d  at 
any  results  truly  scientific ;  though  in  the  speculations  of  others  there 
will  be  found  many  happy  ajjcr^us,  and  valuable  hints  fur  future 
philosophers. 

§  4.  But,  while  it  is  an  imperative  rule  never  to  introduce  any 
generalizations  from  histt)ry  into  the  social  science  unless  sullicient 
grounds  can  be  pointed  out  for  it  in  hunuin  nature,  1  do  not  tiiiiik  any 
one  will  contend  that  it  would  have  been  possible,  setting  out  from  the 
principles  of  human  nature  and  from  the  general  circumstances  of 
man's  position  in  the  universe,  to  determine  a  priori  the  order  in  which 
human  development  must  take  jilace,  and  to  predict,  coiis(«|Ucntly, 
the  general  facts  of  liistory  up  to  the  present  time.  The  initial  stages 
of  human  progress — when  man,  as  yet  unmodified  by  society,  and 
characterized  only  by  the  instincts  resulting  directly  from  his  organi- 
zation, was  acted  upon  by  outward  objects  of  a  comparatively  simple 
and  universal  character — might  indeed,  as  M.  Comle  remarks,  be 
deduced  from  the  laws  of  human  nature  ;  which  moreover  is  the  only 
possible  mode  of  ascertaining  them,  since  of  that  fonn  of  human  ex- 
istence no  direct  memorials  are  preserved.  But  (as  he  justly  observes) 
after  the  first  few  terms  of  the  series,  the  influence  exercised  over  each 
generation  by  the  generations  which  preceded  it,  becomes  more  and 
more  preponderant  overall  other  influences;  until  at  lengtli  what  we 
now  are  and  do,  is  in  a  very  small  degree  the  result  of  the  universal 
circumstances  of  the  human  race,  or  even  of  our  own  circumstances 
acting  through  the  original  qualities  of  our  species,  but  mainly  of  the 
qualities  produced  in  us  by  the  whole  previous  history  of  humanity. 
So  long  a  .series  of  actions  and  reactions  between  Circumstances  and 
Man,  each  successive  term  being  composed  of  an  ever  greater  number 
and  vai-iety  of  parts,  could  not  possibly  be  calculated  from  the  elemen- 
tary laws  which  produce  it,  by  merely  human  faculties.  The  mere 
length  of  the  series  would  be  a  suflficient  obstacle,  since  a  slight  error 
in  any  one  of  the  terms  would  augment  in  ra})id  progression  at  every 
subsequent  step. 

If,  therefore,  the  series  of  the  efft'Cts  themselves  did  not,  when  ex- 
amined as  a  whole,  manifest  any  retjularity,  we  should  in  vain  attempt 
to  construct  a  general  science  of  society.  We  must  in  tliat  ca.sc  have 
contented  ourselves  with  that  subordinate  order  of  sociological  specu- 
lation formerly  noticed,  namely,  with  endeavoring  to  ascertain  what 
would  be  the  effect  of  the  introduction  of  any  new  cause,  in  a  state  of 
society  supposed  to  be  fixed ;  a  knowledge  sufficient  for  most  of  the 
ordinary  exigencies  of  daily  political  practice,  but  liable  to  fail  in  all 
cases  in  whicli  the  progressive  movement  of  society  is  one  of  the  in- 
fluencing elements ;  and  therefore  more  precarious  in  proportion  as 
the  case  is  more  important.  But  since  b(»th  the  natural  varieties  of 
mankind,  and  the  original  diversities  of  local  circumstances,  are  much 
less  considerable  than  the  points  of  agreement,  there  will  naturally  be 
a  certain  degiee  of  uniformity  in  the  progiessive  development  of  man 
and  of  his  works.  And  this  uniformity  (as  M.  Comte  remarks  with 
much  justice)  tends  to  become  greater,  not  less,  as  society  advances  j 
4D 


578  LOGIC    OF    THE    MORAL    SCIENCES. 

since  the  evolution  of  each  people,  which  is  at  first  determined  exclu- 
sively by  the  nature  and  circumstances  of  that  people,  is  gradually 
brought  under  the  influence  (which  becomes  stronger  as  civilization 
advances)  of  the  other  nations  of  the  earth,  and  of  the  circumstances 
by  which  they  have  been  influenced.  History  accordingly  does,  when 
judiciously  examined,  afford  Empirical  Laws  of  Society.  And  the 
problem  of  general  sociology  is  to  ascertain  these,  and  connect  them 
with  the  laws  of  human  nature  by  deductions  showing  that  such  were 
the  derivative  laws  naturally  to  be  expected  as  the  consequences  of 
those  ultimate  ones. 

It  is  indeed,  in  most  cases,  hardly  possible,  even  after  history  has 
suggested  the  derivative  law,  to  demonstrate  a  priori  that  such  was  . 
the  only  order  of  succession  or  of  coexistence  in  which  the  effects 
could,  consistently  with  the  laws  of  human  nature,  have  been  pro- 
duced. We  can  at  most  make  out  that  there  were  strong  a  priori 
reasons  for  expecting  it,  and  that  no  other  order  of  succession  or  co- 
existence would  have  been  by  any  means  so  likely  to  result  from  the 
nature  of  man  and  his  position  upon  earth.  This,  .however — which, 
in  the  Inverse  Deductive  Method  that  we  are  now  characterizing,  is  a 
real  process  of  verification — is  as  indispensable  (to  be  more  so  is  im- 
possible) as  verification  by  specific  experience  has  been  shown  to  be 
where  the  conclusion  is  originally  obtained  by  the  direct  way  of  deduc- 
tion. The  empirical  laws  must  be  the  result  of  but  a  few  instances, 
since  few  nations  have  ever  attained  at  all,  and  still  fewer  by  their  own 
independent  development,  a  high  stage  of  social  progress.  If,  there- 
fore, even  one  or  two  of  these  few  instances  be  insufficiently  kno\vn,  or 
imperfectly  analyzed  into  its  elements,  and  therefore  not  adequately 
compared  with  other  instances,  nothing  is  more  probable  than  that  a 
wrong  empirical  law  will  result  instead  of  the  right  one.  Accordingly,* 
the  most  erroneous  generalizations  are  continually  made  from  the 
course  of  history  :  not  only  in  this  country,  where  history  cannot  yet 
be  said  to  be  at  all  cultivated  as  a  science,  but  in  other  countries, 
where  it  is  so  cultivated,  and  by  persons  well  versed  in  it.  The  only 
check  or  coiTective  is,  constant  verification  by  psychological  and  etho- 
logical  laws.  We  may  add  to  this,  that  no  one  but  a  person  compe- 
tently skilled  in  those  laws  is  capable  of  preparing  the  materials  for 
historical  generalization  by  analyzing  the  facts  of  history,  or  even  by 
observing  the  social  phenomena  of  his  own  time.  No  other  will  be 
aware  of  the  comparative  importance  of  different  facts,  nor  conse- 
quently know  what  facts  he  is  to  look  out  for,  or  what  to  obser\'e ;  still 
less  will  he  be  capable  of  estimating  the  evidence  of  those  facts  which, 
as  is  the  case  with  most,  cannot  be  observed  directly,  but  must  be  in- 
ferred from  marks. 

§  5.  The  Empirical  Laws  of  Society  are  of  two  kinds ;  some  are 
uniformities  of  coexistence,  some  of  succession.  According  as  the 
science  is  occupied  in  asceitaining  and  verifying  the  former  sort  of 
uniformities,  or  the  latter,  M.  Comte  gives  it  the  title  of  Social  Statics, 
or  of  Social  Dynamics ;  conformably  to  the  distinction  in  mechanics 
between  the  conditions  of  equilibrium  and  those  of  movement ;  or  in 
biology,  between  the  laws  of  organization  and  those  of  life.  The  first 
branch  of  the  science  ascertains  the  conditions  of  stability  in  the  social 
union;  the  second,  the  laws  of  progress.     Social  Dynamics  is  the  the- 


lUSTORICAI.    MKTIIOD.  579 

ory  of  Society  consiil(MVtl  in  a  stato  of  jin>t!;rossivo  movcinnit  ;  whilp 
Social  Statics  is  the  tlu-ory  ef  the  niHtfnsus  ahi-aily  spokni  of  as  rxibl- 
ing  ainoiisT  tlie  ililVereiit  parts  of  the  social  oi-jxaiiism  ;  in  other  wordrt, 
the  tlieory  of  the  mutual  actions  ami  reactions  of  conteniporuiicous  so- 
cial phenomena;  "  makinjT  provisionally,  as  far  as  ]»ossil»lo,  ahstrac- 
tion,  for  scientific  purpose.**,  of  the  fundamental  movennMit  which  is  at 
all  times  (riadually  modifyinc;  the  whole  of  tln-m. 

•'  In  this  lirst  }>()int  of  view,"  <-ontiiiues  M.  ('omte,*  *' tho  previsions 
of  sociology  will  enahle  us  to  infer  on^^  from  another  (subject  to  ulte- 
rior verification  by  direct  observation)  tht>  various  charactrristic  marks 
of  each  distinct  mode  of  social  existence;  in  a  manner  ess«'ntially  anal- 
ogous to  what  is  now  habitually  practised  in  the  anatomy  of  the  physi- 
cal body.  This  preliminary  aspect,  therefore,  of  political  science,  of 
necessity  supp.oses  thai  (contrary  to  theexistini^  habits  of  philosoph»'r») 
each  of  the  numerous  elements  ot'tlie  social  state,  ce:usim(  to  be  looked 
at  independently  and  absolutely,  shall  be  always  and  exclusivi-ly  ci»n- 
sidered  relatively  to  all  the  other  elements,  with  the  whole  of  which  it 
is  united  by  mutual  interdependence.  It  would  bo  superllnous  to 
insist  here  upon  the  great  and  constant  utility  of  this  branch  of  socio- 
logical speculation  ;  it  is,  in  the  first  place,  the  indispensable*  biiais  of 
the  theory  of  social  progress,  every  rational  conception  of  whit:h  pru- 
supposes  the  continued  preservation  of  the  correspon<ling  social  or- 
ganism. It  may,  moreover,  bo  employed,  immediately  ami  of  itself, 
to  supply  the  })lace,  provisionally  at  least,  of  direct  ob.servaiion,  which 
in  many  cases  is  not  always  practicable  for  some  of  the  elements  of 
society,  the  real  condition  (»f  which  may  however  be  sufiiciently  judged 
of  by  means  of  the  relations  which  connect  them  with  others  previously 
known.  The  history  of  the  sciences  may  give  us  some  notion  of  tho 
habitual  importance  of  this  auxiliary  resource,  by  reminding  us,  fi>r 
example,  how  the  vulgar  errors  of  mere  eru<lition  concerning  the  pro- 
tended acquirements  of  the  ancient  Egyptians  in  the  higher  astntnomy, 
were  irrev-ocably  dissipated  (even  before  sentence  ha<l  be«'n  passed 
upon  th(!m  by  a  sounder  erudition)  from  the  single  consideration  of  tho 
inevitable  coimexion  between  the  geiu-ral  state  <if  astronomy  and  that 
of  ab.stract  geometry,  then  evidently  in  its  infancy.  It  would  be  ea.sy 
to  cite  a  multitude  of  analogous  cases,  tho  character  of  which  could 
admit  of  no  dispute.  In  order  to  avoid  exaggeration,  however,  it 
should  be  remarked,  that  these  necessary  relations  among  the  different 
aspects  of  society  camiot,  from  tlu-ir  very  nature,  be-  so  siinph-  and 
precise  that  the  results  observed  c(»uld  oidy  have  arisen  from  somo 
one  mode  of  mutual  coordination.  Such  a  notion,  already  too  narrow 
in  the  science  of  life,  woidd  be  comjiletely  at  variance  with  the  still 
moro  comph'X  nature  of  sociological  spi;culations.  Hut  tho  «!xact 
estimation  of  these  limits  of  variation,  bi.lh  in  the  healthy  an<i  in  the 
morbid  state,  constitut(!S,  at  least  as  much  as  in  the  anatomy  ol  tho 
natural  b(jdy,  an  indispensable  complement  to  evj-ry  theory  of  Socio- 
logical Statics;  without  which  the  indirect  exploration  above  spoken 
of  would  often  lead  into  error. 

"  This  is  not  the  place  for  raethcxlically  dem<m8trating  tho  existence 
of  a  nece-ssaiy  relation  between  all  thci  i)ossiblo  aspticU  of  tho  same 
social  organism  ;  a  point  on  which,  mc»reover,  in  principle   at  least, 

•  C(mr$  dc  Phitotophtt  Puntivt,  iv.,  Vlty-O. 


580  LOGIC    OF    THE    MORAL    SCIENCES. 

there  is  now  little  difference  of  opinion  among  sound  thinkers.  From 
whichever  of  the  social  elements  we  choose  to  set  out,  we  may  easily 
recognize  that  it  has  always  a  connexion,  more  or  less  immediate,  with 
all  the  other  elements,  even  with  those  which  at  first  sight  appear  the 
most  independent  of  it.  The  dynamical  consideration  of  the  progress- 
ive development  of  civilized  liumanity,  affords,  no  doubt,  a  still  more 
efficacious  means  of  effecting  this  interesting  verification  of  the  consen- 
sus of  the  social  phenomena,  by  displaying  the  manner  in  which  every 
chan,"-e  in  any  one  part,  operates  immediately,  or  very  speedily,  upon 
all  the  rest.  But  this  indication  may  be  preceded,  or  at  all  events 
followed,  by  a  confirmation  of  a  purely  statical  kind;  for,  in  politics 
as  in  mechanics,  the  communication  of  motion  fi-om  one  object  to 
another  proves  a  connexion  between  them.  Without  descending  to 
the  minute  interdependence  of  the  different  branches  of  any  one 
Bcience  or  art,  is  it  not  evident  that  among  the  different  sciences,  as 
well  as  among  most  of  the  arts,  there  exists  such  a  connexion,  that  if 
the  state  of  any  one  well-marked  division  of  them  is  sufficiently  knowix 
to  us,  we  can  with  real  scientific  assurance  infer,  from  their  necessary 
cori'elation,  the  contemporaneous  state  of  every  one  of  the  others  ]  By 
a  further  extension  of  this  consideration,  we  may  conceive  the  neces- 
sary relation  which  exists  between  the  condition  of  the  sciences  in 
general  and  that  of  the  arts  in  general,  except  that  the  mutual  depen- 
dence is  less  intense  in  proportion  as  it  is  more  indirect.  The  same  is 
the  case  when,  instead  of  considering  the  aggregate  of  the  social  phe- 
nomena in  some  one  people,  we  examine  it  simultaneously  in  different 
contemporaneous  nations  ;  between  which  the  perpetual  reciprocity  of 
influence,  especially  in  modern  times,  cannot  be  contested,  although 
the  consensus  must  in  this  case  be  ordinarily  of  a  less  decided  charac- 
ter, and  must  decrease  gradually  with  the  affinity  of  the  cases  and  the 
multiplicity  of  the  points  of  contact,  so  as  at  last,  in  some  cases,  to 
disappear  almost  entirely ;  as  for  example  between  Western  Europe 
and  Eastern  Asia,  of  which  the  various  general  states  of  society  appear 
to  have  been  hitherto  almost  independent  of  one  another," 

M.  Comte  proceeds  to  illustrate,  with  his  usual  sagacity  and  discrimi- 
nation, one  of  the  most  important,  and  until  lately,  most  neglected,  of 
the  great  principles  which,  in  this  division  of  the  social  science,  may 
be  considered  as  established;  namely,  the  necessary  coiTelation  be- 
tween the  foiTn  of  government  existing  in  any  society,  and  the  contem- 
poraneous state  of  civilization  :  a  natural  law,  which  stamps  the  endless 
discussions  and  innumerable  theories  respecting  fonns  of  government  in 
the  abstract,  as  fruitless  and  worthless,  save  only  (in  some  few  of  the 
more  remarkable  cases)  as  a  preparatory  treatment  of  some  small 
portion  of  what  may  be  afterwards  used  as  material  for  a  better 
philosophy. 

As  already  remarked,  one  of  the  main  results  of  the  science  of  social 
statics  would  be  to  ascertain  the  requisites  of  stable  political  imion. 
There  are  some  circumstances  which,  being  found  in  all  societies  with- 
out exception,  and  in  the  greatest  degree  where  the  social  union  is 
roost  complete,  may  be  considered  (when  psychological  and  ethological 
laws  confirm  the  indication)  as  conditions  of  the  existence  of  society. 
For  example,  no  society  has  ever  been  held  together  without  laws,  or 
usages  equivalent  to  them ;  without  tribunals,  and  an  organized  force 
of  some  sort  to  execute  their  decisions.     There  have  always  been  a 


UISTOUICAL    METHOD.  581 

cliiof,  or  chiefs,  whom,  with  more  or  h\ss  strictness  and  in  cases  nioro 
or  less  accurately  delined,  the  rest  »)1'  tin;  cumnninity  (theyed,  or  ac- 
cording to  general  opinion  were  bound  to  obey.  Jiy  following  out  this 
course  of  inquiry,  we  should  iiyd  u  nuinlu-r  of  rei|ui8ites,  which  have 
been  present  in  every  society  that  has  held  together;  and  on  the  ces- 
sation of  which  it  has  ceased  to  be  a  society,  or  has  reconstructed  itself 
as  such  upon  some  new  basis,  iu  which  the  ronditions  were  conformed 
to.  Although  these  results,  obtained  by  comparing  diHerent  forms  and 
states  of  society,  amount  in  themselves  only  to  empirical  laws;  some  of 
them,  when  once  suggesttnl,  are  found  to  follow  with  so  mucli  proba- 
bility from  general  laws  of  human  naturi>,  that  llu-  ccjiisilienct;  of  tho 
two  processes  raises  the  evidence  to  comjilete  proof,  and  the  generali- 
zations to  the  rank  of  scientific  truths. 

This  seems  to  be  afiirmable  (for  instance)  of  the  conclusions  arrived 
at  in  the  following  passage;  forming  part  of  a  criticism  on  the  neijativo 
philosophy  of  the  eighteenth  century,  and  which  1  quote,  although  (as 
in  some  former  instances)  from  myself,  because  I  have  no  better  way 
of  illustrating  the  conception  1  have  formed  of  the  kind  of  theorems  of 
which  sociological  statics  W(juld  consist. 

"The  very  first  element  of  the  social  union,  obedience  to  a  govern- 
ment of  some  sort,  has  not  been  found  so  easy  a  thing  to  estai)lish  in 
the  world.  Among  a  timid  and  spiritless  race,  like  the  inhabitants  of 
the  vast  plains  of  tropical  countries,  ])assive  obedience  may  be  of 
natural  growth  ;  though  t;ven  there  we  doubt  whether  it  lias  ever  been 
found  among  any  people  with  whom  fatalism,  or  in  other  words,  sub- 
mission to  the  pressure  of  circumstances  as  the  decree  of  (Jod,  did  not 
prevail  as  a  religious  doctrine.  Jiut  the  difiiculty  of  inducing  a  bravo 
and  warlike  race  to  submit  their  individual  arbitriiaii  to  any  common 
umpire,  has  always  been  felt  to  be  so  great,  that  nothing  short  of 
supernatural  power  has  been  deemed  adequate  to  overcome  it;  and 
such  tribes  have  always  assiijned  to  the  first  uistitution  of  civil  society 
a  divine  origin.  So  ditt'erently  did  those  judge  who  knew  savage  man 
by  actual  experience,  from  those  who  had  no  acciuaintanc*'  with  him 
except  in  the  civilized  state.  In  nnxh-rn  Kuro])e  itself,  after  tin;  fall  of 
the  Roman  empire,  to  subdue  the  feudal  anarchy  and  bring  the  whole 
people  of  any  European  nation  into  subjection  tt»  govennnent  (although 
Christianity  in  its  most  concentrated  form  wjis  cooperating  with  all  its 
influences  in  the  work)  required  thrice  as  many  centuries  as  have 
elapsed  since  that  time. 

"  Now  if  these  philosophers  had  kuftwn  human  nature  under  any 
other  type  than  that  of  their  own  age,  ami  of  the  particular  classes  of 
society  among  whom  they  moved,  it  would  have  occurred  to  tlu-m, 
that  wherever  this  habitual  submission  to  law  and  government  has  been 
firmly  and  durably  established,  and  yet  the  vigor  and  manliness  of  char- 
acter which  resisted  its  establishment  have  been  in  any  decrreo  iire- 
served,  certain  requisites  have  existed,  certain  conditions  have  been 
fulfilled,  of  which  the  following  may  be  regarde<l  as  the  nrincipal. 

"First:  there  has  existed,  for  all  who  were  accounted  citizens — for 
all  who  were  not  slaves,  kv\^X  down  by  brute  force — a  system  of  vdu- 
cation,  bomnning  with  infancy  and  contimu'd  through  life,  of  which, 
whatever  else  it  might  include,  one  main  and  incessant  ingredient  wa« 
restraining  discipline.  To  train  the  Iniman  being  in  the  habit,  and 
thence  the  power,  of  subordinating  his  personal  impulses  and  aims  to 


582  LOGIC    OF    THE    MORAL    SCIENCES. 

what  were  considered  the  ends  of  society;  of  adhering,  against  all 
temptation,  to  the  course  of  conduct  which  those  ends  prescribed;  of 
controlHng  in  himself  all  those  feelings  which  were  liable  to  militate 
against  those  ends,  and  encouraging  all  such  as  tended  towards  them;  , 
this  was  the  purpose,  to  which  every  outward  motive  that  the  authority 
directing  the  system  could  command,  and  every  inward  power  or  prin- 
ciple which  its  knowledge  of  human  nature  enabled  it  to  evoke,  were 
endeavored  to  be  rendered  instrumental.  This  system  of  discipline 
wrought,  in  the  Grecian  states,  by  the  conjunct  influences  of  religion, 
poetry,  and  law;  among  the  Romans,  by  those  of  religion  and  law;  in 
modern  and  Christian  countries,  mainly  by  religion,  with  little  of  the 
direct  agency,  but  generally  more  or  less  of  the  indirect  support  and 
countenance,  of  law.  And  whenever  and  in  proportion  as  the  strict- 
ness of  this  discipline  was  relaxed,  the  natural  tendency  of  mankind  to 
anarchy  reasserted  itself;  the  state  became  disorganized  from  within ; 
mutual  conflict  for  selfish  ends,  neutralized  the  energies  which  were 
required  to  keep  up  the  contest  against  natural  causes  of  evil ;  and  the 
nation,  after  a  longer  or  briefer  inter\-al  of  progressive  decline,  became 
either  the  slave  of  a  despotism,  or  the  prey  of  a  foreign  invader, 

"  The  second  condition  of  permanent  political  society  has  been 
found  to  be,  the  existence,  in  some  form  or  other,  of  the  feeling  of 
allegiance  or  loyalty.  This  feeling  may  vary  in  its  objects,  and  is  not 
confined  to  any  particular  form  of  government ;  but  whether  in  a 
democracy  or  in  a  monarchy,  its  essence  is  always  the  same ;  viz., 
that  there  be  in  the  constitution  of  the  state  something  which  is  settled, 
something  permanent,  and  not  to  be  called  in  question  ;  something 
which,  by  general  agreement,  has  a  right  to  be  where  it  is,  and  to  be 
secure  against  disturbance,  whatever  else  may  change.  This  feeling 
may  attach  itself,  as  among  the  Jews  (and  indeed  in  most  of  the  com- 
monwealths of  antiquity),  to  a  common  God  or  gods  ;  the  protectors 
and  guardians  of  their  state.  Or  it  may  attach  itself  to  certain  persons, 
who  are  deemed  to  be,  whether  by  divine  appointment,  by  long  pre- 
scription, or  by  the  general  recognition  of  their  superior  capacity  and 
worthiness,  the  rightful  guides  and  guardians  of  the  rest.  Or  it  may 
attach  itself  to  laws ;  to  ancient  liberties,  or  ordinances  ;  to  the  whole 
or  some  part  of  the  political,  or  even  the  domestic,  institutions  of  the 
state.  But  in  all  political  societies  which  have  had  a  durable  existence, 
there  has  been  some  fixed  point;  something  which  men  agreed  in 
holding  sacred  ;  which  it  might  or  might  not  be  lawful  to  contest  in 
theory,  but  which  no  one  could  either  fear  or  hope  to  see  shaken  in 
practice ;  which,  in  short  (except  perhaps  during  some  temporaiy 
crisis),  was  in  the  common  estimation  placed  above  discussion.  And 
the  necessity  of  this  may  easily  be  made  evident.  A  state  never  is, 
nor  until  mankind  are  vastly  improved,  can  hope  to  be,  for  any  long 
time  exempt  from  internal  dissension  ;  for  there  neither  is  nor  has  ever 
been  any  state  of  society  in  which  collisions  did  not  occur  between  tho 
immediate  interests  and  passions  of  powei-ful  sections  of  the  people. 
"What,  then,  enables  society  to  weather  these  storms,  and  pass  througlj 
turbulent  times  without  any  permanent  weakening  of  the  ties  which 
hold  it  together  %  Precisely  this — that  however  important  tho  interests 
about  which  men  fall  out,  the  conflict  does  not  affect  tho  fundamental 
principles  of  the  system  of  social  union  which  happens  to  exist ;  nor 
threaten  large  portions  of  the  community  with  the  subversion  of  that 


HISTORICAL    MKTIIOD.  583 

on  which  they  have  built  their  calculations,  and  with  which  their  hopes 
and  aims  have  become  identified.  But  when  the  questioning  of  ihcHe 
fundamental  pnncij)le.s  is  (not  an  occasional  disease;,  but)  the  habitual 
condition  of  the  body  politic  ;  and  when  all  the  violent  animositi«ra  aro 
called  forth,  which  spring  naturally  from  such  a  situation,  the  state  is 
virtually  in  a  position  of  civil  war  ;  and  can  never  long  remain  free 
from  it  in  act  and  fad. 

"  The  third  essential  condition,  which  has  existed  in  all  durable  politi- 
cal societies,  is  a  strong  and  active  principle  of  nationality.  We  need 
scarcely  say  that  we  do  not  mean  a  sen.seless  antipathy  to  foreigners; 
or  a  cherishing  of  absurd  j)eculiarities  because  they  are  national ;  or  a 
refusal  to  adopt  what  has  been  found  good  by  other  countries.  In  all 
these  senses,  the  nations  which  have  had  the  strongest  national  spirit 
have  had  the  least  nationality.  We  mean  a  principle  of  sympathy,  not 
of  hostility;  of  union,  not  of  separation.  We  mean  a  feeling  of  com- 
mon interest  among  those  who  live  under  the  same  government,  and 
are  contained  within  the  same  natural  or  historical  boundaries.  We 
mean,  that  one  pait  of  the  community  shall  not  consider  themselves  as 
foreigners  with  regard  to  another  part;  that  they  shall  cherish  the  tie 
which  holds  them  together ;  shall  feel  that  tlu-y  are  one  people,  that 
their  lot  is  cast  together,  that  evil  to  any  of  their  fellow-countrymen  is 
evil  to  themselves,  and  that  they  cannot  selfishly  free  themselves  from 
their  share  of  any  common  inconvenience  by  severing  the  connexion. 
How  strong  this  feeling  was  in  the  ancient  commonwealths  every  one 
knows.  How  happily  Rome,  in  spite  of  all  her  tyranny,  succeeded 
in  establishing  the  feeling  of  a  common  counti-y  among  the  provinces 
of  her  vast  and  divided  empire,  will  appear  when  any  one  who  has 
given  due  attention  to  the  subject  shall  take  the  trouble  to  j)oint  it  out. 
In  modem  times  the  countries  which  have  had  that  feeling  in  the 
strongest  degree  have  been  the  most  powerful  countries  ;  England, 
France,  and,  in  proportion  to  their  territory  and  resources,  Holland 
and  Switzerland;  while  England,  in  her  connexion  with  Ireland,  is  one 
of  the  most  signal  examples  of  the  consequences  of  its  absence.  Every 
Italian  knows  why  Italy  is  under  a  foreign  yoke ;  every  German  knows 
what  maintains  despotism  in  the  Austrian  empire;  the  evils  of  Spain 
flow  as  much  from  the  absence  of  nationality  among  the  Spaniards 
themselves,  as  from  the  presence  of  it  in  their  relations  with  foreigners; 
while  the  completest  illustration  of  all  is  afforded  by  the  rejiublics  of 
South  America,  where  the  j)arts  of  one  and  the  same  state  adhere  so 
slightly  together,  that  no  sooner  does  any  province  think  itself  ag- 
grieved by  the  general  government  than  it  j)roclaims  itself  a  separate 
nation." 

§  6.  While  the  derivative  laws  of  social  statics  are  ascertained  by 
analyzing  different  states  of  society,  and  comparing  them  with  one 
another,  without  regard  to  the  order  of  their  succession  ;  the  considera- 
tion of  the  successive  order  is,  on  the  contrary,  pnjdominant  in  the 
study  of  social  dynamics,  of  which  the  aim  is  to  observe  and  explain 
the  sequences  of  social  conditions.  This  branch  of  the  rt(x;ial  science 
would  be  as  complete  as  it  can  be  made,  if  every  one  of  the  leading 
general  circumstances  of  each  generation  were  traced  to  its  causes  in 
the  generation  immediately  preceding.  ]iut  the  conscnsux  is  8<»  (Com- 
plete (especially  in  modern  hislftry),  thai  in  the  filiation  of  one  genor- 


584  LOGIC    OF    THE    MORAL    SCIENCES. 

ation  and  another,  it  is  the  whole  which  produces  the  whole,  rather 
than  any  part  a  part.  Little  progiess  therefore  can  be  made  in  estab- 
lishing the  filiation,  directly  from  laws  of  human  nature,  without  having 
first  ascertained  the  immediate  or  derivative  laws  according  to  which 
social  states  generate  one  another  as  society  advances ;  the  axiomata 
media  of  General  Sociology. 

The  empirical  laws  which  are  most  readily  obtained  by  generaliza- 
tion from  history  do  not  amount  to  this ;  they  are  not  the  "  middle 
principles"  themselves,  but  only  evidence  towards  the  establishment 
of  such  principles.  They  consist  of  certain  general  tendencies  which 
may  be  perceived  in  society ;  a  progressive  increase  of  some  social 
elements  and  diminution  of  others,  or  a  gradual  change  in  the  general 
character  of  certain  elements.  It  is  easily  seen,  for  instance,  that,  as 
society  advances,  mental  tend  more  and  more  to  prevail  over  bodily 
qualities,  and  masses  over  individuals  :  that  the  occupation  of  all  that 
portion  of  mankind  who  are  not  under  external  restraint  is  at  first 
chiefly  military,  but  society  becomes  progressively  more  and  more  en- 
grossed with  productive  pursuits,  and  the  military  spirit  gi'adually  gives 
way  to  the  industrial :  to  which  many  other  similar  truths  might  easily 
be  added.  And  wvth  generalizations  of  this  description,  ordinary  in- 
quirers, even  of  the  historical  school  now  predominant  on  the  Conti- 
nent, are  satisfied.  But  these  and  all  such  results  are  still  at  too  great 
a  distance  from  the  elementary  laws  of  human  nature  on  which  they 
depend, — too  many  links  intervene,  and  the  concurrence  of  causes  at 
each  link  is  far  too  complicated, — to  enable  these  propositions  to  be 
presented  as  direct  corollaries  from  those  elementary  principles.  They 
have,  therefore,  in  the  minds  of  most  inquirers,  remained  in  the  state 
of  empirical  laws,  applicable  only  within  the  bounds  of  actual  obser- 
vation ;  without  any  means  of  determining  their  real  limits,  and  of 
judging  whether  the  changes  which  have  hitherto  been  in  progi'ess 
are  destined  to  continue  indefinitely,  or  to  terminate,  or  even  to  be 
reversed. 

§  7.  In  order  to  obtain  better  empirical  laws,  we  must  not  rest  sat- 
isfied with  noting  the  progressive  changes  which  manifest  themselves 
in  the  separate  elements  of  society,  and  in  which  nothing  is  indicated 
but  the  relation  of  the  fragments  of  the  effect  to  corresponding  frag- 
ments of  the  cause.  It  is  necessary  to  combine  the  statical  view  of 
social  phenomena  with  the  dynamical,  considering  not  only  the  pro- 
gressive changes  of  the  different  elements,  but  the  contemporaneous 
condition  of  each  ;  and  thus  obtain  empirically  the  law  of  correspond- 
ence not  only  between  the  simultaneous  states,  but  between  the  simul- 
taneous changes,  of  those  elements.  This  law  of  correspondence  it  is, 
which,  after  being  duly  verified  a  priori,  will  become  the  real  scien- 
tific derivative  law  of  the  development  of  humanity  and  human  affairs. 

In  the  difficult  process  of  obsei-sation  and  comparison  which  is  here 
required,  it  would  evidently  be  a  very  great  assistance  if  it  should 
happen  to  be  the  fact,  that  some  one  element  in  the  complex  existence 
of  social  man  is  preeminent  over  all  others  as  the  prime  agent  of  the 
social  movement.  For  we  could  then  take  the  progress  of  that  one 
element  as  the  central  chain,  to  each  successive  link  of  which,  the  cor- 
responding links  of  all  the  other  progressions  being  appended,  the  suc- 
cession of  the  facts  would  by  this  alon^be  presented  in  a  kind  of  spon- 


HISTORICAI,    METHOD.  585 

tanenus  cnder,  far  more  iioarly  approacliint;  to  tlie  n-al  onl<«r  of  tlioir 
filiation  than  couM  ho  <)l)taint'il  liy  any  oilier  merely  empirical  |irocc88. 

Now,  tlie  ovidenre  of  liisl«)ry  uiul  the  eviileiice  of  human  nature 
combine,  by  a  most  striking  instance  of  consilience,  to  nbow  that  there 
is  really  one  social  element  which  is  tlnis  predominant,  and  almost 
paramount,  amonp;  the  agents  of  the  social  progression.  This  is,  tlio 
state  of  the  speculative  faculties  of  mankind  ;  incbxling  the  natiu'e  of 
the  sjieculative  beliefs  which  by  any  means  tlu-y  havt-  arrived  at,  con- 
cerning themselves  and  the  world  by  which  they  are  surr«)unded. 

It  would  be  a  great  error,  and  one  very  little  likely  to  b<'  committed, 
to  assert  that  speculation,  intellectual  activity,  the  pursuit  of  truth,  ia 
among  the  more  powerful  propensities  of  human  nature,  or  fills  a  large 
place  in  the  lives  of  any,  save  decidedly  exceptional  individuals.  But 
notwithstanding  the  relative  weakness  of  this  jirinciple  among  other 
sociological  agents,  its  inlluence  is  the  main  determining  cause  of  the 
social  progress ;  all  the  otlier  dispositions  of  our  nature  which  con- 
tribute to  that  progress,  being  dependent  upon  it  for  the  means  of 
accomplishing  their  share  of  the  work.  Thus  (to  take  the  most  obvious 
case  first),  the  impelling  force  to  most  of  the  improvejnents  effected  in 
the  arts  of  life,  is  the  desire  of  increased  material  condbrt ;  but  as  we 
can  only  act  upon  external  objects  in  proportion  to  our  knowledge  of 
them,  the  state  of  knowledge  at  any  time  is  the  impassable  limit  of 
the  industrial  improvements  possible  at  that  time ;  and  the  progress  of 
industry  must  follow,  and  depend  upon,  the  progress  of  knowledge. 
The  same  thing  may  be  shown  to  be  true,  though  it  is  not  cpiite  so 
obvious,  of  the  progress  of  the  fine  arts.  Further,  as  the  strongest 
propensities  of  human  nature  (being  tlie  purely  selfish  ones,  and  those 
of  a  sympathetic  character  which  partake  most  of  the  nature  of  selfish- 
ness) evidently  tend  in  themselves  to  disunite  mankind,  not  to  unite 
them  —  to  make  them  rivals,  not  confederates;  social  existence  is  only 
possible  by  a  disciplining  of  those  more  powerful  propi'Tisities,  which 
consists  in  subordinating  them  to  a  cominon  system  of  oj)inions.  The 
degree  of  this  subordination  is  the  measure  of  the  completeni-ss  of  the 
social  union,  and  the  nature  of  the  common  opinions  d(>termines  its 
kind.  But  in  order  that  mankind  should  conform  their  actions  to  any 
set  of  opinions,  these  opinions  must  exist,  must  be  believed  by  them. 
And  thus,  the  state  of  the  speculative  faculties,  the  character  of  the 
propositions  assented  to  by  the  intellect,  essentially  determines  the 
moral  and  political  state  of  the  community,  as  we  have  already  seen 
tliat  it  determines  the  physical. 

These  conclusions,  deduced  from  the  laws  of  human  nature,  are  in 
entire  accordance  with  the  gtmend  facts  of  history.  Every  considera- 
ble change  histoiically  knowTi  to  us  in  the  condition  of  any  portion  of 
mankind,  ha.s  been  pn;ceded  by  a  (change,  of  proportional  extent,  in 
the  state  of  their  knowledge,  or  in  their  prevalent  beliefs.  As  between 
any  given  state  of  speculation,  and  the  conelative  state  of  everything 
else,  it  was  almost  always  tin;  former  which  first  showed  itself;  th<»ugh 
the  effects,  no  doubt,  reacted  potently  upon  the  cause.  Every  con- 
siderable advance  in  material  civilization  has  been  preceded  by  an 
advance  in  knowledge;  and  when  any  great  social  change  has  come 
to  pass,  a  great  change  in  the  opinions  and  modes  of  thinkiiiLf  of  society 
had  taken  place  shortly  before.  Polytheism,  .Judaism,  Christianitif, 
Protestantism,  the  negative  philosophy  of  modem  Europe,  and  its 
4E 


686  LOGIC    OF    THE    MORAL    SCIENCES, 

positive  science  —  each  of  these  has  been  a  primary  agent  in  making 
society  what  it  was  at  each  successive  period,  while  society  was  but 
secondarily  instrumental  in  making  them,  each  of  them  (so  far  as  causes 
can  be  assigned  for  its  existence)  being  mainly  an  emanation  not  from 
the  practical  life  of  the  period,  but  from  the  state  of  belief  and  thought 
during  some  time  previous.  The  weakness  of  the  speculative  pro- 
pensity has  not,  therefore,  prevented  the  progress  of  speculation  from 
governing  that 'of  society  at  large  ;  it  has  only,  and  too  often,  prevented 
progress  altogether,  where  the  intellectual  progression  has  come  to  an 
early  stand  for  want  of  sufficiently  favorable  circumstances. 

From  this  accumulated  evidence,  we  are  justified  in  concluding,  that 
the  order  of  human  progi'ession  in  all  respects  will  be  a  corollary  dedu- 
cible  from  the  order  of  progression  in  the  intellectual  convictions  of 
mankind,  that  is,  from  the  law  of  the  successive  transformations  of 
religion  and  science.  The  question  remains,  whether  this  law  can  be 
determined  ;  at  first  from  history  as  an  empirical  law,  then  converted 
into  a  scientific  theorem  by  deducing  it  d  priori  from  the  principles  of 
human  nature.  As  the  progress  of  knowledge  and  the  changes  in  the 
opinions  of  mankind  are  very  slow,  and  manifest  themselves  in  a  well- 
defined  manner  only  at  long  intervals  ;  it  cannot  be  expected  that  the 
general  order  of  sequence  should  be  discoverable  from  the  examination 
of  less  than  a  very  considerable  part  of  the  duration  of  the  social 
progress.  It  is  necessary  to  take  into  consideration  the  whole  of  past 
time,  from  the  first  recorded  condition  of  the  human  race  ;  and  it  is 
probable  that  all  the  terms  of  the  series  already  past  were  indispensable 
to  the  operation ;  that  the  memorable  phenomena  of  the  last  generation, 
and  even  those  of  the  present,  were  necessary  to  manifest  the  law,  and 
that  consequently  the  Science  of  History  has  only  become  possible  in 
cur  own  time. 

§  S.  The  investigation  which  I  have  thus  endeavored  to  characterize, 
has  been  systematically  attempted,  up  to  the  present  time,  by  M,  Comte 
alone.  It  is  not  here  that  a  critical  examination  can  be  undertaken  or 
the  results  of  his  labors;  which  besides  are  as  yet,  comparatively  speak- 
ing, only  in  their  commencement.  But  his  works  are  the  only  source 
to  which  the  reader  can  resort  for  practical  exemplification  of  the  study 
of  social  phenomena  on  the  true  principles  of  the  Historical  Method. 
Of  that  method  I  do  not  hesitate  to  pronounce  them  a  model;  what  is 
the  value  of  his  conclusions  is  another  question,  and  one  on  which  this 
is  not  the  place  to  decide. 

I  cannot,  however,  omit  to  mention  one  important  generalization, 
which  he  regards  as  the  fundamental  law  of  the  progress  of  human 
knowledge.  Speculation  he  conceives  to  have,  on  every  subject  of 
human  inquiry,  three  successive  stages ;  in  the  first  of  which  it  tends 
to  explain  the  phenomena  by  supernatural  agencies,  in  the  second  by 
metaphysical  abstractions,  and  in  the  third  or  final  state  confines  itself 
to  ascertaining  their  laws  of  succession  and  similitude.  This  general- 
ization appears  to  me  to  have  that  high  degree  of  scientific  evidence, 
which  is  derived  from  the  concurrence  of  the  indications  of  history 
with  the  probabilities  derived  from  the  constitution  of  the  human  mind. 
Nor  could  it  be  easily  conceived,  from  the  mere  enunciation  of  such  a 
proposition,  what  a  flood  of  light  it  lets  in  upon  the  whole  course  ot 
nistory ;  when  its  consequences  are  traced,  by  connecting  with  each  of 


HISTORICAL    MRTIIOD.  587 

the  three  states  of  human  intellect  which  it  distinguishes,  an<l  with  (-ach 
successive  modification  of  those  three  states,  the  correlative  coiuliiion 
of  all  other  social  phenomena. 

But  whatever  decision  competent  judges  may  pronounce  on  the 
results  arrived  at  hy  any  individual  incpiirer,  the  method  has  been  fiiuiid 
by  which  an  indeHnite  lunnhcr  of  the  derivative  laws  both  of  social 
order  and  of  social  jiroi^ress  may  in  time  be  asciMtaini'd.  l?y  the  aid 
of  these  we  may  hereafter  succeed  not  only  in  lookiii'^  far  forward  into 
the  future  history  of  the  human  race,  but  in  determiiiini;  what  artificial 
means  may  be  used,  and  to  what  extent,  to  accelerate  the  natural  pro- 
gress in  so  far  as  it  is  beneficial  ;  to  compensate  for  whatever  may  be 
its  inherent  inconveniences  or  disadvantages;  and  to  guard  against  the 
dangers  or  accidents  to  which  our  species  is  exposed  fnmi  tlie  neces- 
sary incidents  of  its  progression.  Such  j)racticai  instructions,  founded 
on  the  highest  branch  of  speculative  sociology,  will  form  the  noblest 
and  most  beneficial  portion  of  the  Political  Art. 

That  of  this  science  and  art  even  the  foundations  are  but  beginning 
to  be  laid,  is  sufficiently  evident.  But  the  most  powerfiil  and  accom- 
plished minds  of  the  present  age  are  fairly  turning  themselves  towards 
that  object,  and  it  is  the  point  towards  wliich  the  speculative  tenden- 
cies of  mankind  have  now  for  some  time  been  converging.  For  the 
first  time,  it  has  become  the  aim  of  the  greatest  scientific  thiiik<Ms  to 
connect  by  theories  tlu5  facts  of  universal  history  :  for  the  first  time  it 
is  acknowledged,  that  no  social  doctrine  is  of  any  value  unless  it  can 
explain  the  whole  and  every  part  of  history,  so  far  as  the  data  exist ; 
and  that  a  Philosophy  of  History  is  at  once  the  verification,  and  the 
initial  form,  of  the  Philosophy  of  the  Progress  of  Society. 

If  the  endeavors  now  making  in  all  the  more  cultivated  nations,  and 
beginning  to  be  made  even  in  England  (generally  the  hust  to  adopt 
whatever  does  not  originate  with  herself),  for  the  construction  of  a 
Philosophy  of  History,  shall  be  directed  and  controlled  by  those  views 
of  the  nature  of  sociological  evidence  which  I  have  atte]nj)ted  to  state, 
but  which  hitherto  are  to  my  knowledge  exemplified  nowhere  but  in 
the  writings  of  M.  Comte  ;  they  caimot  fail  to  give  birth  to  a  sociologi- 
cal system  widely  removed  from  the  vague  and  conjectural  chai-actor 
of  all  former  attempts,  and  worthy  to  take  its  place,  at  last,  among 
established  sciences.  When  tliis  time  shall  come,  no  important  branch 
of  human  affairs  will  be  any  longer  abandoned  to  empiricism  and  un- 
scientific surmise  :  the  circle  of  huiuan  knowledge  will  be  complete, 
and  it  can  only  thereafter  receive  further  enlargement  by  perpetual 
expansion  from  within. 


588  LOGIC    OF    THE    MORAL    SCIENCES. 

CHAPTER  XI. 

OP  THE  LOGIC   OF   PRACTICE,  OR  ART ;  INCLUDING  MORALITY  AND  POLICY. 

§  1.  In  the  preceding  chapters  we  have  endeavored  to  characterize 
the  present  state  of  those  among  the  branches  of  knowledge  called 
Moral,  which  are  sciences  in  the  only  proper  sense  of  the  term,  that 
is,  inquiries  into  the  course  of  natui-e.  It  is  customary,  however,  to 
include  under  the  term  moral  knowledge,  and  even  (though  improper- 
ly) under  that  of  moral  science,  an  inquiry  the  results  of  which  do  not 
express  themselves  in  the  indicative,  but  in  the  imperative  mood,  or  in 
periphrases  equivalent  to  it ;  what  is  called  the  knowledge  of  duties  j 
practical  ethics,  or  morality. 

Now,  the  imperative  mood  is  the  characteristic  of  Art,  as  distin- 
guished from  Science.  Whatever  speaks  in  rules  or  precepts,  not  in 
assertions  resjjecting  matters  of  fact,  is  art ;  and  ethics,  or  morality,  is 
properly  a  portion  of  the  art  corresponding  to  the  sciences  of  human 
nature  and  society  :  the  remainder  consisting  of  prudence  or  policy,  and 
the  art  of  education. 

The  Method,  therefore,  of  Ethics,  can  be  no  other  than  that  of  Art, 
or  Practice,  in  general  :  and  the  portion  yet  uncompleted,  of  the  task 
which  we  proposed  to  ourselves  in  the  concluding  Book,  is  to  charac- 
terize the  general  Method  of  Art,  as  distinguished  from  Science. 

§  2.  In  all  branches  of  practical  business,  there  are  cases  in  which 
an  individual  is  bound  to  conform  his  practice  to  a  pre-established  rule, 
while  there  are  others  in  which  it  is  part  of  his  task  to  find  or  construct 
the  rule  by  which  he  is  to  govern  his  conduct.  The  first,  for  example, 
is  the  case  of  a  judge,  under  a  definite  written  code.  The  judge  is  not 
called  upon  to  determine  what  course  would  be  intrinsically  the  most 
advisable  in  the  particular  case  in  hand,  but  only  within  what  rule  of 
law  it  falls  ;  what  the  legislator  has  commanded  to  be  done  in  the  kind 
of  case,  and  must  therefore  be  presumed  to  have  intended  in  the  in- 
dividual case.  The  method  must  here  be  wholly  and  exclusively  one 
of  ratiocination  or  syllogism ;  and  the  process  is  obviously,  what  in  our 
analysis  of  the  syllogism  we  showed  that  all  ratiocination  is,  namely, 
the  interpretation  of  a  formula. 

In  order  that  an  illustration  of  the  opposite  case  may  be  taken  from 
the  same  class  of  subjects  as  the  former,  we  will  suppose,  in  contrast 
with  the  situation  of  the  judge,  the  position  of  a  legislator.  As  the 
judge  has  laws  for  his  guidance,  so  the  legislator  has  rules,  and  maxims 
of  policy ;  but  it  would  be  a  manifest  error  to  suppose  that  the  legis- 
lator is  bound  by  these  maxims,  in  the  same  manner  as  the  judge  is 
bound  by  the  laws,  and  that  all  he  has  to  do  is  to  argue  down  from 
them  to  the  particular  case,  as  the  judge  does  from  the  laws.  The  legis- 
lator is  bound  to  take  into  consideration  the  reason  or  grounds  of  the 
maxim ;  the  judge  has  nothing  to  do  with  those  of  the  law,  except  so 
far  as  a  consideration  of  them  may  throw  light  upon  the  intention  of 
the  law-maker,  where  his  words  have  left  it  doubtful.  To  the  judge, 
the  rule,  once  positively  ascertained,  is  final ;  but  the  legislator,  or 
other  practitioner,  who  goes  by  rules  rather  than  by  their  reasons,  like 


LOGIC    OF    PRACTICE,    OR    ART.  5S9 

die  olJ-fashioned  German  tacticians  who  were  vanquLshcd  l»y  Napoleon, 
or  the  physician  who  preterroil  that  his  patients  should  di«;  l)y  rule 
rather  tiian  recover  contrary  to  it,  is  rightly  judged  to  he  a  mrrv  ped- 
ant, and  the  slave  of  his  formulas. 

Now,  the  reasons  of  a  maxim  of  policy,  or  of  any  other  rule  of  art, 
caji  be  no  other  than  the  theorems  of  the  coriesponding  science. 

The  relation  in  whicli  rules  of  art  staml  to  doctrines  of  science  may 
be  thus  characterized.  The  art  proposes  to  itself  an  end  to  be  at- 
tained, defmes  the  end,  and  hands  it  over  to  the  science.  The  science 
receives  it,  considers  it  as  a  phenomenon  or  eflect  to  be  studied,  and 
having  investigated  its  causes  and  conditions,  sends  it  back  to  Art  with 
a  theorem  of  the  combinations  of  circumstances  by  which  it  could  be 
produced.  Art  then  examines  these  combinations  of  circumslaiiccs, 
and  according  as  any  of  them  are  or  arc  not  in  human  power,  pro- 
nounces the  etid  attainable  or  not.  The  only  one  of  the  premisses, 
therefore,  which  Art  supplies,  is  the  original  major  premiss,  which  a.s- 
serts  that  the  attainment  of  the  given  end  is  desirable.  iScienco  then 
lends  to  Art  the  proposition  (obtained  by  a  series  of  inductions  or 
of  deductions)  that  the  perlbrmance  of  certain  actions  will  attain  the 
end.  From  these  premisses  Art  concludes  that  the  perfonnance  of 
these  actions  is  desirable,  and  finding  it  also  practicable,  converts  the 
theorem  into  a  rule  or  prccept- 

§  3.  It  deserves  particular  notice,  that  the  theorem  or  speculative 
truth  is  not  ripe  for  being  turned  into  a  precept,  until  all  that  ]>art  of 
the  operation  which  belongs  to  science  has  been  completely  performed. 
Suppose  that  we  have  comj)leted  the  scientific  process  only  up  to  a 
certain  point ;  have  discovered  that  a  particular  cause  will  produce 
the  desired  effect,  but  not  ascertained  all  the  negative  conditi(tns  which 
are  necessary,  that  is,  all  the  circumstances  which,  if  present,  would 
prevent  its  production.  If,  in  this  imperfect  state  of  the  scientific  the- 
ory, we  attempt  to  frame  a  rule  of  ait,  we  perfoi-m  that  operati(m 
prematurely.  Whenever  any  counteracting  cause,  overlooked  by  the 
theorem,  takes  place,  the  rule  will  be  at  fault :  we  shall  employ  the 
means  and  the  end  will  not  follow.  No  arguing  from  or  about  the 
rule  itself  will  then  help  us  through  the  difficulty  :  there  is  notliing  for 
it  but  to  turn  back  and  finish  the  scientific  process  which  should  have 
preceded  the  formation  of  the  rule.  We-  nnist  reopen  the  investigation, 
to  inquire  into  the  remainder  of  the  conditions  upon  which  the  effect 
depends ;  and  only  after  we  have  a.scertained  tlu;  whole  of  these,  are 
we  prepared  to  transform  the  completed  law  of  the  effect  into  a  pre- 
cept, in  which  those  circumstances  or  combinations  of  circumstances 
which  the  science  exhibits  as  conditions,  are  prescribed  as  means. 

It  is  true  that,  for  the  sake  of  convenience,  ruli-s  must  be  formed 
from  something  less  than  this  ideally  peifect  theory;  in  the  first  ])lace, 
because  the  theoiy  can  seldom  be  made  ideally  perfect ;  and  next, 
because,  if  all  the  counteracting  contingencies,  whether  of  fiequi-nt  or 
of  rare  occurrence,  were  inchuhMl,  the  rules  would  be  too  cund)rous  to 
be  apprehended  and  remembered  by  ordinaiy  capacities,  on  the  com- 
mon occasions  of  life.  The  ndes  of  ait  do  not  attempt  tr>  comprise  more 
conditions  than  require  to  be  attemled  to  in  ordinary  cases,  and  arc 
theref(jre  always  impei-fect.  In  tlw  manual  arts,  where  the  requisite 
conditions  are  not  numerous,  and  where  those  which  the  rules  do  not 


590  LOGIC    OF    THE    MORAL    SCIENCES. 

specify,  are  generally  either  plain  to  common  observation  or  speed- 
ily learnt  from  practice,  rules  may  be  safely  acted  upon  by  persons 
who  know  nothing  more  than  the  rule.  But  in  the  complicated  affairs 
of  life,  and  still  more  in  those  of  states  and  societies,  rules  cannot  be 
relied  on,  without  constantly  refen'ing  back  to  the  scientific  laws  on 
which  they  are  founded.  To  know  what  are  the  practical  contingen- 
cies which  require  a  modification  of  the  rule,  or  which  are  altogether 
exceptions  to  it,  is  to  know  what  combinations  of  circumstances  would 
interfere  with,  or  entirely  counteract,  the  consequences  of  those  laws  : 
and  this  can  only  be  leanit  by  a  reference  to  the  theoretical  grounds 
of  the  rule. 

By  a  wise  practitioner,  therefore,  rules  of  conduct  will  only  be  con- 
sidered as  provisional.  Being  made  for  the  most  numerous  cases,  or 
for  those  of  most  ordinary  occuiTence,  they  point  out  the  manner  in 
which  it  will  be  least  perilous  to  act,  where  time  or  means  do  not  exist 
for  analyzing  the  actual  circumstances  of  the  case,  or  where  for  any 
reason  we  cannot  trust  our  judgment  in  estimating  them.  But  they  do 
not  at  all  supersede  the  propriety  of  going  through  (when  circum- 
stances permit)  the  scientific  process  requisite  for  framing  a  rule  from 
the  data  of  the  particular  case  before  us.  At  the  same  time,  the  com- 
mon rule  may  very  properly  serve  as  an  admonition,  that  a  certain 
mode  of  action  has  been  found  by  ourselves  and  others  to  succeed  in 
the  cases  of  most  common  occurrence  ;  so  that  if  it  be  unsuitable  in  the 
case  in  hand,  the  reason  of  its  being  so  will  be  likely  to  arise  from 
some  unusual  circumstance. 

§  4.  The  error  is  therefore  apparent,  of  those  who  would  deduce  the 
line  of  conduct  proper  to  particular  cases,  from  supposed  universal 
practical  maxims ;  overlooking  the  necessity  of  constantly  referring 
back  to  the  principles  of  the  speculative  science,  in  order  to  be  sure  of 
attaining  even  the  specific  end  which  the  rules  have  in  view.  How 
much  gieater  still,  then,  must  the  error  be,  of  setting  up  such  unbend- 
ing principles,  not  merely  as  universal  rules  for  attaining  a  given  end, 
but  as  rules  of  conduct  generally  ;  without  regard  to  the  possibility, 
not  only  that  some  modifying  cause  may  prevent  the  attainment  of 
the  given  end  by  the  means  which  the  rule  prescribes,  but  that  success 
itself  may  conflict  with  some  other  end,  which  may  possibly  chance  to 
be  more  desirable. 

This  is  the  habitual  error  of  many  of  the  political  speculators  whom 
I  have  characterized  as  the  geometrical  school ;  especially  in  France, 
where  ratiocination  fi'om  rules  of  practice  forms  the  staple  commodity 
of  journalism  and  political  oratory;  a  misapprehension  of  the  functions 
of  Deduction  which  has  brought  much  discredit,  in  the  estimation  of 
foreigners,  upon  the  spirit  of  generalization  so  honorably  characteristic 
of  the  French  mind.  The  common-places  of  politics,  in  France,  are 
large  and  sweeping  practical  maxims,  from  which  as  ultimate  premisses 
men  reason  downwards  to  particular  applications,  and  this  they  call 
being  logical  and  consistent.  For  instance,  they  are  perpetually  ar- 
guing that  such  and  such  a  measure  ought  to  be  adopted,  because  it  is 
a  consequence  of  the  principle  on  which  the  form  of  government  is 
founded;  of  the  principle  of  legitimacy,  or  the  principle  of  the  sove- 
reignty of  the  people.  To  which  it  may  be  answered,  that  if  these  be 
really  practical  principles,  they  must  rest  upon  speculative  grounds ; 


LOGIC    OF    PRACTICE,    OU    ART.  591 

the  sovereignty  of  the  people  (for  example)  must  be  a  right  fttuiulation 
for  goveninumt,  because  a  government  thus  t^onstituted  tentls  tit  pro- 
duce certain  beneficial  effects.  Inasmuch,  however,  as  nci  gt)vcnunent 
produces  all  possible  beneficial  effects,  but  all  are  attended  with  more 
or  fewer  inconveniences;  and  since  thcsj;  cannot  be  combati^d  by 
means  drawn  from  the  very  causes  which  produce  them;  it  would  bo 
often  a  much  stronger  recommendation  of  some  practical  arrangemi.mt, 
that  it  does  not  follow  from  what  is  called  the  general  principle  <»f  the 
government,  than  that  it  does.  Under  a  government  of  legitimacy,  the 
presumption  is  far  rather  in  favor  of  institiitions  of  popular  origin;  and 
in  a  democracy,  in  favor  of  arrangements  tending  to  check  the  impetus 
of  popular  will.  The  line  of  argumentation  so  commonly  mistaken  in 
France  for  political  philosophy,  tends  to  the  practical  conclusion  that 
wc  should  exert  our  utmost  ettbrts  to  aggravates,  instead  of  alleviating, 
whatever  are  the  characteristic  imperfections  of  the  system  of  institu- 
tions which  we  prefer,  or  under  which  we  happen  to  live. 

§  5.  The  Logic  of  Art  (it  appears  from  all  that  has  now  been  said) 
consists  essentially  of  this  one  principle,  that  intpiiry  and  discussion 
should  take  place  on  the  field  of^  science  alone.  The  rules  of  art  are 
required  to  conform  to  the  conclusions  of  science,  not  to  principles  or 
premisses  of  its  own. 

An  Art,  or  a  body  of  Art,  consists  of  the  rules,  together  with  as 
much  of  the  speculative  propositions  as  comprises  the  justification  of 
those  rules.  The  complete  art  of  any  matter,  includes  a  selection  of 
such  a  portion  finom  the  science,  as  is  necessary  to  show  on  what  con- 
ditions the  effects,  which  the  art  aims  at  producing,  depend.  And  Art 
in  general,  consists  of  the  truths  of  Science,  arranged  in  the  most  con- 
venient order  for  practice,  instead  of  the  order  which  is  the  most  con- 
venient for  thought.  Science  gi'oups  and  arranges  its  truths  so  as  to 
enable  us  to  take  in  at  one  view  as  hnuch  as  possible  of  the  general  order 
of  the  universe.  Art,  though  it  must  assume  the  same  general  laws, 
follows  them  only  into  such  of  their  detailed  conse(|uences  as  have  led 
to  the  fomiation  of  rules  of  conduct;  and  brings  together  from  parts  of 
the  field  of  science  most  remote  from  one  another,  the  truths  relating 
to  the  production  of  the  different  and  heterogeneous  conditions  neces- 
sary to  each  effect  which  the  exigencies  of  practical  life  require  to  bo 
produced. 

On  this  natural  difference  between  the  order  of  the  propositions  of 
Science  and  those  of  Art  (science  following  one  cause  to  its  various 
effects,  while  art  traces  one  effect  to  its  multiplied  and  diversified 
causes  and  conditions),  a  principle  may  be  grounded,  which  has  b(;en 
suggested  \vith  his  usual  sagacity,  but  not  dwelt  upon  or  accompanied 
with  the  necessary  explanations,  by  M.  Comte.  It  is,  that  there  ought 
to  be  a  set  of  intermediate  scientific  truths,  derived  from  the  higher 
generalities  of  science,  and  destined  to  serve  as  the  geiwralla  or  first 
principles  of  the  various  arts.  The  scientific  operation  of  framing 
these  intei-mediate  principles,  M.  Comte  considers  as  one  of  those  re- 
sults of  pliilo.sophy  which  are  reserved  for  futurity.  The  only  c(»m- 
plete  example  which  he  can  point  out  as  actually  realized,  and  which 
can  be  held  up  as  a  type  'to  be  imitated  in  more  important  matters,  is 
the  general  theory  of  the  art  of  Descriptive  (letjmetry,  as  conceived  by 
M.  Moufi^e.     It  is  not,  however,  difhcult  to  understand  what  the  naturo 


592  liOGIC    OF    THE    MORAL    SCIENCES. 

of  these  intermediate  general  principles  must  be.  After  framing  the 
most  comprehensive  possible  conception  of  the  end  to  be  aimed  at,  that 
is,  of  the  effect  to  be  produced,  and  determining  in  the  same  compre- 
hensive manner  the  set  of  conditions  on  which  that  effect  depends; 
there  remains  to  be  taken,  a  general  survey  of  the  resources  which  can 
be  commanded  for  realizing  this  set  of  conditions;  and  when  the  result 
of  this  survey  has  been  embodied  in  the  fewest  and  most  extensive 
propositions  possible,  those  propositions  will  express  the  general  rela- 
tion between  the  available  means  and  the  end,  and  from  them,  there- 
fore, the  practical  methods  of  the  art  will  follow  as  corollaries.  But 
the  further  development  of  this  idea  may  be  left  to  those  who  have  the 
means  and  on  whom  the  special  office  devolves,  of  practically  apply- 
ing it  for  the  purpose  of  constructing,  on  scientific  principles,  the  gen- 
eral theories  of  the  diffei'ent  arts.* 

§  6.  After  these  observations  on  the  Logic  of  Practice  in  general, 
little  needs  here  be  said  of  that  department  of  Practice  which  has 
received  the  name  of  Morality ;  since  it  forms  no  part  of  the  appro- 
priate object  of  this  work  to  discuss  how  far  morality  depends,  like 
other  arts,  upon  the  consideration  of  means  and  ends,  and  how  far,  if 
at  all,  upon  anything  else. 

This,  however,  may  be  said ;  that  questions  of  practical  morality 
are  partly  similar  to  those  which  are  to  be  decided  by  a  judge,  and 
partly  to  those  which  have  to  be  solved  by  a  legislator  or  adminis- 
trator. In  some  things  our  conduct  ought  to  conform  itself  to  a  pre- 
scribed rule ;  in  others,  it  is  to  be  guided  by  the  best  judgment  which 
can  be  formed  of  the  merits  of  the  particular  case. 

Without  entering  into  the  disputed  questions  respecting  the  founda- 
tion of  morality,  we  may  consider  as  a  conclusion  following  alike  from 
all  systems  of  ethics,  that,  in  a  certain  description  of  cases  at  least, 
morality  consists  in  the  simple  observance  of  a  rule.  The  cases  in 
question  are  those  in  which,  although  any  rule  Vv^hich  can  be  formed  is 
probably  (as  we  remarked  on  maxims  of  policy)  more  or  less  imper- 
fectly adajDted  to  a  portion  of  the  cases  which  it  comprises,  there  is 
still  a  necessity  that  some  rule,  of  a  nature  simple  enough  to  be  easily 
understood  and  remembered,  should  not  only  be  laid  down  for 
guidance,  but  universally  observed,  in  order  that  the  vai'ious  persons 
concerned  may  know  what  they  have  to  expect :  the  inconvenience  of 
uncertainty  on  their  part  being  a  gi'eater  evil  than  that  which  may 
possibly  arise,  in  a  minority  of  cases,  from  the  imjjerfect  adaptation  of 
the  rule  to  those  cases. 

Such,  for  example,  is  the  rule  of  veracity ;  that  of  not  infringing  the 
legal  rights  of  others ;  and  so  forth :  concerning  which  it  is  obvious 
that  although  many  cases  exist  in  which  a  deviation  from  the  rule 
would  in  the  particular  case  produce  more  good  than  evil,  it  is  neces- 
sary for  general  secimty,  either  that  the  rules  should  be  inflexibly 
obsei-ved,  or  that  the  license  of  deviating  fi-om  them,  if  such  be  ever 
permitted,  should  be  confined  to  definite  classes  of  cases,  and  of  a  very 
peculiar  and  extreme  nature. 

♦  A  systematic  treatise  on  the  general  means  which  man  possesses  of  acting  upon  na- 
ture, is  one  of  the  works  which  M.  Comte  holds  out  the  hope  of  his  producing  at  some 
future  time  ;  and  no  subject  affords  a  larger  scope  for  the  faculties  of  so  original  and  com- 
prehensive a  mmd. 


LOGIC    OF    PRACTICE,    OR    ART.  JO.'l 

With  respect,  therefore,  to  these  cases,  jMactical  ethics  must,  like 
the  administration  of  positive  law,  follow  a  method  strictly  and  dirorily 
ratiocinative  :  whether  the  rules  themsi-lves  are  obtained,  likc^  those 
of  other  aits,  from  a  scientific  consi<leration  of  tendencies,  or  are 
referred  to  the  autliority  of  intuitive  consciousness  or  express  reve- 
lation. 

In  cases,  however,  in  which  tiiere  does  not  exist  a  necessity  for  a 
common  rule,  to  be  acknowledijeil  and  relied  upon  a.H  the  basis  of 
social  life;  where  we  are  at  liberty  to  iiujuire  what  is  the  most  moral 
course  under  the  particular  circumstances  of  the  case,  without  rcfi-r- 
ence  to  the  authorized  expectations  of  other  people  ;  then?  the  Methoil 
of  Ethics  cannot  differ  materially  fi-om  the  method  of  every  other 
department  of  practice.  Like  other  arts,  it  sets  out  from  a  general 
principle,  or  orisxinal  major  premiss,  eimnciative  of  its  particular  end: 
whether  that  end  be  the  <rivatesr  possible  happiness,  a.s  is  contended 
by  some,  or  the  conformity  of  our  character  to  ideal  perfection 
according  to  some  particular  standard,  as  others  hold.  But  on  this  as 
on  other  subjects,  when  the  end  has  been  laid  dowTi,  it  belongs  to 
Science  to  inquire  what  are  the  kinds  of  actions  by  which  this  end, 
this  happiness  or  this  perfection  of  clraracter,  is  capable  of  being 
realized,  ^\^len  Science  has  framed  propositions,  which  are  the  com- 
pleted expression  of  the  whole  of  the  conditions  necessary  to  the 
desired  end,  these  are  handed  over  to  Art,  which  has  nothing  fiirther 
to  do  but  to  ti-ansform  them  into  corresponding  rules  of  conduct. 

§  7.  "With  these  remarks  we  must  close  this  summary  view  of  the 
application  of  the  general  logic  of  scientific  inijuiry  to  the  moral  and 
social  departments  of  science.  Notwithstanding  the  extremi>  gener- 
ality of  the  principles  of  method  which  I  have  laid  dowii  (a  generality 
which  I  trust  is  not,  in  this  instance,  synonymous  with  vagueness),  I 
have  indulged  the  hope  that  to  some  of  those  on  whom  the  tiLsk  will 
devolve  of  bringing  those  most  important  of  all  sciences  into  a  more 
satisfactory  state,  these  obsci-vations  may  be  useful,  both  in  removing 
erroneous  and  in  clearing  up  the  true  conceptions  of  the  means  by 
which,  on  subjects  of  so  high  a  degree  of  complication,  truth  can  be 
attained.  Should  this  have  been  accomplished,  something  not  unim- 
portant will  have  been  contributed  towards  what  is  probably  destined 
to  be  the  great  intellectual  achievemi-nt  of  the  next  two  or  three  gen- 
erations of  European  thinkers:  although,  t'ur  the  realization  of  the 
important  results,  of  which  it  has  been  thus  indirectly  attempted  to 
facilitate  the  attainment,  mankind  must  ever  bo  principally  in<lebted 
to  the  genius  and  industry  of  ethical  and  sociological  philosophers, 
whether  of  the  present  or  of  future  times. 


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